Question

A cylinder with a moveable piston contains 198 mL of nitrogen gas at a pressure of 1.22 atm and a temperature of 302 K. What must the final volume be for the pressure of the gas to be 1.52 atm at a temperature of 370 K?

A) 200 mL
B) 196 mL
C) 194 mL
D) 195 mL

Answer 1

To find the final volume for the pressure of gas to be 1.52 atm at 370 K, the combined gas law is used. By solving the equation with the given initial conditions, the final volume is determined to be approximately 196 mL.

Step-by-step explanation:

To determine the final volume of nitrogen gas at a different pressure and temperature, we can use the combined gas law, which is written as:

P1 × V1 / T1 = P2 × V2 / T2

Where P1 and V1 are the initial pressure and volume, T1 is the initial temperature, P2 and V2 are the final pressure and volume, and T2 is the final temperature. Inserting the values given in the problem:

(1.22 atm) × (198 mL) / (302 K) = (1.52 atm) × V2 / (370 K)

We can solve for V2, the final volume:

V2 = (1.22 atm × 198 mL × 370 K) / (1.52 atm × 302 K)

V2 ≈ 196 mL

So the final volume of nitrogen gas should be approximately 196 mL to maintain the conditions specified in the problem.