Multiple Choice
Using the Ideal Gas Law, calculate the pressure in atmospheres if 0.00255 mol of gas occupies 413 mL at 138 °C. Assume R = 0.0821 L·atm/mol·K.
7. Gases
The Ideal Gas Law
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The gas is located in a closed container with a volume of 10.0 L at a pressure of 100,000.0 Pa and a temperature of 10.0°C. What would be the temperature of this gas in degrees Celsius if it was compressed to a new volume of 5.0 L and the pressure was decreased to 50,000.0 Pa?
A
25.0°C
B
-123.0°C
C
0.0°C
D
100.0°C
Verified step by step guidance1
Start by identifying the initial and final conditions of the gas. The initial volume \( V_1 \) is 10.0 L, the initial pressure \( P_1 \) is 100,000.0 Pa, and the initial temperature \( T_1 \) is 10.0°C. The final volume \( V_2 \) is 5.0 L, and the final pressure \( P_2 \) is 50,000.0 Pa. We need to find the final temperature \( T_2 \) in degrees Celsius.
Convert the initial temperature from degrees Celsius to Kelvin, as gas law calculations require temperatures in Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \). So, \( T_1 = 10.0 + 273.15 \).
Apply the combined gas law, which relates pressure, volume, and temperature: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \). Rearrange this equation to solve for \( T_2 \): \( T_2 = \frac{P_2 V_2 T_1}{P_1 V_1} \).
Substitute the known values into the rearranged equation: \( T_2 = \frac{50,000.0 \times 5.0 \times (10.0 + 273.15)}{100,000.0 \times 10.0} \).
After calculating \( T_2 \) in Kelvin, convert it back to degrees Celsius using the formula: \( T(°C) = T(K) - 273.15 \). This will give you the final temperature in degrees Celsius.
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