Answer:
241 kPa
Explanation:
The ideal gas law states that:
[tex]pV=nRT[/tex]
where
p is the gas pressure
V is its volume
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
We can rewrite the equation as
[tex]\frac{pV}{T}=nR[/tex]
For a fixed amount of gas, n is constant, so we can write
[tex]\frac{pV}{T}=const.[/tex]
Therefore, for a gas which undergoes a transformation we have
[tex]\frac{p_1 V_1}{T_1}=\frac{p_2 V_2}{T_2}[/tex]
where the labels 1 and 2 refer to the initial and final conditions of the gas.
For the sample of gas in this problem we have
[tex]p_1 = 98 kPa=9.8\cdot 10^4 Pa\\V_1 = 750 mL=0.75 L=7.5\cdot 10^{-4}m^3\\T_1 = 30^{\circ}C+273=303 K\\p_2 =?\\V_2 = 250 mL=0.25 L=2.5\cdot 10^{-4} m^3\\T_2 = -25^{\circ}C+273=248 K[/tex]
So we can solve the formula for [tex]p_2[/tex], the final pressure:
[tex]p_2 = \frac{p_1 V_1 T_2}{T_1 V_2}=\frac{(9.8\cdot 10^4 Pa)(7.5\cdot 10^{-4} m^3)(248 K)}{(303 K)(2.5\cdot 10^{-4} m^3)}=2.41\cdot 10^5 Pa = 241 kPa[/tex]
