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Solution: A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg and a temperature of 28.0 °C. The balloon rises in the atmosphere to an altitude of approximately 25,000 feet, where the pressure is 385 mmHg and the temperature is -15.0 °C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude. 

Problem

A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg and a temperature of 28.0 °C. The balloon rises in the atmosphere to an altitude of approximately 25,000 feet, where the pressure is 385 mmHg and the temperature is -15.0 °C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude. 

Solution

Initially, a weather balloon has a volume of 28.5 L at 28.0 ˚C and 748 mmHg. We’re being asked to determine the volume of the weather balloon if the pressure changes to 385 mmHg and the temperature changes to –15.0 ˚C.


Recall that the ideal gas law is:



The pressure, volume, and temperature of a gas are related to the number of moles of gas and the universal gas constant:



The value nR is constant. For a given moles of gas, the initial and final pressure, volume, and temperature of the gas are related by the combined gas law:



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