9th Class Chemistry · Punjab Board · Complete learning guide
Chapter 12Empirical Data Collection and Analysis
Every topic, every MCQ and every exercise question, explained step by step in simple language. Written for the Punjab Board new-syllabus Chemistry book, English medium.
Science is a systematic study of this world through observation and experimentation. Scientific research is done in every country, but not in the same way everywhere, so scientists must share ideas and standardise their approach.
One of the most usual problems faced by the scientific community is the issue of units. If scientists in one country measure length in metres and in another in feet, they have to convert. Comparing quantities in different units is not only confusing but a wastage of time as well.
Definition
SI units
Standard and user-friendly units adopted by scientists all over the world, called SI (Système International) units. They make communication easy worldwide and allow scientists to share data easily.
Why SI units are preferred
Fewer conversions: SI units reduce the number of conversions needed to coordinate information among scientists.
Base 10: like our number system, so they are easy to learn, remember and convert.
Definite standards: they are based on definite and precise standards.
Interrelated: one unit is derived from other units without conversion factors (1 N = 1 kg m s⁻²).
Interesting information
The following systems of units are commonly used in the world: (1) International System (SI), (2) Centimetre-gram-second (CGS), (3) Metre-kilogram-second (MKS), (4) Imperial system (foot, pound, gallon).
SI units are used almost everywhere in the world. This brings accuracy, consistency and universal understanding in scientific communication: a measurement taken in one part of the world can be easily understood and verified in another part without any confusion. Using SI units, scientists can compare results, replicate experiments and take benefit of each other's work. All of this ensures safety, reliability, reproducibility and progress.
Term
Meaning
Consistent
results agree with each other when measured the same way, in the same units
Reliable
the same scientist gets the same result when the experiment is repeated
Reproducible
a different scientist, with different equipment or in another lab, gets the same result
Topic 2
SI base units in chemistry
There are seven base units in the SI system for physical quantities, out of which we use five in chemistry: length, time, amount of substance, mass and temperature.
Quantity
Unit
Symbol
Length
metre
m
Time
second
s
Amount of substance
mole
mol
Mass
kilogram
kg
Temperature
kelvin
K
Metre (m)
Definition
Metre
The standard unit of length. Metre is the distance travelled by light in vacuum in about one 300-millionth of a second.
Fig 12.1: a metre rod, 100 cm long.
Check your book
Exactly, the metre is the distance light travels in vacuum in 1/299 792 458 of a second. "About one 300-millionth" is the rounded value.
Kilogram (kg)
Definition
Kilogram
The standard unit of mass, symbol kg. A block kept in France was taken as the standard unit of mass. It is also described as the mass of 1000 cm³ of water.
Fig 12.2: standard masses of 1 kg, 500 g and 250 g.
Check your book
The platinum-iridium block near Paris was the standard until 2019; the kilogram is now fixed by the Planck constant. 1000 cm³ of water has a mass of 1 kg only near 4 °C.
Second (s)
Definition
Second
The standard unit of time. It is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium-133 atom.
Interesting information
Symbols are not changed in plural forms: 100 millimetres is written 100 mm, not 100 mms.
Kelvin (K)
Definition
Kelvin
The standard unit of temperature, symbol K. It is 1/273.16 of the thermodynamic temperature of the triple point of water, the point at which all three states of water (ice, liquid, vapour) exist at the same time.
Check your book
The book prints "1/273rd". The triple point of water is 273.16 K (0.01 °C), so one kelvin is 1/273.16 of it.
Mole (mol)
Definition
Mole
The base unit of the amount of a pure substance, symbol mol. It is defined as having exactly 6.022 × 10²³ particles of a substance.
Note
The exact defined number is 6.02214076 × 10²³; 6.022 × 10²³ is the four-figure value used in calculations.
Topic 3
Derived units and other quantities
Definition
Derived units
Units of quantities that are mathematically derived from the base units.
Quantity
How it is derived
Unit
Area
length × length
square metre (m²)
Volume
length × length × length
cubic metre (m³)
Density
mass ÷ volume
kg per cubic metre (kg m⁻³)
In addition to derived units, there are other specific quantities commonly used in chemistry:
Quantity
Formula
Unit
In base units
Force
mass × acceleration
newton (N)
kg m s⁻²
Pressure
force ÷ area
pascal (Pa)
N m⁻² = kg m⁻¹ s⁻²
Energy (work, heat)
force × distance
joule (J)
N m = kg m² s⁻²
Check your book
The book's Table 12.3 prints newton as "kg m²⁻" and pascal as "N m²⁻". They are kg m s⁻² and N m⁻².
There are seven base units and twenty-two named derived units in the SI system; chemistry generally uses five base units and three derived units.
Topic 4
Prefixes: kilo, deci, milli and the rest
Since the SI system is a metric system, it is based around the number 10. A set of prefixes indicates whether the unit is a multiple or a fraction of the base ten. It allows the reduction of zeros of a very small or a very large number. Each prefix has a symbol that comes before the unit symbol.
