Chapter U3, Problem 18STP

Interpretation Introduction

Interpretation:

Number of moles of the gas needs to be determined.

Concept introduction:

Ideal gas equation: This equation relates pressure, temperature, volume and number of moles of a gas. This equation is consists of three laws i.e. Boyle’s law, Charles’s law and Avogadro’s law.

1. Boyle’s Law : $\text{V}\propto \frac{\text{1}}{\text{P}}\text{(Where n,T are constant )}$
2. Charles’s Law : $\text{V}\propto \text{T (Where P, n are constant )}$
3. Avogadro’s Law : $\text{V}\propto \text{n (Where P,T are constant )}$

The ideal gas equation can be obtained by combining these three equation

Thus,

$\text{}\text{V}\propto \frac{nT}{P}$

By convention the proportionality constant is the gas constant, which is expressed in R. The value of R = $0.0821{\text{ L-atm mol}}^{-1}{\text{sec}}^{-1}$

So, the final ideal gas equation is

$\text{}\text{V=}\frac{nRT}{P}or\text{ PV = nRT}$

Answer to Problem 18STP

The number of mole $n=0.34\text{ mol}$

Explanation of Solution

Given, the Volume (V) of the gas $=\text{11}.\text{2 L}$

Temperature ( $T$ ) of the system = $300K$

Pressure ( $P$ ) of the system = $0.75\text{ atm}$

Gas constant (R) = $0.0821{\text{ L-atm mol}}^{-1}{\text{K}}^{-1}$

Number of moles ( $n$ ) = ?

By putting all the given values in the final ideal gas equation,

$\begin{array}{l}\text{}\text{ PV = nRT}\\ \text{(0}\text{.75 atm)}\times \text{(11}\text{.2L) = n }\times \text{(}0.0821{\text{ L-atm mol}}^{-1}{\text{K}}^{-1}\text{)}\times \text{(300K)}\\ \text{n = }\frac{0.75\times 11.2\cancel{\text{L-atm}}}{0.0821\times \text{300 }\cancel{\text{L-atm}}{\text{ mol}}^{-1}\cancel{{\text{K}}^{-1}}\cancel{\text{K}}}\\ n=0.34\text{ mol}\text{.}\end{array}$

Thus, the correct option is (A) and the number of mole $n=0.34\text{ mol}$