Question

If I initially have a gas at a pressure of 10.0 atm, a volume of 24.0 liters, and a temperature of 200. K, and then I raise the pressure to 14.0 atm and increase the temperature to 300. K, what is the new volume of the gas?

Answer 1

Hello!

If I initially have a gas at a pressure of 10.0 atm, a volume of 24.0 liters, and a temperature of 200. K, and then I raise the pressure to 14.0 atm and increase the temperature to 300. K, what is the new volume of the gas?

We have the following data:

P1 (initial pressure) = 10 atm

V1 (initial volume) = 24 L

T1 (initial temperature) = 200 K

P2 (final pressure) = 14 atm

T2 (final temperature) = 300 K

V2 (final volume) = ? (in L)

Now, we apply the data of the variables above to the General Equation of Gases, let's see:

$\dfrac{P_1*V_1}{T_1} =\dfrac{P_2*V_2}{T_2}$

$\dfrac{10*24}{200} =\dfrac{14*V_2}{300}$

$\dfrac{240}{200} =\dfrac{14\:V_2}{300}$

multiply the means by the extremes

$200*14\:V_2 = 240*300$

$2800\:V_2 = 72000$

$V_2 = \dfrac{72000\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}{2800\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}$

$\boxed{\boxed{V_2 \approx 25.71\:L}}\:\:\:\:\:\:\bf\blue{\checkmark}$

Answer:

The new volume is approximately 25.71 Liters

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