Prefix
Symbol
Factor
Example
mega
M
10⁶
1 MJ = 1 000 000 J
kilo
k
10³
1 kg = 1000 g
hecto
h
10²
1 hm = 100 m
deca
da
10¹
1 dam = 10 m
deci
d
10⁻¹
1 dm = 0.1 m
centi
c
10⁻²
1 cm = 0.01 m
milli
m
10⁻³
1 mg = 0.001 g
micro
μ
10⁻⁶
1 μm = 0.000001 m
nano
n
10⁻⁹
1 nm = 10⁻⁹ m
pico
p
10⁻¹²
1 pm = 10⁻¹² m
Check your book
Table 12.4 in the book has its column headings swapped (the "Symbol" column holds the prefix names); micro is printed "u" for μ.
Prefixes on a powers-of-ten ladder: each step down from kilo to milli is ÷ 10.
Combining a prefix with a unit
Worked exampleConvert 2.5 kg into grams.
kilo = 10³, so 1 kg = 1000 g.
2.5 × 1000 = 2500 g.
Answer2.5 kg = 2500 g = 2.5 × 10³ g
Worked exampleConvert 250 mL (cm³) into dm³.
1 dm³ = 1000 cm³.
250 ÷ 1000 = 0.25.
Answer250 cm³ = 0.25 dm³
Worked exampleConvert 0.045 m into mm.
milli = 10⁻³, so 1 m = 1000 mm.
0.045 × 1000 = 45.
Answer0.045 m = 45 mm
Scientific notation
A number is written as a × 10ⁿ, where a is between 1 and 10. Move the decimal point to leave one non-zero digit in front; the number of places moved is n (negative if moved to the right).
Worked exampleWrite 0.000840 in scientific notation.
Move the point 4 places right: 8.40.
Moved right, so the power is −4.
Answer8.40 × 10⁻⁴
Topic 5
Why chemists use g, cm³ and °C
Grams instead of kilograms
In chemistry we measure the masses of reactants in grams. It is essential because the unit of molar mass is grams per mole; a mass measured in grams with the molar mass lets us find the moles of a substance. Moreover, the quantities in the laboratory are likely to be small, so the choice of gram rather than kg is sensible. Grams give more manageable numbers and prevent excessively large or small values.
moles = mass (g) ÷ molar mass (g mol⁻¹)
e.g. 9 g of water ÷ 18 g mol⁻¹ = 0.5 mol
Celsius instead of kelvin
The Celsius scale is most often used to measure temperature in chemistry because it is more convenient. It has 100 divisions in total, which makes it compatible with the base-ten format of the SI system. It is also easy to convert Celsius into kelvin:
K = °C + 273
°C = K − 273
Celsius and kelvin scales side by side: the same size degree, shifted by 273.
Worked exampleConvert 65 °C into kelvin.
K = °C + 273
= 65 + 273
Answer338 K
Worked exampleConvert 100 K into °C.
°C = K − 273
= 100 − 273
Answer−173 °C
Cubic centimetres instead of cubic metres
The unit of volume in chemistry is the cubic centimetre (cm³) instead of the cubic metre (m³), because it is easy to measure and calculate with, and it is precise. In the laboratory we usually measure small volumes of liquid, which are more manageable in cm³. 1 cm³ = 1 mL; 1000 cm³ = 1 dm³ = 1 L; 1 m³ = 10⁶ cm³.
Remember
So the practical units in the lab are g, cm³, s and °C, while the SI base units are kg, m³, s and K.
Topic 6
Errors in measurement
Measurement is the foundation for all experiments in science. Every measurement carries a level of uncertainty which is known as error.
Definition
Error
The difference between the measured value and the actual value.
If two students use the same instrument, they need not get the same result. An error may occur due to two factors: the limitation of the measuring instrument and the skill of the student making the measurement.
Systematic error
Definition
Systematic error
Errors that naturally occur in measuring tools (which we assume give correct results). They may be removed by adding or subtracting a constant adjustment to each measurement, and they affect the accuracy of the measurement.
All measuring instruments contribute to systematic error, e.g. a pipette, burette and measuring cylinder may deliver a volume slightly different from the one indicated by their graduation. A balance that is not set to zero, or a thermometer that reads 1 °C high, gives the same error every time.
Random error
Definition
Random error
The error which causes one measurement to differ slightly from the next. It comes from unpredictable changes during an experiment.
The main reasons for random errors are limitations of instruments, environmental factors and slight variation in procedure. Reading a measuring cylinder from a different angle each time (parallax), or a balance disturbed by moving air, gives readings that scatter. A random error often determines the precision of the experiment.
Parallax: only the eye level with the mark gives the true reading.Read a measuring cylinder at the bottom of the meniscus, eye level with it.
Systematic error
Random error
Cause
faulty or badly calibrated instrument, wrong method
unpredictable changes: reading angle, air draughts, temperature
Direction
same direction every time (always high or always low)
sometimes high, sometimes low
Affects
accuracy
precision
Removed by
calibrating; adding or subtracting a constant correction
repeating readings and taking the average; careful technique
Remember
The goal of any experiment is to obtain accurate and precise results.
Topic 7
Accuracy and precision
Accuracy and precision are both ways to measure the correctness of results. They are used interchangeably in everyday life, but in science they mean different things.
