Multiple Choice
A 75.0 g sample of dinitrogen monoxide (N2O) is confined in a 4.12 L vessel. What is the pressure (in atm) at 205.0°F? Use the combined gas law equation and assume ideal gas behavior.
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7. Gases
Chemistry Gas Laws: Combined Gas Law
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If the pressure and the temperature of a gas are both decreased by 50%, what will happen to the volume of the gas according to the combined gas law (assuming the amount of gas remains constant)?
A
The volume will double.
B
The volume will increase by 50%.
C
The volume will decrease by 50%.
D
The volume will remain unchanged.
Verified step by step guidance1
Recall the combined gas law, which relates pressure (P), volume (V), and temperature (T) for a fixed amount of gas: \(\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}\).
Identify the initial and final conditions: both pressure and temperature decrease by 50%, so \(P_2 = 0.5 \times P_1\) and \(T_2 = 0.5 \times T_1\).
Substitute these values into the combined gas law equation: \(\frac{P_1 \times V_1}{T_1} = \frac{(0.5 \times P_1) \times V_2}{0.5 \times T_1}\).
Simplify the right side of the equation: \(\frac{(0.5 \times P_1) \times V_2}{0.5 \times T_1} = \frac{0.5 P_1 V_2}{0.5 T_1} = \frac{P_1 V_2}{T_1}\).
Since the left side equals the right side, it follows that \(V_1 = V_2\), meaning the volume remains unchanged.
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