Question

a gas has an initial volume of 21.7 l at a pressure of 0.4 atm and a temperature of 252 k. the pressure of the gas increases to 2 atm as the temperature increases to 323 k. what is the final volume of the gas?
○ 3.4 l
○ 5.6 l
○ 8.5 l
○ 11.1 l

Explanation:

Step1: Recall Combined Gas Law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 0.4\) atm, \(V_1 = 21.7\) L, \(T_1 = 252\) K, \(P_2 = 2\) atm, \(T_2 = 323\) K, and \(V_2\) is the final volume we need to find.

Step2: Rearrange the formula to solve for \(V_2\)

From \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), we can solve for \(V_2\) by cross - multiplying: \(V_2=\frac{P_1V_1T_2}{P_2T_1}\)

Step3: Substitute the given values into the formula

Substitute \(P_1 = 0.4\) atm, \(V_1 = 21.7\) L, \(T_1 = 252\) K, \(P_2 = 2\) atm, and \(T_2 = 323\) K into the formula for \(V_2\):

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Answer:

5.6 L