Definition
Accuracy
How close results are to the true or known value.
Definition
Precision
The closeness of two or more measurements to each other.
For example, the volume of a liquid is 26 cm³. A student measures it three times and finds 27 cm³ each time: the student is not accurate. If you weigh a substance five times and get 3.2 kg every time, your measurement is precise but not necessarily accurate.
Precision is independent of accuracy. A student may be accurate but not precise, and vice versa.
Four targets: precise and accurate, precise not accurate, accurate not precise, neither.
The book's 20 g example
True mass 20 g: Student A 17.3, 17.4, 17.2 g; Student B 19.8, 20.5, 19.6 g.
Student
Readings (g)
Mean
Spread
Verdict
A
17.3, 17.4, 17.2
17.3 g
0.2 g
precise but not accurate
B
19.8, 20.5, 19.6
19.97 g
0.9 g
more accurate but not precise
Worked exampleA student weighs a substance three times and gets 5.2 g each time. The true mass is 5.0 g. Is the work precise, accurate, or both?
The three readings are identical → precise.
They are all 0.2 g away from 5.0 g → not accurate (a systematic error, e.g. the balance not zeroed).
The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.
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Set A: Textbook exercise 10 MCQs
The multiple-choice questions at the end of Chapter 12 in your book, in the book's option order.
Q12.1Base and Derived Units
Which of the following pairs of quantities may be measured in the same unit?
Answer(c) Heat and work
Step by step
Heat → joule.
Work → joule (N m).
Why the others are wrong
(a) heat is in joules, temperature in kelvin (or °C).
(b) kelvin and square metre.
(d) metre and joule.
Remember
Energy family (heat, work, energy) = joule.
Q12.2Prefixes and Practical Units
In which unit we usually measure the energy present in the food?
Answer(a) Kilojoules
Step by step
A slice of bread ≈ 300 kJ.
kilo = 10³, a manageable number.
Why the others are wrong
(b) far too large for one food item.
(c) Calories (kcal) are also printed, but the Calorie is not an SI unit.
(d) too small; numbers would run into hundreds of thousands.
Remember
SI + food = kJ.
Q12.3Prefixes and Practical Units
What prefix is used for 10⁻¹²?
Answer(b) Pico
Step by step
milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹, pico 10⁻¹².
Why the others are wrong
(a) 10⁶.
(c) 10⁹.
(d) no such prefix (tera is 10¹²).
Remember
m-μ-n-p: every step ÷ 1000.
Q12.4Base and Derived Units
In SI unit of pressure is expressed in:
Answer(d) Pascal
Step by step
Pressure = force ÷ area = N ÷ m² = N m⁻² = Pa.
Why the others are wrong
(a) N m⁻¹ is not pressure (force per length).
(b) as a choice: it equals 1 Pa, but the SI unit is named the pascal.
Set A: Textbook exercise short questions 8 questions
The short questions at the end of the chapter in your book.
Short Q 12.1
What is consistency of results?
Answer
Results are consistent when repeated measurements of the same quantity, made in the same way and in the same units, agree with each other. SI units help consistency: a measurement taken in one part of the world can be easily understood and verified in another part without any confusion.
Example: three titrations giving 24.1, 24.2 and 24.1 cm³ are consistent.
Short Q 12.2
Why are SI units user friendly?
Answer
SI units use base 10, just like our number system, so they are easy to learn, remember and convert.
They are based on definite and precise standards.
They are interrelated: one unit is derived from others without conversion factors (1 J = 1 N m).
One prefix set (kilo, milli...) works for every unit.
Short Q 12.3
Define systematic error and random error.
Answer
Systematic error: errors that naturally occur in measuring tools; they may be removed by adding or subtracting a constant adjustment to each measurement, and they affect accuracy. E.g. a burette delivering slightly more than its graduation shows.
Random error: the error which causes one measurement to differ slightly from the next; it comes from unpredictable changes during an experiment and determines precision. E.g. reading a cylinder from a different angle each time.
Short Q 12.4
What is the reason behind a random error?
Answer
Random errors come from unpredictable changes during an experiment. The main reasons are:
Limitations of instruments (the last digit of a reading has to be estimated).
Environmental factors (air currents on a balance, temperature changes).
Slight variation in procedure (reading the volume from a different angle each time).
Short Q 12.5
Does systematic error affect the accuracy?
Answer
Yes. Systematic error affects the accuracy of the measurement. It shifts every reading in the same direction by the same amount, so the results move away from the true value even if they agree with each other. Example: a balance reading 0.2 g too high gives 5.2 g for a 5.0 g sample every time: precise but not accurate.
Short Q 12.6
Which other systems of measurement are used apart from SI units?
Local units are also still used in markets: tola, seer and maund for mass, gaz (yard) for length.
Short Q 12.7
Define metre.
Answer
The metre is the standard unit of length, symbol m. It is the distance travelled by light in vacuum in about one 300-millionth of a second (exactly 1/299 792 458 s).
Short Q 12.8
Mention two benefits scientists get by using SI units.
