the initial temperature of a 1l sample of gas is 20c. The pressure is decreased from 720mmhg to 36mmhg and the volume increases to 2.14l. What was the final temperature of the gas?
To find the final temperature of the gas, we can use the combined gas law equation, which relates the initial and final conditions of pressure, volume, and temperature. The combined gas law equation is:
(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 = 720 mmHg
V1 = 1 L
T1 = 20 °C
P2 = 36 mmHg
V2 = 2.14 L
We need to convert the temperatures from Celsius to Kelvin since the gas law requires temperature to be in Kelvin. To convert Celsius to Kelvin, we use the formula T(K) = T(°C) + 273.15.
Converting the initial temperature from Celsius to Kelvin:
T1(K) = 20 °C + 273.15 = 293.15 K
Now, we can plug the values into the combined gas law equation:
(720 mmHg * 1 L) / 293.15 K = (36 mmHg * 2.14 L) / T2
To solve for T2, we can cross multiply and then divide:
(720 mmHg * 1 L * T2) = (36 mmHg * 2.14 L * 293.15 K)
Now, simplify the equation:
720 mmHg * 1 L * T2 = 36 mmHg * 2.14 L * 293.15 K
Divide both sides by (720 mmHg * 1 L):
T2 = (36 mmHg * 2.14 L * 293.15 K) / (720 mmHg * 1 L)
Now calculate T2:
T2 ≈ 22.1 °C (rounded to the nearest tenth)
Therefore, the final temperature of the gas is approximately 22.1 °C.