# Gay Lussac’s law of gaseous volume is derived from:

A.Law of definite proportions

B.Law of multiple proportions

C.Law of reciprocal proportions

D.Experimental observation

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**Hint:**Gay Lussac’s law states that at constant temperature, pressure of a fixed amount of gas varies directly with the temperature.

**Complete step by step answer:**

-This law was given in 1808 by a French chemist named Joseph Gay Lussac.

-Gay Lussac’s law also known as pressure temperature relationship states that for a given fixed mass of gas at constant volume the pressure exerted by the gas varies directly with the absolute temperature of the gas.

-Mathematically it is written as:

$P\alpha T$

$P/T = {k_3}$

where,

P=pressure exerted by the gas,

T=absolute temperature of the gas,

${k_3}$ =constant for Gay Lussac’s law

This relationship can be derived from Boyle’s Law and Charles Law which are both experimental.

(Boyle’s Law: $PV = {k_1}$ and Charles law: $V/T = {k_2}$)

-For a gas of fixed mass and at constant volume:

${P_1}/{T_1} = k$ And ${P_2}/{T_2} = k$

${P_1}/{T_1} = {P_2}/{T_2}$

-Law of definite proportions: It states that a given chemical compound always contains its component elements in a fixed ratio (by mass) and does not depend on its source or method of preparation.

This law has nothing to do with Gay Lussac’s law so we rule this out.

-Law of multiple proportions: It states that when 2 or more elements combine with each other to form more than one compound, the weights of one element that combine with the fixed weight of the other are in a ratio of small whole numbers.

Even this law has nothing to do with Gay Lussac’s Law.

-Law of reciprocal proportions: It states that if two different elements combine separately with the same weight of a third element, the ratios of the masses in which they do so are either the same or a simple multiple of the mass ratio in which they combine.

This law also has nothing to do with Gay Lussac’s Law.

-Since we have seen that these three laws are laws of chemical combinations they have nothing to do with the Gay-Lussac’s law which is a gas law and is experimental. Hence we conclude that it is based on experimental observations.

**So, the correct option is: D) experimental observation.**

**Note:**

Gay Lussac’s law is applied only when a gas has fixed amount of mass and at constant volume. But pressure varies with change in absolute temperature.