The volume of a gas increases from 18.7 m3 to 25.1 m3 while the pressure changes from 1.82 atm to 1.41 atm. If the initial temperature is 353 K, the final temperature of the gas is K.

To find the final temperature of the gas, we can use the combined gas law, which relates the initial and final states of a gas sample.

The combined gas law can be defined as:
(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

Given:
P1 = 1.82 atm
V1 = 18.7 m^3
T1 = 353 K
P2 = 1.41 atm
V2 = 25.1 m^3
T2 = unknown (to be found)

Substituting the given values into the combined gas law equation, we have:
(1.82 atm * 18.7 m^3) / 353 K = (1.41 atm * 25.1 m^3) / T2

To isolate T2, we can cross-multiply and then divide:
(1.82 atm * 18.7 m^3 * T2) = (1.41 atm * 25.1 m^3 * 353 K)

Now, we solve for T2:
T2 = (1.41 atm * 25.1 m^3 * 353 K) / (1.82 atm * 18.7 m^3)

Using a calculator, we can find the value of T2:
T2 ≈ 455.12 K

Therefore, the final temperature of the gas is approximately 455.12 K.

Since PV=kT, PV/T is constant. So, you want T where

(1.41)(25.1)/T = (1.82)(18.7)/353