Answer
Easy communication and data sharing: a measurement made in one country is understood and verified in another without conversion.
Comparing and replicating: scientists can compare results, replicate experiments and build on each other's work.
It also saves time and avoids conversion mistakes.
Set B: More short questions 38 questions
The book's in-text exercises first, then short questions on every topic of the chapter (SLO-based), as asked in board papers.
Practice exercise questions (in text)
SQ 12.1
What is the difference between reliable and reproducible results?
Answer
Reliable
Reproducible
The same person, with the same method and equipment, gets the same result on repeating the experiment.
A different person, in another lab or with different equipment, gets the same result.
Tests the consistency of one experimenter.
Tests whether the result holds for everyone.
SQ 12.2
How have SI units brought harmony in the scientific community?
Answer
SI units are used almost everywhere in the world, giving scientists a single standard for exchanging data. This brings accuracy, consistency and universal understanding. Scientists of different countries and cultures share a common language, so they can compare results, replicate experiments and work together, without confusion or conversion.
SQ 12.3
A student weighs a substance three times and gets 5.2 g each time. The true weight is 5.0 g. Is the work (i) precise and accurate (ii) accurate but not precise (iii) precise but not accurate?
Answer
(iii) Precise but not accurate. The readings agree exactly (precise), but all are 0.2 g above the true value (not accurate). The constant 0.2 g shift points to a systematic error, such as a balance not set to zero.
SQ 12.4
How will you avoid systematic and random errors?
Answer
Systematic: calibrate instruments against a standard, set the balance to zero, check the zero error and apply a constant correction, use good-quality glassware.
Random: take several readings and use the average, keep the eye level with the mark, shield the balance from air currents, keep conditions (temperature) steady, follow the same procedure each time.
SI units and their need
SQ 12.5
What are SI units?
Answer
Standard and user-friendly units adopted by scientists all over the world, called the Système International (SI) units. They make communication easy and allow data to be shared.
SQ 12.6
Why do scientists need standard units?
Answer
If scientists in one country measure lengths in metres and in another in feet, they have to convert. Comparing quantities in different units is not only confusing but a wastage of time. Standard units remove this.
SQ 12.7
Why are SI units said to reduce conversions?
Answer
Everyone uses the same units, so data from any lab can be used directly; and because SI units are base-10 and interrelated, any conversion needed is only a power of ten.
SQ 12.8
Name four systems of units used in the world.
Answer
SI (International System), CGS (centimetre-gram-second), MKS (metre-kilogram-second) and the Imperial system.
SQ 12.9
What does "SI units ensure safety, reliability, reproducibility and progress" mean?
Answer
Doses, concentrations and pressures read the same everywhere (safety); repeated results agree (reliability); other labs can repeat the work (reproducibility); scientists build on each other's results (progress).
Base and derived units
SQ 12.10
Name the five SI base units used in chemistry.
Answer
Quantity
Unit (symbol)
Length
metre (m)
Time
second (s)
Amount of substance
mole (mol)
Mass
kilogram (kg)
Temperature
kelvin (K)
SQ 12.11
How many base units are there in the SI system?
Answer
Seven: metre, kilogram, second, kelvin, mole, ampere and candela. Chemistry uses five of them.
SQ 12.12
Define kilogram.
Answer
The standard unit of mass, symbol kg. A block kept in France was taken as the standard; it is also described as the mass of 1000 cm³ of water. (Since 2019 it is defined through the Planck constant.)
SQ 12.13
Define second.
Answer
The standard unit of time, symbol s: the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium-133 atom.
SQ 12.14
Define kelvin.
Answer
The standard unit of temperature, symbol K: 1/273.16 of the thermodynamic temperature of the triple point of water, the point at which all the states of water exist at the same time.
SQ 12.15
Define mole.
Answer
The base unit of the amount of a pure substance, symbol mol, defined as exactly 6.022 × 10²³ particles of a substance.
SQ 12.16
What is the triple point of water?
Answer
The point at which all three states of water (ice, liquid water and water vapour) exist at the same time: 273.16 K (0.01 °C) at a pressure of 611.657 Pa.
SQ 12.17
What are derived units? Give two examples.
Answer
Units of quantities mathematically derived from the base units. Volume: m³ (length³); density: kg m⁻³ (mass ÷ volume); area: m².
SQ 12.18
Write the units of force, pressure and energy in base units.
Answer
Quantity
Unit
Base units
Force
newton (N)
kg m s⁻²
Pressure
pascal (Pa)
N m⁻² = kg m⁻¹ s⁻²
Energy
joule (J)
N m = kg m² s⁻²
SQ 12.19
Why is the symbol of a unit not written in plural?
Answer
Symbols are not changed in plural forms, so that a symbol always means exactly one thing: 100 mm, not 100 mms ("mms" could be misread).
Prefixes and practical units
SQ 12.20
What is the use of prefixes with SI units?
Answer
They indicate whether the unit is a multiple or a fraction of the base ten, and reduce the zeros of very small or very large numbers: 0.000 001 m = 1 μm; 5 000 000 J = 5 MJ.
SQ 12.21
Give the values of kilo, deci and milli.
