MHT-CET Chemistry · Some Basic Concepts of Chemistry

Laws of Chemical Combination and Percentage Composition

Five named laws fix the ratios in which elements combine (conservation of mass, definite and multiple proportions, reciprocal proportions and combining volumes, Avogadro's law), while percentage composition converts a formula into the mass fraction of each element.

All Some Basic Concepts of Chemistry notes MHT-CET Chemistry strategy

Why this matters

Seven PYQs, split two ways. Four of them test the law of multiple proportions as a recognition task — pick the pair of compounds that does (or does not) demonstrate it — and the single give-away is whether the two compounds share the SAME two elements. The remaining three are one name-the-law question (definite proportions) and two short calculations (percentage of an element by mass, percent atom economy). So this subtopic is one recall table plus two one-line formulas — all EASY-to-MODERATE and heavily recall-driven.

Concept 1 of 3

The five laws of chemical combination

Intuition

These are the named rules the paper asks you to recognise from a one-line statement or a worked example. Learn each law's name, its one-line statement, and one stock example — that is exactly what the MCQs test.

Definition

Five laws govern how elements combine, each tested by either its definition or a 'which law is shown' example:

Law of conservation of mass — total mass of reactants equals total mass of products.
Law of definite (constant) proportions — a pure compound always has the same elements in the same fixed mass ratio.
Law of multiple proportions — when the same two elements form more than one compound, the masses of one that combine with a fixed mass of the other are in small whole-number ratios.
Gay-Lussac's law of combining volumes — gases combine in simple whole-number volume ratios (at the same temperature and pressure).
Avogadro's law — equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Law	Statement	Stock example
Law of conservation of mass	Matter can neither be created nor destroyed in a chemical reaction; total mass of reactants = total mass of products.	$1.7$ g $\text{AgNO}_3 + 0.585$ g $\text{NaCl}$ give $1.435$ g $\text{AgCl} + 0.85$ g $\text{NaNO}_3$ ; both sides total $2.285$ g.
Law of definite (constant) proportions	A given pure compound always contains the same elements in the same fixed proportion by mass, whatever its source.	Water is always $1 : 8$ hydrogen to oxygen by mass.Q Also called Proust's law. The tell-tale phrase in an MCQ is 'a given compound always contains the same proportion of elements'.
Law of multiple proportions	When the same two elements form more than one compound, the masses of one that combine with a fixed mass of the other are in a ratio of small whole numbers.	$\text{CO}$ and $\text{CO}_2$ : oxygen masses per fixed carbon are in a $1 : 2$ ratio.Q The most-asked law here. It ONLY applies when both compounds contain the SAME two elements — this is the whole basis of the 'which pair cannot demonstrate it' questions.
Gay-Lussac's law of combining volumes	Gases combine (and form gaseous products) in volume ratios that are simple whole numbers, at the same temperature and pressure.	$1$ volume $\text{N}_2 + 3$ volumes $\text{H}_2 \to 2$ volumes $\text{NH}_3$ (a $1 : 3 : 2$ ratio). Sometimes phrased as the law of reciprocal proportions in older texts — both express fixed combining relationships; for gases the paper uses the combining-volumes form.
Avogadro's law	Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.	$22.4$ L of any gas at STP contains $1$ mole $(6.022\times10^{23}$ molecules $)$ .

Recognise the law from either its definition or a worked example.

Practice this conceptself-check · 4 quick reps

Try it yourself

Which law is illustrated by the compounds H2O and H2O2, both formed from the two elements H and O?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Which law states matter can neither be created nor destroyed?
2.
'A given compound always contains the same proportion of elements' states which law?
3.
CO and CO2 (oxygen in a 1 : 2 ratio per fixed carbon) illustrate which law?
4.
Which law says equal volumes of gases at the same T and P have equal numbers of molecules?

From the bank · past-year question

Example 1Some Basic Concepts of ChemistryEASY

Which law is illustrated by compounds

\text{H}_2\text{O}

and

\text{H}_2\text{O}_2

formed from two different elements, H and O?

