To find the final volume, we can use the combined gas law equation. Rearranging the equation, we plug in the values and solve for V2. The final volume of the gas is approximately 122.06 L.
To solve this problem, we can use the combined gas law which states that for a given amount of gas, the ratio of pressure to temperature is constant when the volume is held constant. The formula is:
P1/T1 = P2/T2
Given:
P1 = 1.22 atm (initial pressure)
T1 = 302 K (initial temperature)
P2 = 1.52 atm (final pressure)
T2 = 370 K (final temperature)
V1 = 198 mL (initial volume)
V2 = ? (final volume)
We can rearrange the formula to solve for V2:
V2 = (P2 * V1 * T1) / (P1 * T2)
Plugging in the values:
V2 = (1.52 atm * 198 mL * 302 K) / (1.22 atm * 370 K)
V2 = 122059.02 mL
Converting mL to L:
V2 = 122.06 L
So, the final volume of the gas must be approximately 122.06 L for the pressure of the gas to be 1.52 atm at a temperature of 370 K.