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I have an unknown volume of gas at a pressure of 0.5 atm and a temperature of 325 K. If I raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas?



Answer :

MathPhys

Answer:

117 L

Explanation:

Assuming the gas can be modeled as an ideal gas, we can apply the ideal gas law, which states that the pressure (P) times the volume (V) is equal to the number of moles (n) times the universal gas constant (R) times the temperature (T).

PV = nRT

Since n, the number of moles (amount of gas), is constant, we can use the ideal gas law to write and solve a proportion.

[tex]\Large \text {$ n_1R=n_2R $}\\\\\huge \text {$ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} $}\\\\\huge \text {$ \frac{(0.5\ atm)V_1}{325\ K}=\frac{(1.2\ atm)(48\ L)}{320\ K} $}\\\\\Large \text {$ V_1=117\ L $}[/tex]

The initial volume of the gas is therefore 117 L.

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