[Q93 · 10th May Shift 2 · 2023]

Multiple proportions needs the SAME two elements

A pair like

\text{Na}_2\text{S}

and

\text{NaF}

(elements S and F differ), or

\text{NaNO}_3

and

\text{CaCO}_3

, CANNOT demonstrate multiple proportions — the law compares two compounds built from the identical pair of elements (like

\text{CO}/\text{CO}_2

\text{NO}/\text{NO}_2

). Check the elements first, not the subscripts.

Definite vs multiple proportions

Definite proportions = ONE compound with ONE fixed internal ratio. Multiple proportions = TWO different compounds of the same two elements, in small whole-number ratios. If the question names two compounds being compared, it is multiple; if it describes one compound's constant make-up, it is definite.

Drill 4 more on the five laws of chemical combination

Concept 2 of 3

Percentage composition by mass

Intuition

The percentage of an element in a compound is just its total mass inside one formula unit divided by the whole molar mass, times 100. Count the atoms of that element, multiply by its atomic mass, divide by the compound's molar mass.

Definition

Percentage composition rule:

Molar mass = sum of (atoms × atomic mass) over every element in the formula.
Percentage of an element $= \dfrac{(\text{atoms of that element}) \times (\text{its atomic mass})}{\text{molar mass of the compound}} \times 100$ .
The percentages of all elements in the compound add up to $100\%$ .

Mass percentage of an element

\%\,\text{element} = \dfrac{n \times A}{M} \times 100

nnumber of atoms of that element in one formula unit
Aatomic mass of that element
Mmolar mass of the whole compound

Worked example

Find the percentage by mass of nitrogen in ammonium nitrate, NH4NO3. (N = 14, H = 1, O = 16)

Molar mass of $\text{NH}_4\text{NO}_3 = 2(14) + 4(1) + 3(16) = 28 + 4 + 48 = 80$ g/mol.
There are 2 nitrogen atoms, contributing $2 \times 14 = 28$ g.
$\% \text{N} = \dfrac{28}{80} \times 100 = 35\%$ .

Answer:

35\%

Practice this conceptself-check · 3 quick reps

Try it yourself

Find the percentage by mass of carbon in CO2. (C = 12, O = 16)

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Molar mass of NaOH (Na = 23, O = 16, H = 1)?
2.
% by mass of sodium in NaOH?
3.
% by mass of hydrogen in H2O (H = 1, O = 16)?

From the bank · past-year question

Example 2Some Basic Concepts of ChemistryEASY

What is the percentage by mass of oxygen in NaOH? (Atomic mass of Na=23u, O=16u, H=1u)

[Q52 · 15th May Shift 1 · 2023]

Multiply by the number of atoms, not just the atomic mass

For water

\text{H}_2\text{O}

, hydrogen contributes

2 \times 1 = 2

g, not

1

g — there are two H atoms. Always use

n \times A

in the numerator, and remember the percentages of every element must sum to

100\%

Concept 3 of 3

Percent atom economy

Intuition

Atom economy asks what fraction of the reactant mass actually ends up in the product you want. Divide the formula weight of the desired product by the total formula weight of all reactants, then multiply by 100 — a green-chemistry efficiency measure.

Definition

Percent atom economy:

Percent atom economy $= \dfrac{\text{formula weight of desired product}}{\text{sum of formula weights of all reactants}} \times 100$ .
A higher value means less mass is wasted as by-products; a value of $100\%$ means every atom of the reactants ends up in the wanted product.

Percent atom economy

\%\,\text{atom economy} = \dfrac{\text{FW of desired product}}{\sum \text{FW of reactants}} \times 100

Worked example

Reactants with a total formula weight of 78 u form a desired product of formula weight 65 u. What is the percent atom economy?

$\% \text{atom economy} = \dfrac{\text{FW of product}}{\sum \text{FW of reactants}} \times 100$ .
$= \dfrac{65}{78} \times 100$ .
$\approx 83.3\%$ .

