A sample of an ideal gas at 2.0 atm and 300 K is compressed to half its original volume and cooled to 150 K. What is the final pressure of the gas?

• A. 1.0 atm
• B. 1.0 atm
• C. 2.0 atm
• D. 4.0 atm

Answer: (A)

Verified step by step guidance

1. Identify the known initial conditions: initial pressure \(P_1 = 2.0\) atm, initial temperature \(T_1 = 300\) K, and the volume is compressed to half its original volume, so \(V_2 = \frac{1}{2} V_1\). The final temperature is \(T_2 = 150\) K.
2. Recall the combined gas law which relates pressure, volume, and temperature for an ideal gas: \[P_1 \times V_1 \div T_1 = P_2 \times V_2 \div T_2\]
3. Substitute the known values into the combined gas law equation, keeping \(P_2\) as the unknown: \[2.0 \times V_1 \div 300 = P_2 \times \frac{1}{2} V_1 \div 150\]
4. Cancel out the common volume term \(V_1\) from both sides since it appears in numerator and denominator, simplifying the equation to: \[\frac{2.0}{300} = \frac{P_2}{2 \times 150}\]
5. Solve the resulting equation for \(P_2\) by cross-multiplying and isolating \(P_2\) to find the final pressure.