QuestionMay 23, 2025

The pressure inside a 4.85 L balloon at 44^circ C was 453. mmHg. What is the pressure inside the balloon when it is cooled to -45^circ C and expands to 9.65 Lin volume? Round your answer to 3 significant figures. square mmHg

The pressure inside a 4.85 L balloon at 44^circ C was 453. mmHg. What is the pressure inside the balloon when it is cooled to -45^circ C and expands to 9.65 Lin volume? Round your answer to 3 significant figures. square mmHg
The pressure inside a 4.85 L balloon at 44^circ C was 453. mmHg. What is the pressure inside the balloon when it is cooled to -45^circ C and expands to 9.65 Lin volume? Round your answer to 3 significant figures. square mmHg

Solution
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Answer

170 mmHg Explanation 1. Convert Temperatures to Kelvin T_1 = 44^{\circ}C + 273.15 = 317.15 \, K; T_2 = -45^{\circ}C + 273.15 = 228.15 \, K 2. Apply Combined Gas Law Use **\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}** to find P_2. 3. Solve for Final Pressure P_2 P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} = \frac{453 \, \text{mmHg} \times 4.85 \, L \times 228.15 \, K}{9.65 \, L \times 317.15 \, K} 4. Calculate P_2 = \frac{453 \times 4.85 \times 228.15}{9.65 \times 317.15} \approx 169.5 \, \text{mmHg}

Explanation

1. Convert Temperatures to Kelvin<br /> $T_1 = 44^{\circ}C + 273.15 = 317.15 \, K$; $T_2 = -45^{\circ}C + 273.15 = 228.15 \, K$<br /><br />2. Apply Combined Gas Law<br /> Use **$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$** to find $P_2$.<br /><br />3. Solve for Final Pressure $P_2$<br /> $P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} = \frac{453 \, \text{mmHg} \times 4.85 \, L \times 228.15 \, K}{9.65 \, L \times 317.15 \, K}$<br /><br />4. Calculate<br /> $P_2 = \frac{453 \times 4.85 \times 228.15}{9.65 \times 317.15} \approx 169.5 \, \text{mmHg}$
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