Answer
kilo (k) = 10³, deci (d) = 10⁻¹, milli (m) = 10⁻³. E.g. 1 kg = 1000 g; 1 dm = 0.1 m; 1 mL = 10⁻³ L.
SQ 12.22
Convert 3.5 kg into grams and 450 mg into grams.
Answer
3.5 kg = 3.5 × 1000 = 3500 g. 450 mg = 450 × 10⁻³ = 0.450 g.
SQ 12.23
How many cm³ are there in 1 dm³ and in 1 m³?
Answer
1 dm = 10 cm → 1 dm³ = 1000 cm³. 1 m = 100 cm → 1 m³ = 100³ = 10⁶ cm³.
SQ 12.24
Why do chemists measure mass in grams rather than kilograms?
Answer
Because the unit of molar mass is grams per mole, so a mass in grams gives the moles directly; and laboratory quantities are small, so grams give manageable numbers.
SQ 12.25
Why is the Celsius scale used in chemistry rather than kelvin?
Answer
It is more convenient: it has 100 divisions between the freezing and boiling points of water, compatible with base ten, and it is easy to convert into kelvin (K = °C + 273).
SQ 12.26
Why is volume measured in cm³ in the laboratory?
Answer
Laboratory volumes are small; cm³ is easy to measure and calculate with, and precise. Burettes, pipettes and cylinders are graduated in cm³.
SQ 12.27
Convert 37 °C and −10 °C into kelvin.
Answer
37 + 273 = 310 K; −10 + 273 = 263 K.
SQ 12.28
Write 6 500 000 and 0.0072 in scientific notation.
Answer
6 500 000 = 6.5 × 10⁶; 0.0072 = 7.2 × 10⁻³.
Errors, accuracy and precision
SQ 12.29
What is an error in measurement?
Answer
The difference between the measured value and the actual value. Every measurement carries some uncertainty.
SQ 12.30
Give two factors on which an error depends.
Answer
The limitation of the measuring instrument and the skill of the student making the measurement.
SQ 12.31
Give examples of systematic error in the laboratory.
Answer
A pipette, burette or measuring cylinder delivering a volume slightly different from its graduation; a balance not set to zero; a thermometer reading 1 °C high.
SQ 12.32
Give examples of random error.
Answer
Reading the volume from a measuring cylinder from a different angle each time; a balance giving different values as the surrounding air affects it.
SQ 12.33
Define accuracy.
Answer
Accuracy measures how close results are to the true or known value. E.g. a liquid of 26 cm³ measured as 27 cm³ is not accurate.
SQ 12.34
Define precision.
Answer
The closeness of two or more measurements to each other. Weighing a substance five times and getting 3.2 kg every time is precise, but not necessarily accurate.
SQ 12.35
Is precision dependent on accuracy?
Answer
No. Precision is independent of accuracy; a student may be accurate but not precise, and vice versa.
Accuracy and precision.
SQ 12.36
Which type of error affects precision and which affects accuracy?
Answer
Random error determines precision; systematic error affects accuracy.
SQ 12.37
How does taking the average of many readings help?
Answer
Random errors are sometimes high and sometimes low, so they partly cancel in the average, which is closer to the true value. Averaging does not remove a systematic error.
SQ 12.38
How should a measuring cylinder be read?
Answer
Place it on a level surface, bring the eye level with the bottom of the meniscus (top for mercury), and read the mark that touches it. This avoids parallax error.
These test whether you really understand. Give a reason every time.
CRQ 12.1
Compare the units in the SI system with those in the MKS system.
Answer
SI system
MKS system
Base units
seven: m, kg, s, K, mol, A, cd
three mechanical units: metre, kilogram, second
Quantities covered
all of science: mechanics, heat, amount of substance, electricity, light
mainly length, mass and time (mechanics)
Temperature, amount
kelvin and mole are base units
not included
Status
the modern international standard
older system on which SI was built
Length, mass and time have the same units in both (m, kg, s), so mechanical units (newton, joule, pascal) are the same. SI simply extends MKS to every branch of science and adds the prefixes.
CRQ 12.2
What are the five basic SI units which are used in Chemistry?
Answer
Quantity
Unit
Symbol
Defined by
Length
metre
m
distance light travels in 1/299 792 458 s
Time
second
s
9,192,631,770 cycles of caesium-133 radiation
Amount of substance
mole
mol
6.022 × 10²³ particles
Mass
kilogram
kg
formerly a standard block in France; now the Planck constant
Temperature
kelvin
K
1/273.16 of the triple point of water
CRQ 12.3
Explain the three units derived from the basic SI units.
Answer
Area: square metre (m²)
Area = length × width = m × m = m².
Volume: cubic metre (m³)
Volume = length × width × height = m³. In the lab its fraction cm³ (= 10⁻⁶ m³) is used.
Density: kilogram per cubic metre (kg m⁻³)
Density = mass ÷ volume = kg ÷ m³ = kg m⁻³. Water: 1000 kg m⁻³ = 1 g cm⁻³.
Each is built from base units with no conversion factor, which is why SI units are called interrelated.
CRQ 12.4
Explain why we prefer to use smaller units of mass and volume in Chemistry.
