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

Answer: (A)

Verified step by step guidance

1. 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.
2. Recall the combined gas law which relates pressure, volume, and temperature for a fixed amount of gas: \[\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}\]
3. Rearrange the combined gas law to solve for the final pressure \(P_2\): \[P_2 = \frac{P_1 \times V_1 \times T_2}{T_1 \times V_2}\]
4. Substitute the known values into the equation: \[P_2 = \frac{1\,atm \times 10\,L \times 250\,K}{273\,K \times 7\,L}\]
5. Calculate the expression to find the final pressure \(P_2\) in atm, which will give the pressure of the gas after compression and cooling.