A sample of gas initially has a volume of 859 mL at 565 K and 2.20 atm. What pressure will the sample have if the volume changes to 268 mL while the temperature is increased to 815 K?

• A. 2.20 atm
• B. 7.89 atm
• C. 3.45 atm
• D. 5.67 atm

Answer: (D)

Verified step by step guidance

1. Identify the initial and final conditions of the gas: initial volume (V1) = 859 mL, initial temperature (T1) = 565 K, initial pressure (P1) = 2.20 atm, final volume (V2) = 268 mL, and final temperature (T2) = 815 K.
2. Use the combined gas law, which relates pressure, volume, and temperature: \( \frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2} \). This equation allows us to solve for the unknown final pressure (P2).
3. Rearrange the combined gas law to solve for the final pressure (P2): \( P2 = \frac{P1 \cdot V1 \cdot T2}{T1 \cdot V2} \).
4. Substitute the known values into the equation: \( P2 = \frac{2.20 \text{ atm} \cdot 859 \text{ mL} \cdot 815 \text{ K}}{565 \text{ K} \cdot 268 \text{ mL}} \).
5. Perform the calculations to find the final pressure (P2). Ensure that units are consistent and cancel appropriately, leaving the pressure in atm.