Question

# Gay Lussac’s law of gaseous volume is derived from:A.Law of definite proportionsB.Law of multiple proportionsC.Law of reciprocal proportionsD.Experimental observation

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

-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.