Question

A sample of gas has a volume of 3.5 L at a pressure of 72.6 kPa and a temperature of 25 C. What will be the volume of the gas if the pressure is changed to 124 kPa and the temperature is changed to 0 C?

Answer 1

1.88 L (3 s.f.)

Step-by-step explanation:

To find the final volume of the gas, use the combined gas law.

Combined Gas Law

`\boxed{\sf (P_1V_1)/(T_1)=(P_2V_2)/(T_2)}`

where:

• P₁ is the initial pressure.
• V₁ is the initial volume.
• T₁ is the initial temperature (in kelvin).
• P₂ is the final pressure.
• V₂ is the final volume.
• T₂ is the final temperature (in kelvin).

As the temperatures have been given in Celsius, we need to first convert the temperatures from Celsius to kelvin by adding 273.15:

`\implies \sf T_1=25+273.15=298.15\;K`

`\implies \sf T_2=0+273.15=273.15\;K`

Therefore, the values to substitute into the formula are:

• P₁ = 72.6 kPa
• V₁ = 3.5 L
• T₁ = 298.15 K
• P₂ = 124 kPa
• T₂ = 273.15 K

Substitute the values into the formula and solve for V₂:

`\implies \sf (72.6 \cdot 3.5)/(298.15)=(124 \cdot V_2)/(273.15)`

`\implies \sf V_2=(72.6 \cdot 3.5 \cdot 273.15)/(298.15\cdot 124)`

`\implies \sf V_2=(69407.416)/(36970.6)`

`\implies \sf V_2=1.8773678...`

`\implies \sf V_2=1.88\;L\;(3\;s.f.)`

Therefore, the volume of the gas at the new pressure and temperature will be 1.88 L (3 s.f.)