Question

The molecular weight of a gas is $40$. At $400K$, if $120g$ of the gas has a volume $20litres$, the pressure of the gas in atm is:
A) 4.92
B) 5.02
C) 49.6
D) 0.546

Answer 1

An ideal gas follows the Raoult’s law, and the equation is known as the ideal gas equation. This equation is the total combination of Boyle’s law, Charles law, Avogadro’s law and Gay lussac law. Moles can be defined as the ratio of given mass of a substance to its molar mass.
$PV = nRT$ and $n = \dfrac{{G.M}}{{M.M}}$

Complete step by step answer:
An ideal solution can be termed as the solution which follows Raoult’s law for the entire range of concentration at specified temperature as mentioned in the given question also.
The partial pressure of an ideal gas be calculated by the equation-
$p = p_A^\circ {\chi _A} + p_B^\circ {\chi _B}$ Where $p_A^\circ$ and $p_B^\circ$ are the partial pressure of pure solvent and ${\chi _A}$ , ${\chi _B}$ are the mole fraction of the solvent A and B.
The conditions which an ideal gas satisfies are that Raoult's law is obeyed, Enthalpy of mixing the solvents will be zero and the total volume change after the mixing of two solvents will also be zero.
The ideal gas equation can be written as $PV = nRT$ , where P is the pressure of gas in atm, V is the volume of gas in litres, n is the number of moles presence of the gas, T is the temperature and R is the gas constant with the value $0.0821 \text{L atm}{K^{ - 1}}mo{l^{ - 1}}$ .
According to the given question the values are-
$V = 20L$ , $R = 0.0821 \text{L atm}{K^{ - 1}}mo{l^{ - 1}}$ , Molar mass of gas is $40g$ , given mass of gas is $120g$
The moles can be calculated as –
$n = \dfrac{{G.M}}{{M.M}}$
$\Rightarrow n = \dfrac{{120}}{{40}}$
$\Rightarrow n = 3moles$
Putting in the ideal gas equation,
$PV = nRT$
$\Rightarrow P = \dfrac{{nRT}}{V}$
$\Rightarrow P = \dfrac{{3mol \times 0.0821 \text{L atm}{K^{ - 1}}mo{l^{ - 1}} \times 400K}}{{20L}}$
On simplifying the equation-
$P = \dfrac{{98.52atm}}{{20}}$
$\Rightarrow P = 4.92atm$
Hence the value of Pressure of gas is equal to $4.92atm$ .
The correct option is (A).

Note:
The conversion of different units of gas constant into each other is very important. There is no intermolecular attraction in ideal gas. According to the kinetic theory of gas, the energy can be calculated by the formula, $E = \dfrac{3}{2} \times nRT$ .