Question

What temperature would be necessary to double the volume of a gas STP if the pressure is decreased by 50%?

Answer 1

$\frac{PV}{T}=\frac{P^{\prime }{V}^{\prime }}{T^{\prime }}$
$P=2P^{\prime }$ as pressure is decreased by 50%
$V=0.5V^{\prime }$ as volume is doubled

$T=273.15K$ under STP conditions

$\frac{PV}{T}=\frac{P^{\prime }{V}^{\prime }}{T^{\prime }}$

$\frac{2P^{\prime }\times 0.5V^{\prime }}{273.15K}=\frac{P^{\prime }{V}^{\prime }}{T^{\prime }}$

$\frac{2\times 0.5}{273.15K}=\frac{1}{T^{\prime }}$

$\frac{1}{273.15K}=\frac{1}{T^{\prime }}$

$T^{\prime }=273.15K$

Hence, temperature of 273.15 K would be necessary to double the volume of a gas STP if the pressure is decreased by $50\%$.