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 $n_{2}=\frac{p_{2} V_{2}}{R T_{2}}$
$\Rightarrow \, \, \, \frac{n_{2}}{n_{1}}=\frac{p_{2} V_{2}}{p_{1} V_{1}}\times \frac{T_{1}}{T_{2}}=\left(\frac{p_{2}}{p_{1}}\right)\left(\frac{V_{2}}{V_{1}}\right)\left(\frac{T_{1}}{T_{2}}\right)$
$\frac{n_{2}}{n_{1}}=\left(2\right)\left(\frac{1}{2}\right)\left(2\right)$
$n_{2}=2n_{1}$