The pressure of a sample of an inert gas reduced significantly from 100 kPa to 30kPa. The temperature increases from 27degreeC to 93degreeC. If the initial volume is 20 L, what is the final volume?
55 L
54.5 L
81 L
96 L
Assuming the amount of gas remains constant (i.e. no gas is added or removed), we can use the combined gas law to solve for the final volume:
(P1V1)/T1 = (P2V2)/T2
where P1 = initial pressure, V1 = initial volume, T1 = initial temperature, P2 = final pressure, V2 = final volume, and T2 = final temperature.
Plugging in the given values and solving for V2:
(100 kPa)(20 L)/(300 K) = (30 kPa)(V2)/(366 K)
V2 = (100 kPa)(20 L)(366 K)/(30 kPa)(300 K)
V2 ≈ 54.5 L
Therefore, the final volume is approximately 54.5 L. The answer is B.
To find the final volume of the gas, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure of the gas = 100 kPa
V1 = initial volume of the gas = 20 L
T1 = initial temperature of the gas = 27 degrees Celsius + 273.15 (converting to Kelvin) = 300.15 K
P2 = final pressure of the gas = 30 kPa
T2 = final temperature of the gas = 93 degrees Celsius + 273.15 (converting to Kelvin) = 366.15 K
Now, we can substitute these values into the equation and solve for V2 (final volume):
(100 kPa * 20 L) / (300.15 K) = (30 kPa * V2) / (366.15 K)
Simplifying the equation:
2000 kPa*L / 300.15 K = 30 kPa * V2 / 366.15 K
Cross multiplying:
(2000 kPa * 366.15 K) / (300.15 K) = 30 kPa * V2
Dividing both sides by 30 kPa:
V2 = (2000 kPa * 366.15 K) / (30 kPa * 300.15 K)
Simplifying:
V2 = (732300 kPa*K) / (9004.5 kPa*K)
V2 ≈ 81.29 L
Therefore, the final volume is approximately 81 L.