Question

If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

• A. Become half
• B. Become two times
• C. Become four times
• D. Remain constant

Answer 1

Answer: (B)

Applying ideal gas equation, we have
$pV=nRT$
Where, $p=$ pressure of the gas
$V=$ volume of the gas
$n=$ number of moles
$R=$ gas constant
$T=$ temperature of the gas
$\therefore n_1=\frac{p_1{V}_1}{R{T}_1}$
and $n_2=\frac{p_2{V}_2}{R{T}_2}$
$\Rightarrow \frac{n_2}{n_1}=\frac{p_2{V}_2}{p_1{V}_1}\times \frac{T_1}{T_2}=\left(\frac{p_2}{p_1}\right)\left(\frac{V_2}{V_1}\right)\left(\frac{T_1}{T_2}\right)$
$\frac{n_2}{n_1}=\left(2\right)\left(\frac{1}{2}\right)\left(2\right)$
$n_2=2n_1$