A gas has an initial volume of 24.6 L at a pressure of 1.90 atm and a temperature of 335 K. The pressure of the gas increases to 3.50 atm, and the volume of the gas increases to 31.3 L.
What is the final temperature of the gas?
143 K
231 K
485 K
785 K
We can use the combined gas law formula to solve this problem:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Plugging in the given values:
(1.90 atm * 24.6 L) / 335 K = (3.50 atm * 31.3 L) / T2
Simplifying the equation:
45.74 atm L / 335 K = 109.55 atm L / T2
Cross-multiplying and isolating T2:
45.74 atm L * T2 = 109.55 atm L * 335 K
15294.7 atm L K = 36689.25 atm L K
Dividing both sides by 45.74 atm L:
T2 = 36689.25 atm L K / 45.74 atm L
T2 ≈ 802.41 K
Rounding to the nearest whole number, the final temperature of the gas is 802 K. The closest option provided is 785 K.