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. 1.98 atm
• B. 4.56 atm
• C. 3.45 atm
• D. 6.72 atm

Answer: (D)

Verified step by step guidance

1. Start by identifying the initial and final conditions of the gas sample. The initial volume (V1) is 859 mL, the initial temperature (T1) is 565 K, and the initial pressure (P1) is 2.20 atm. The final volume (V2) is 268 mL, and the final temperature (T2) is 815 K. We need to find the final pressure (P2).
2. Use the combined gas law, which relates pressure, volume, and temperature: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \). This equation allows us to solve for the unknown pressure (P2) when the other variables are known.
3. Rearrange the combined gas law equation to solve for the final pressure (P2): \( P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} \). This formula will give us the final pressure once we substitute the known values.
4. Substitute the known values into the rearranged equation: \( P_2 = \frac{2.20 \text{ atm} \times 859 \text{ mL} \times 815 \text{ K}}{268 \text{ mL} \times 565 \text{ K}} \). Ensure that all units are consistent and correctly placed in the equation.
5. Calculate the expression to find the final pressure (P2). This involves multiplying and dividing the values as per the equation. The result will give you the final pressure in atm.