Question

One mole of an ideal gas at STP has its temperature changed to ${15}^{\circ }C$ and its pressure changed to $700$ torr. What is the new volume of this gas?

• A. $\frac{\left(760\right)\left(22.4\right)\left(288\right)}{\left(273\right)\left(700\right)}$ L
• B. $\frac{\left(273\right)\left(700\right)}{\left(760\right)\left(22.4\right)\left(288\right)}$ L
• C. $\frac{\left(760\right)\left(22.4\right)\left(273\right)}{\left(288\right)\left(700\right)}$ L
• D. $\frac{\left(700\right)\left(22.4\right)\left(287\right)}{\left(273\right)\left(760\right)}$ L
• E. $\frac{\left(760\right)\left(1.0\right)\left(288\right)}{\left(273\right)\left(700\right)}$ L

Answer 1

The correct option is A $\frac{\left(760\right)\left(22.4\right)\left(288\right)}{\left(273\right)\left(700\right)}$ L

$PV=nRT$
$P^{\prime }{V}^{\prime }=nR{T}^{\prime }$

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

$V^{\prime }=V\times \frac{P}{P^{\prime }}\times \frac{T^{\prime }}{T}$
One mole of an ideal gas at STP has its temperature changed to ${15}^o$C and its pressure changed to 700 torr
.The new volume of this gas is $V^{\prime }=22.4\times \frac{760}{700}\times \frac{288}{273}$ L
Note: STP conditions correspond to a pressure of 760 torr and temperature of 273 K. The temperature 15 deg C corresponds to $15+273=288$ K