Question

A sample of gas with a volume of 750 mL exerts a pressure of 98 kPa at 30 °C.What pressure will the sample exert when it is compressed to 250 mL and cooled to -25 °C?

Answer 1

Answer:

240 kPa

Explanation:

The ideal gas law states:

$pV=nRT$

where

p is the gas pressure

V is the gas volume

n is the number of moles

R is the gas constant

T is the absolute temperature of the gas

For a fixed amount of gas, n and R are constant, so we can rewrite the equation as

$\frac{pV}{T}=const.$

For the gas in the problem, which undergoes a transformation, this can be rewritten as

$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$

where we have:

$p_1 = 98 kPa=9.8\cdot 10^4 Pa$ is the initial pressure

$V_1 = 750 mL=0.75 L=0.75\cdot 10^{-3} m^3$ is the initial volume

$T_1 =30^{\circ}C =303 K$ is the initial temperature

$p_2$ is the final pressure

$V_2=250 mL=0.25 L=0.25\cdot 10^{-3} m^3$ is the final volume

$T_2=-25^{\circ}C=248 K$ is the final temperature

Solving the formula for p2, we find the final pressure of the gas:

$p_2 = \frac{p_1 V_1 T_2}{T_1 V_2}=\frac{(9.8\cdot 10^4 Pa)(0.75\cdot 10^{-3}m^3)(248 K)}{(303 K)(0.25\cdot 10^{-3} m^3)}=2.4\cdot 10^5 Pa = 240 kPa$