Answer
Mass in grams
The unit of molar mass is grams per mole, so a mass measured in grams with the molar mass directly gives the moles. Laboratory quantities are small (a few grams), so grams give manageable numbers and avoid very small decimals (2.5 g, not 0.0025 kg).
Volume in cubic centimetres
Laboratory volumes of liquid are small and more manageable in cm³; it is easy to measure and calculate with, and precise. 25.0 cm³ is easier than 0.000025 m³, and glassware is graduated in cm³.
CRQ 12.5
What difficulties would we expect to encounter if we used different units of measurement in daily life?
Answer
Confusion and wastage of time: every comparison needs a conversion (a seer in one market, a kilogram in another).
Mistakes: wrong conversions in medicine doses, fuel, building materials or recipes can be dangerous or costly.
Unfair trade: buyers cannot compare prices; local units (seer, maund) varied from place to place.
Poor communication: instructions, labels and scientific data cannot be understood elsewhere.
Technology problems: spare parts made in inches will not fit a machine designed in millimetres.
Set A: Textbook comprehensive questions 6 questions
The long questions at the end of the chapter in your book.
Long Q 12.1
What are our indigenous units of measurement of mass, volume and length?
Answer
Before the metric system was adopted in Pakistan, the subcontinent used its own units; some are still heard in markets and villages.
Mass
Unit
Relation
About
Ratti
8 ratti = 1 masha
0.12 g
Masha
12 masha = 1 tola
0.97 g
Tola
still used for gold and silver
11.66 g
Chhatank
5 tola
58 g
Pao
4 chhatank = ¼ seer
233 g
Seer
16 chhatank = 80 tola
0.933 kg
Maund (mun)
40 seer
37.3 kg
Volume
Liquids such as milk and oil were sold by the seer and pao using standard measuring pots, and the imperial gallon (about 4.55 L) was used for petrol and kerosene before litres.
Length
Unit
About
Inch (anch)
2.54 cm
Foot (fut)
12 inch, 30.5 cm
Hath (cubit, elbow to fingertip)
18 inch, 46 cm
Gaz (yard)
3 feet, 0.914 m
Kos
about 2-3 km, varied by region
Area (land)
Marla, kanal, acre, murabba are still used for land (20 marla = 1 kanal; 8 kanal = 1 acre).
Why SI
These units varied from region to region, which is exactly the problem SI solves.
Long Q 12.2
Elaborate the difference between precision and accuracy.
Answer
Accuracy
Accuracy measures how close results are to the true or known value. Example: a liquid has a volume of 26 cm³; a student measures 27 cm³ three times; the student is not accurate.
Precision
The closeness of two or more measurements to each other is called precision. If you weigh a substance five times and get 3.2 kg every time, your measurement is precise, but not necessarily accurate.
Independent of each other
Precision is independent of accuracy. A student may be accurate but not precise and vice versa. The exact mass of an object is 20 g:
Student A: 17.3, 17.4, 17.2 g. Student B: 19.8, 20.5, 19.6 g.
Student A (17.3, 17.4, 17.2 g): close together, far from 20 g → precise but not accurate.
Student B (19.8, 20.5, 19.6 g): average ≈ 20.0 g but spread out → more accurate but not precise.
The four combinations.
Comparison
Accuracy
Precision
Closeness to the true value.
Closeness of readings to each other.
Needs the true value to judge.
Judged from repeated readings alone.
Spoiled by systematic error.
Spoiled by random error.
Improved by calibration.
Improved by careful repeated readings.
Long Q 12.3
How can you avoid systematic errors in your measurements?
Answer
What a systematic error is
Errors that naturally occur in measuring tools, affecting the accuracy of the measurement; they may be removed by adding or subtracting a constant adjustment to each measurement. They shift every reading the same way.
Ways to avoid them
Calibrate instruments against a known standard (check a balance with a standard 100 g mass; a thermometer in melting ice should read 0 °C).
Check and correct the zero error: set the balance to zero (tare) before weighing; subtract any constant offset from every reading.
Use good-quality, graduated glassware (grade-A pipettes and burettes) and clean it, since drops on the walls change the delivered volume.
Use the correct method: read at the bottom of the meniscus at eye level; let hot objects cool before weighing; rinse a burette with the solution it will hold.
Cross-check with a different instrument or method: if two methods agree, a systematic error is unlikely.
Control conditions such as temperature, which changes the volume of glassware and liquids.
Exam tip
Repeating readings does NOT remove a systematic error; only calibration or correction does.
Long Q 12.4
How does taking measurements in SI units ensure safety and reliability?
Answer
Safety
Medicine doses in mg and mL are understood the same everywhere; mixing units (grains, teaspoons) has caused overdoses.
Engineering and aviation: loads, pressures and fuel in one system prevent disasters. In 1983 an Air Canada jet ran out of fuel because its fuel was worked out in pounds instead of kilograms.
Laboratory safety: concentrations, temperatures and pressures on labels and in instructions are read correctly by everyone.
Reliability
SI units are based on definite and precise standards, so a measurement means the same in every lab.
