A gas at 155 kPa and 25°C occupies a container with an initial volume of 1.00 L. By changing the volume, the pressure of the gas increases to 605 kPa as the temperature is raised to 125°C. What is the new volume if the number of moles is constant?

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Answer 1 · 2018-02-20T15:58:16

The new volume is $= 0.34 L$ $=0.34L$

$P V = n R T$ $PV=nRT$

$\frac{P V}{T} = n R = constant$ $(PV)/T=nR = "constant"$ , The number of moles is constant.

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$

The initial pressure is $P_{1} = 155 k P a$ $P_1=155kPa$

The initial temperature is $T_{1} = 25^{\circ} C + 273 = 298 K$ $T_1=25^@C+273=298K$

The initial volume is $V_{1} = 1 L$ $V_1=1L$

The final pressure is $P_{2} = 605 k P a$ $P_2=605kPa$

The final temperature is $T_{2} = 125^{\circ} C + 273 = 398 K$ $T_2=125^@C+273=398K$

The final volume is

$V_{2} = \frac{P_{1}}{P_{2}} \cdot \frac{T_{2}}{T_{1}} \cdot V_{1}$ $V_2=P_1/P_2*T_2/T_1*V_1$

$= \frac{155}{605} \cdot \frac{398}{298} \cdot 1$ $=155/605*398/298*1$

$= 0.34 L$ $=0.34L$