Name: Law of Multiple Proportions
Uploaded: 2019-07-19
Duration: 6 min 43 s
Description: The Law of multiple proportions is applicable only when two elements combine to form two or more compounds. Watch this video to know how this law is applicable.

Question

State and explain Avogadro's hypothesis. Derive the relations between molecular mass and vapour density of a gas.

Accepted Answer

Avogadro's hypothesis states that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules. Avogadro's hypothesis explains correctly the reaction between hydrogen and oxygen forming water vapour.

$2 H_{2} + O_{2} \to 2 H_{2} O 2 vol 1 vol 2 vol$

$2$ volumes of hydrogen gas combine with $1$ volume of oxygen gas to form $2$ volumes of water vapour measured under the same condition of temperature and pressure.

Determination of the relationship between molecular mass and vapour density
The vapour density of a gas or vapour is defined as the ratio of the mass of a definite volume of the gas or vapour to the mass of the same volume of hydrogen, both the volumes measured at the same temperature and pressure.

Vapour density of a gas or vapour $= \frac{Mass of a definite volume of gas or vapour}{Mass of the same volume of hydrogen}$ (at the same temperature and pressure)

The vapour density of a gas or vapour can be measured experimentally. Let $V mL$ of a gas or vapour contain $n$ molecules.
Vapour density (V.D) $= \frac{Mass of V mL of the gas or vapour}{Mass of V mL of hydrogen}$ (at the same temperature and pressure)

According to Avogadro's hypothesis, $V mL$ of hydrogen gas under the same conditions of temperature and pressure would also contain $n$ molecules of hydrogen. Therefore,
Vapour density $= \frac{Mass of n molecules of the gas or vapour}{Mass of n molecules of hydrogen} = \frac{Mass of 1 molecule of the gas or vapour}{Mass of 1 molecule of hydrogen}$

Since, hydrogen molecule is diatomic.

V.D. $= \frac{Mass of 1 molecule of the gas or vapour}{Mass of 2 atoms of hydrogen}$

So, V.D. $\times 2$ $= \frac{Mass of 1 molecule of the gas or vapour}{Mass of 1 atom of hydrogen}$

$=$ The relative molecular mass of the gas or vapour.

Thus, the relative molecular mass of a gas or vapour is twice its vapour density.
Molecular mass $= 2 \times$ Vapour density.

State and explain Avogadro's hypothesis. Derive the relations between molecular mass and vapour density of a gas.

Important Questions on Basic Concepts Atoms & Molecules

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