Answer:
240 kPa
Explanation:
The ideal gas law states:
[tex]pV=nRT[/tex]
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
[tex]\frac{pV}{T}=const.[/tex]
For the gas in the problem, which undergoes a transformation, this can be rewritten as
[tex]\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}[/tex]
where we have:
[tex]p_1 = 98 kPa=9.8\cdot 10^4 Pa[/tex] is the initial pressure
[tex]V_1 = 750 mL=0.75 L=0.75\cdot 10^{-3} m^3[/tex] is the initial volume
[tex]T_1 =30^{\circ}C =303 K[/tex] is the initial temperature
[tex]p_2[/tex] is the final pressure
[tex]V_2=250 mL=0.25 L=0.25\cdot 10^{-3} m^3[/tex] is the final volume
[tex]T_2=-25^{\circ}C=248 K[/tex] is the final temperature
Solving the formula for p2, we find the final pressure of the gas:
[tex]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[/tex]
