Question

A helium filled balloon had a volume of 30.2 L on the ground at 28°C and a pressure of 745 torr. After the balloon was released, it rose to an altitude where the temperature was -8°C and the pressure was 495 torr. What was the volume of the gas in the balloon at this altitude?

Answer 1

The final volume of gas in the balloon is 40.0 L (nearest tenth).

Step-by-step explanation:

To solve this problem we can 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 (measured in kelvin).
• P₂ is the final pressure.
• V₂ is the final volume.
• T₂ is the final temperature (measured in kelvin).

Convert the temperatures given in Celsius to kelvin by adding 273.15:

`\implies \sf 28^(\circ)C=28+273.15=301.15\;K`

`\implies \sf -8^(\circ)C=-8+273.15=265.15\;K`

Therefore, the values to substitute into the formula are:

• P₁ = 745 torr
• V₁ = 30.2 L
• T₁ = 301.15 K
• P₂ = 495 torr
• T₂ = 265.15 K

Substitute the values into the formula and solve for V₂:

`\implies \sf (P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

`\implies \sf (745 \cdot 30.2)/(301.15)=(495 \cdot V_2)/(265.15)`

`\implies \sf V_2=(745 \cdot 30.2 \cdot 265.15)/(301.15 \cdot 495)`

`\implies \sf V_2=40.01905...`

`\implies \sf V_2=40.0\;L\;(nearest\;tenth)`

Therefore, the final volume of gas in the balloon is 40.0 L (nearest tenth).