A weather balloon contains 222 L of helium at 20 °C and 760 mm Hg. What is the volume of the balloon when it ascends to an altitude where the temperature is –40 °C and 540 mm Hg?

Question

A weather balloon contains 222 L of helium at 20 °C and 760 mm Hg. What is the volume of the balloon when it ascends to an altitude where the temperature is –40 °C and 540 mm Hg?
Analysis
Since this question deals with pressure, volume, and temperature, the combined gas law is used to determine a final volume ([latex]V_{2}[/latex]) because five quantities are known—the initial pressure, volume, and temperature ([latex]P_{1}, V_{1}, and T_{1}[/latex]), and the final pressure and temperature ([latex]P_{2} and T_{2}[/latex]).

Accepted Answer

[1] Identify the known quantities and the desired quantity.

[latex]P_{1}[/latex] = 760 mm Hg [latex]P_{2}[/latex]= 540 mm Hg
[latex]T_{1}[/latex] = 20 °C [latex]T_{2}[/latex]= –40 °C
[latex]V_{1}[/latex] = 222 L [latex]V_{2}[/latex]= ?
known quantities desired quantity

• Both temperatures must be converted to Kelvin temperatures.
• [latex]T_{1}[/latex]= °C + 273 = 20 °C + 273 = 293 K
• [latex]T_{2}[/latex]= °C + 273 = –40 °C + 273 = 233 K

[2] Write the equation and rearrange it to isolate the desired quantity, [latex]V_{2}[/latex], on one side.
Use the combined gas law.

[3] Solve the problem.
• Substitute the five known quantities into the equation and solve for [latex]V_{2}[/latex].

Question 6.sp.5: A weather balloon contains 222 L of helium at 20 °C and 760 ...

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