When two elements combine to form two
or more than two different compounds then the different masses of one element B
which combine with fixed mass of the other element bear a simple ratio to one
another.

**For example:**Carbon forms two oxides in oxygen

The ratio of masses of oxygen in CO
and CO

is

_{2}for fixed mass of carbon (12)is

**16: 32 = 1: 2.****ILLUSTRATIVE EXAMPLE (9):**The law of multiple proportions is illustrated by the pair of compounds:

(A) Sodium chloride and sodium bromide

(B) Water and heavy water

(C) Sulphur dioxide and sulphur trioxide

(D) Magnesium hydroxide and magnesium oxide

**SOLUTION**: In SO

_{2}32 gram of suphur react with 32 gram of oxygen. Similarly for SO

_{3}fixed mass of sulphur (32 gram) react with 48 gram of oxygen. The ratio of oxygen’s mass = 32:48 = 2:3 which support law of multiple proportions. Hence

**(C)**is correct answer.

**ILLUSTRATIVE EXAMPLE (10):**Carbon is found to form two oxides, which contain 42.9% and 27.3% of carbon respectively. Show that these figures illustrate the law of multiple proportions.

**SOLUTION**:

**Step 1:**To calculate the percentage composition of carbon and oxygen in each of the two oxides

**Step 2:**

**To calculate the weights of carbon which combine with a fixed weight i.e., one part by weight of oxygen in each of the two oxides.**

In the first oxide, 57.1 parts by weight of oxygen combine with
carbon = 42.9 parts.

1 part by weight of oxygen will combine with carbon =
42.9/57.1=0.751

In the second oxide 72.7 parts by weight of oxygen combine with
carbon = 27.3 parts.

1 part by weight of oxygen will combine with carbon
=27.3/72=0.376

**Step 3:**

**To compare the weights of carbon which combine with the same weight of oxygen in both the oxides-The ratio of the weights of carbon that combine with the same weight of oxygen (1 part) is 0.751: 0.376 or 2:1**

Since this is a simple whole number
ratio, so the above data illustrate the law of multiple proportions.

**TRY YOURSELF:**

**Exercise (1):**

**Metal M and chlorine combine in different proportions to form two compounds A and B. The mass ratio M: Cl is 0.895: 1 in A and 1.791: 1 in B. What law of chemical combination is illustrated?**

**Exercise (2):**

**By means of the following analytical results show that law of multiple proportions is true:**

**Exercise (3):**

**1 g of a metal, having no variable valency, produces 1.67 g of its oxide when heated in air. Its carbonate contains 28.57% of the metal. How much oxide will be obtained by heating 1 g of carbonate?**

**Exercise (4):**

**Phosphorous and chlorine form two compounds. The first contains 22.54% by mass of phosphorous and the second 14.88% of phosphorous. Show that these data are consistent with law of multiple proportions.**

**TRY YOURSELF:**

**SOLUTION:**

(1) Mass of metal which combine with 1 part of chlorine
are in the ratio of 1:2, which is a simple ratio. Hence, law of multiple
proportions is illustrated.

(2)
The masses of mercury which combine with 1 part of chlorine are in the ratio of
2:1 which is simple ratio. Hence, law of multiple proportions is illustrated.

(3)
0.477 g

(4)
Prove yourself ….

**Limitation of law of multiple proportions:**Non Stoichiometric compound do not follow this law for example Fe

_{0.93}O

_{1}.

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