Question

A vessel having a volume of $5$ litres contains $1.4\text{g}$ of nitrogen at a temperature of $1800\text{K}$. The pressure of the gas if $30\%$ of its molecules are dissociated into atoms at this temperature is:

• A. $4.05\text{atm}$
• B. $2.025\text{atm}$
• C. $3.84\text{atm}$
• D. $1.92\text{atm}$

Answer 1

The correct option is D $1.92\text{atm}$

$N_2\to 2N$
$\text{at t}=0\frac{1.4}{28}=\frac{1}{20}0$
$\text{at t}=t_f\frac{1}{20}-x2x$
but, $x=30\%\text{of}\frac{1}{20}=\frac{1}{20}\times \frac{30}{100}=\frac{3}{200}$
Final number of moles
$\frac{1}{20}-x+2x=\frac{1}{20}+x$
$=\frac{1}{20}+\frac{3}{200}$
$=\frac{13}{200}$
$\therefore P=\frac{13}{200}\times \frac{0.0821\times 1800}{5}=1.92\text{atm}$