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Chapter 5: Problem 35

A gas-filled balloon having a volume of \(2.50 \mathrm{~L}\) at \(1.2 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) is allowed to rise to the stratosphere (about \(30 \mathrm{~km}\) above the surface of Earth), where the temperature and pressure are \(-23^{\circ} \mathrm{C}\) and \(3.00 \times 10^{-3}\) atm, respectively. Calculate the final volume of the balloon.

Short Answer

Expert verified
The final volume of the balloon when it reaches the stratosphere is 250 L.

Step by step solution

01

Convert Celsius temperatures to Kelvin

Temperatures must be in Kelvin for the ideal gas law to be applicable. Convert the initial and final temperatures from Celsius to Kelvin using the formula \(K = ^\circ C + 273.15\). So the initial temperature T1 is \(25^\circ C + 273.15 = 298.15 K\) and the final temperature, T2, is \(-23^\circ C + 273.15 = 250.15 K\).
02

Input values into the combined gas law

Rearrange the formula \(P_1V_1/T_1 = P_2V_2/T_2\) to solve for the final volume, \(V_2\). This gives you \(V_2 = P_1V_1T_2/(T_1P_2)\). Substitute in the given values of \(P_1 = 1.2 atm\), \(V_1 = 2.5 L\), \(T_1 = 298.15 K\), \(P_2 = 3.00 × 10^{-3} atm\) and \(T_2 = 250.15 K\).
03

Calculate the final volume

Now, calculate the final volume, \(V_2\), by multiplying and dividing the inserted values: \(V_2 = (1.2 atm × 2.5 L × 250.15 K) / (298.15 K × 3.00 × 10^{-3} atm) = 250 L\). Therefore, the final volume of the balloon when it reaches the stratosphere is 250 L.

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