Answer:About

83\%

Practice this conceptself-check · 3 quick reps

Try it yourself

Reactants of total formula weight 120 u give a desired product of formula weight 90 u. Find the percent atom economy.

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Product FW 50 u from reactants totalling 100 u — atom economy?
2.
Product FW 44 u from reactants totalling 44 u — atom economy?
3.
Does a higher atom economy mean more or less wasted mass?

From the bank · past-year question

Example 3Some Basic Concepts of ChemistryEASY

What is value of percent atom economy when reactants having sum of formula weight 78 u results in the formation of a product with formula weight 65 u?

[Q80 · 15th May Shift 1 · 2023]

Product over reactants, not the other way round

The desired product's formula weight is the NUMERATOR and the total reactant weight is the denominator. Flipping them (e.g.

78/65

) gives a nonsensical value above

100\%

. Atom economy can never exceed

100\%

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Percentage composition by mass
Mass percentage of an element
$\%\,\text{element} = \dfrac{n \times A}{M} \times 100$
Percent atom economy
Percent atom economy
$\%\,\text{atom economy} = \dfrac{\text{FW of desired product}}{\sum \text{FW of reactants}} \times 100$

Reference tables (1)

The five laws of chemical combination5 rows

Law	Statement	Stock example
Law of conservation of mass	Matter can neither be created nor destroyed in a chemical reaction; total mass of reactants = total mass of products.	$1.7$ g $\text{AgNO}_3 + 0.585$ g $\text{NaCl}$ give $1.435$ g $\text{AgCl} + 0.85$ g $\text{NaNO}_3$ ; both sides total $2.285$ g.
Law of definite (constant) proportions	A given pure compound always contains the same elements in the same fixed proportion by mass, whatever its source.	Water is always $1 : 8$ hydrogen to oxygen by mass.Q Also called Proust's law. The tell-tale phrase in an MCQ is 'a given compound always contains the same proportion of elements'.
Law of multiple proportions	When the same two elements form more than one compound, the masses of one that combine with a fixed mass of the other are in a ratio of small whole numbers.	$\text{CO}$ and $\text{CO}_2$ : oxygen masses per fixed carbon are in a $1 : 2$ ratio.Q The most-asked law here. It ONLY applies when both compounds contain the SAME two elements — this is the whole basis of the 'which pair cannot demonstrate it' questions.
Gay-Lussac's law of combining volumes	Gases combine (and form gaseous products) in volume ratios that are simple whole numbers, at the same temperature and pressure.	$1$ volume $\text{N}_2 + 3$ volumes $\text{H}_2 \to 2$ volumes $\text{NH}_3$ (a $1 : 3 : 2$ ratio). Sometimes phrased as the law of reciprocal proportions in older texts — both express fixed combining relationships; for gases the paper uses the combining-volumes form.
Avogadro's law	Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.	$22.4$ L of any gas at STP contains $1$ mole $(6.022\times10^{23}$ molecules $)$ .

Recognise the law from either its definition or a worked example.

Watch out for (4)

Multiple proportions needs the SAME two elements
→ The five laws of chemical combination
Definite vs multiple proportions
→ The five laws of chemical combination
Multiply by the number of atoms, not just the atomic mass
→ Percentage composition by mass
Product over reactants, not the other way round
→ Percent atom economy

Mastery check — 4 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Some Basic Concepts of ChemistryEASY

Which of the following pair of compounds demonstrates the law of multiple proportions?

[Q77 · 14th May Shift 2 · 2024]

Example 2Some Basic Concepts of ChemistryEASY

"A given compound always contains the same proportion of elements" is a statement of —

[Q56 · 3rd May Shift 2 · 2023]

Example 3Some Basic Concepts of ChemistryMODERATE

Which of the following pair of compounds does not demonstrate the law of multiple proportions?

[Q89 · 3rd May 2nd Shift · 2023]

Example 4Some Basic Concepts of ChemistryMODERATE

Which of the following pair of compounds cannot demonstrate law of multiple proportion?

[Q93 · 11th May Shift 1 · 2023]

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