A measurement taken in one part of the world can be easily understood and verified in another without confusion, so results can be checked and repeated (reproducibility).
Fewer conversions mean fewer arithmetic mistakes.
Data from many labs can be combined and compared, so conclusions rest on more evidence.
Long Q 12.5
Can a student be both inaccurate and imprecise in his measurements?
Answer
Yes. Precision is independent of accuracy, so all four combinations are possible, including neither accurate nor precise.
Example
The true mass of an object is 20 g. A student records 17.1 g, 18.9 g and 16.2 g. The readings are far from each other (spread 2.7 g, imprecise) and their average (17.4 g) is far from 20 g (inaccurate).
The fourth target: neither accurate nor precise.
Causes
Both a systematic error (e.g. a balance not zeroed, shifting all readings) and random errors (careless reading, air draughts) are present at the same time.
Remedy
Calibrate and zero the instrument (removes the systematic error), then take several careful readings and average them (reduces random error).
Long Q 12.6
(Investigative) Elaborate the importance of using SI units in space exploration.
Answer
Many countries, one mission
Space missions are built by teams in many countries (the International Space Station: USA, Russia, Europe, Japan, Canada). Parts, fuel, forces and distances must be in one system, or they will not fit or work together.
A real lesson: Mars Climate Orbiter (1999)
NASA lost the Mars Climate Orbiter because one team's software gave thruster impulse in pound-force seconds while the navigation team expected newton seconds (SI). The 4.45-fold error put the spacecraft too close to Mars, and it was destroyed. A mission costing over 300 million dollars was lost to a units mix-up.
Why SI matters there
Precision: trajectories need exact values of speed (m s⁻¹), mass (kg), thrust (N) and time (s); base-10 SI avoids conversion errors.
Safety of astronauts: oxygen supply, cabin pressure (kPa) and temperature (K) must be read correctly by every crew and ground team.
Data sharing: telescope and probe data in SI can be used directly by scientists everywhere.
Consistency: SI units are interrelated (1 N = 1 kg m s⁻²), so calculations need no hidden conversion factors.
Pakistan's space agency SUPARCO, working with China on satellites such as PRSS-1 and the lunar mission iCube-Qamar (2024), also relies on SI units.
Set B: More important long questions 5 questions
Long questions often set in board papers from this chapter, answered in the same full style.
Imp. LQ 1
What are SI units? Why have scientists adopted them? Describe their advantages.
Answer
Definition
Standard and user-friendly units, called SI (Système International) units, that scientists all over the world have agreed to adopt.
The problem they solve
If scientists in one country measure lengths in metres and in another in feet, then they have to convert. Comparing quantities in different units is not only confusing but a wastage of time as well.
Advantages
Easy communication worldwide: scientists share data easily.
Fewer conversions are needed to coordinate information.
Base 10, like our number system: easy to learn, remember and convert.
Definite and precise standards.
Interrelated: one unit is derived from others without conversion factors.
Accuracy, consistency and universal understanding: a measurement taken in one part of the world can be understood and verified in another.
Collaboration: scientists compare results, replicate experiments and benefit from each other's work.
All of this ensures safety, reliability, reproducibility and progress.
Imp. LQ 2
Describe the five SI base units used in chemistry with their definitions.
Answer
There are seven base units in the SI system, out of which chemistry uses five: length, time, amount of substance, mass and temperature.
1. Metre (m), length
The distance travelled by light in vacuum in about one 300-millionth of a second (exactly 1/299 792 458 s).
A metre rod.
2. Kilogram (kg), mass
A block kept in France was taken as the standard unit of mass; it is also described as the mass of 1000 cm³ of water.
1 kg, 500 g and 250 g masses.
3. Second (s), time
The time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium-133 atom.
4. Kelvin (K), temperature
1/273.16 of the thermodynamic temperature of the triple point of water, where all three states of water exist together.
5. Mole (mol), amount of substance
Exactly 6.022 × 10²³ particles of a substance.
Imp. LQ 3
What are SI prefixes? How are they used? Give examples of conversions.
Answer
Definition and use
Since SI is a metric system based on 10, a set of prefixes indicates whether the unit is a multiple or a fraction of the base ten. It allows the reduction of zeros of a very small or very large number. The prefix symbol comes before the unit symbol.
Prefix
Symbol
Factor
mega
M
10⁶
kilo
k
10³
hecto
h
10²
deca
da
10¹
deci
d
10⁻¹
centi
c
10⁻²
milli
m
10⁻³
micro
μ
10⁻⁶
nano
n
10⁻⁹
pico
p
10⁻¹²
The prefix ladder.
Conversions
Change
Working
Answer
2.5 kg → g
2.5 × 10³
2500 g
750 mg → g
750 × 10⁻³
0.750 g
0.25 dm³ → cm³
0.25 × 1000
250 cm³
3.4 MJ → kJ
3.4 × 10⁶ ÷ 10³
3400 kJ
500 nm → m
500 × 10⁻⁹
5.00 × 10⁻⁷ m
Exam tip
Replace the prefix by its power of ten, then simplify. Write a symbol once even in plural: 5 kg, not 5 kgs.
