Question

At constant temperature and pressure, the volume of a gas is directly proportional to its number of moles.
A True
B False

Answer 1

Hint: The law of gas laws which contains terms of pressure(P) ,volume(V), absolute temperature(T) as variables, gives a relation between them. Which is \[{\text{PV = nRT}}\]. This is also known as ideal gas. This ideal gas equation can be formed by combining the gas law equations.

Complete step by step solution:
There are total three gas laws, which are
- Charles’ law: according to this law that the volume of ideal gases changes with the change of absolute temperature proportionally, when pressure of the system is constant throughout the experiment. i.e. the volume to temperature ratio at a constant when pressure is always constant.
\[\dfrac{{{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}}{\text{ = }}\dfrac{{{{\text{V}}_{\text{2}}}}}{{{{\text{T}}_{\text{2}}}}}{\text{ when P and n are constant}}{\text{.}}\].
- Boyle’s law: According to this law at a constant temperature, the pressure is applied on an ideal gas is inversely proportional to the volume of that system. i.e., the product of pressure and volume is constant when absolute temperature is constant.
\[{{\text{P}}_{\text{1}}}{{\text{V}}_{\text{1}}}{\text{ = }}{{\text{P}}_{\text{2}}}{{\text{V}}_{\text{2}}}{\text{ when n , T is constant}}\]
- Avogadro’s law: According to this law at constant pressure and absolute temperature, the number of molecules is directly proportional with the volume of an ideal gas. i.e. the ratio of volume to number of molecules(n) is constant at constant pressure and absolute temperature.
\[\dfrac{{{{\text{V}}_{\text{1}}}}}{{{{\text{n}}_{\text{1}}}}}{\text{ = }}\dfrac{{{{\text{V}}_{\text{2}}}}}{{{{\text{n}}_{\text{2}}}}}{\text{ when P and T are constant}}{\text{.}}\]
Therefore according to the Avogadro’s law, at constant temperature and pressure, the volume of a gas is directly proportional to its number of moles

So, the given statement is true. Hence option A is correct.

Note:
Now if Boyle’s law and Charles law is combined a new gas law equation will generate, which can be written as,
\[\dfrac{{{{\text{P}}_{\text{1}}}{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}}{\text{ = }}\dfrac{{{{\text{P}}_{\text{2}}}{{\text{V}}_{\text{2}}}}}{{{{\text{T}}_{\text{2}}}}}\]
In this relation pressure(P), volume(V), and absolute temperature(T) are variables. Where the product of pressure and volume changes proportionally with absolute temperature.