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A hot air balloon has a volume of 74,000,000 L at 25°C. If n and P do not change what must the volume...

4. A hot air balloon has a volume of 74,000,000 L at 25°C. If n and P do not change what must the volume expand to if the air is heated to 250°F?
5. At constant temperature, a sample of helium at 765 torr in a closed container was compressed from 5.00 L to 3.00 L. What was the new pressure, in atm, exerted by the helium on its container?
6. Consider an air-tight balloon that is filled with helium gas at room temperature and atmospheric pressure as seen below. Select the letter of the balloon diagram that corresponds to a scenario where there is an increase in temperature but no change in pressure.

Answer

  1. To solve this, use Charles's Law: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \). Convert temperatures to Kelvin: \( T_1 = 25°C = 298.15 K \) and \( T_2 = 250°F = 394.26 K \). Solve for \( V_2 \):

    \( V_2 = V_1 \times \frac{T_2}{T_1} = 74,000,000 \times \frac{394.26}{298.15} \approx 97,800,000 \text{ L} \).

  2. Use Boyle's Law: \( P_1V_1 = P_2V_2 \). Convert 765 torr to atm: \( P_1 = \frac{765}{760} \approx 1.007 \text{ atm} \). Solve for \( P_2 \):

    \( P_2 = \frac{P_1V_1}{V_2} = \frac{1.007 \times 5.00}{3.00} \approx 1.678 \text{ atm} \).

  3. The balloon diagram that corresponds to an increase in temperature with no change in pressure is the one where the volume increases. This is typically represented by a larger balloon, so select the letter corresponding to the largest balloon.

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