Question

A sample of gas at 240K and 670 mmHg occupies a 1.28L volume. What volume (in Liters) will the gas occupy at 198K if the pressure is changed to 680 mmHg?

Answer 1

1.04 L.

Step-by-step explanation:

What is given?

Temperature 1 (T1) = 240 K.

Pressure 1 (P1) = 670 mmHg.

Volume 1 (V1) = 1.28 L.

Temperature 2 (T2) = 198 K.

Pressure 2 (P2) = 680 mmHg.

What do we need? Volume 2 (V2).

Step-by-step solution:

To solve this problem, we have to use the combined gas law. The combined gas law expresses the relationship between the pressure, volume, and absolute temperature of a fixed amount of gas. For a combined gas law problem, only the amount of gas is held constant. The formula of combined gas law is:

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2).`

We need to find the volume 2 (V2), so let's solve for this unknown value and let's replace the given data that we have:

`\begin{gathered} V_2=(P_1V_1T_2)/(T_1P_2), \\ V_2=\frac{670\text{ mmHg}\cdot1.28\text{ L}\cdot198K}{240K\cdot680\text{ }mmHg}, \\ V_2=1.04\text{ L.} \end{gathered}`

The final volume for this case would be 1.04 L, the volume is being reduced.