Imp. LQ 4
Describe the types of errors in measurement. How can they be reduced?
Answer
Error
Every measurement carries a level of uncertainty known as error: the difference between the measured value and the actual value. It depends on the limitation of the instrument and the skill of the person measuring.
1. Systematic error
Errors that naturally occur in measuring tools; they may be removed by adding or subtracting a constant adjustment to each measurement. They affect accuracy. All measuring instruments contribute: a pipette, burette or measuring cylinder may deliver a volume slightly different from the one indicated by its graduation.
Reduce: calibrate, set the zero, apply a constant correction, use better instruments.
2. Random error
Causes one measurement to differ slightly from the next; comes from unpredictable changes during an experiment: limitations of instruments, environmental factors and slight variation in procedure. It often determines precision. E.g. reading a cylinder from a different angle, air moving the balance.
Parallax: a cause of random error.
Reduce: repeat readings and average, read at eye level, shield the balance, keep conditions steady.
Systematic
Random
Direction
one way
both ways
Affects
accuracy
precision
Fix
calibration / correction
averaging / care
Imp. LQ 5
Why do chemists use grams, cubic centimetres and degrees Celsius instead of the SI base units kg, m³ and K?
Answer
Grams
The unit of molar mass is grams per mole; given a mass in grams and the molar mass, we find the moles directly. Laboratory quantities are small, so grams are sensible and give manageable numbers, avoiding excessively large or small values.
n = m ÷ M: 4.4 g CO₂ ÷ 44 g mol⁻¹ = 0.1 mol
Cubic centimetres
cm³ is easy to measure and calculate with, and precise; laboratory volumes are small and more manageable in cm³ than in m³. (1 m³ = 10⁶ cm³.)
Degrees Celsius
Celsius is more convenient; its 100 divisions fit the base-ten SI format, and it converts easily into kelvin: K = °C + 273.
Celsius and kelvin.
°C
K
−273
0 (absolute zero)
0
273
25
298
65
338
100
373
Remember
A temperature change is the same number on both scales: a rise of 10 °C is a rise of 10 K.
closeness to the true value (spoilt by systematic error)
Precision
closeness of readings to each other (spoilt by random error)
Scientific notation
a × 10ⁿ, 1 ≤ a < 10 (0.000840 = 8.40 × 10⁻⁴)
Key definitions 12 terms
SI units
Standard and user-friendly units adopted by scientists all over the world, called SI (Système International) units. They make communication easy worldwide and allow scientists to share data easily.
Metre
The standard unit of length. Metre is the distance travelled by light in vacuum in about one 300-millionth of a second.
Kilogram
The standard unit of mass, symbol kg. A block kept in France was taken as the standard unit of mass. It is also described as the mass of 1000 cm³ of water.
Second
The standard unit of time. It is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium-133 atom.
Kelvin
The standard unit of temperature, symbol K. It is 1/273.16 of the thermodynamic temperature of the triple point of water, the point at which all three states of water (ice, liquid, vapour) exist at the same time.
Mole
The base unit of the amount of a pure substance, symbol mol. It is defined as having exactly 6.022 × 10²³ particles of a substance.
Derived units
Units of quantities that are mathematically derived from the base units.
Error
The difference between the measured value and the actual value.
Systematic error
Errors that naturally occur in measuring tools (which we assume give correct results). They may be removed by adding or subtracting a constant adjustment to each measurement, and they affect the accuracy of the measurement.
Random error
The error which causes one measurement to differ slightly from the next. It comes from unpredictable changes during an experiment.
Accuracy
How close results are to the true or known value.
Precision
The closeness of two or more measurements to each other.
Common mistakes to avoid
Writing K for kilogram: kilogram is kg; K is kelvin, k alone is kilo.
Adding "s" to symbols: 100 mm, not 100 mms.
Writing 840 × 10⁻⁶ as scientific notation: the first number must be between 1 and 10.
Forgetting to cube: 1 dm³ = 1000 cm³, not 10 cm³.
Mixing up accuracy and precision.
Thinking averaging removes a systematic error.
Writing °K: kelvin has no degree sign.
Subtracting 273 when converting °C to K.
Extra practice tap a question to see its answer
Pair measured in the same unit?Show answer
Heat and work (joule)
Prefix for 10⁻¹²?Show answer
Pico
SI unit of pressure?Show answer
Pascal (N m⁻²)
Symbol of kilogram?Show answer
kg
What does a mole represent?Show answer
A number (6.022 × 10²³ particles)
Unit of volume used in chemistry?Show answer
Cubic centimetre
0.000840 in scientific notation?Show answer
8.40 × 10⁻⁴
Nano means?Show answer
10⁻⁹
65 °C in kelvin?Show answer
338 K
Error that affects accuracy?Show answer
Systematic error
Error that affects precision?Show answer
Random error
Readings 5.2, 5.2, 5.2 g for a true 5.0 g?Show answer
Precise but not accurate
Final self-test
Final self-test: all 24 MCQs, no answers
Give yourself 25 minutes. Pick one option for each question, then submit to see your score and which questions to revise. Any question you get wrong tells you which topic to read again.
