Multiple Choice
Using the ideal gas law, what is the temperature in degrees Celsius of 5.20 moles of gas in a 40.0 L container at a pressure of 4.50 atm?
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7. Gases
The Ideal Gas Law Applications
Multiple Choice
If 10 L of O_2 at 273 K and 1 atm is compressed to a 7 L container at 250 K, what will be the final pressure of the gas (in atm), assuming ideal gas behavior?
A
1.56 atm
B
0.70 atm
C
2.00 atm
D
1.00 atm
Verified step by step guidance1
Identify the known variables: initial volume \(V_1 = 10\,L\), initial temperature \(T_1 = 273\,K\), initial pressure \(P_1 = 1\,atm\), final volume \(V_2 = 7\,L\), and final temperature \(T_2 = 250\,K\). The final pressure \(P_2\) is unknown.
Recall the combined gas law which relates pressure, volume, and temperature for a fixed amount of gas:
\[\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}\]
Rearrange the combined gas law to solve for the final pressure \(P_2\):
\[P_2 = \frac{P_1 \times V_1 \times T_2}{T_1 \times V_2}\]
Substitute the known values into the equation:
\[P_2 = \frac{1\,atm \times 10\,L \times 250\,K}{273\,K \times 7\,L}\]
Calculate the expression to find the final pressure \(P_2\) in atm, which will give the pressure of the gas after compression and cooling.
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