A 5.0 L sample of gas at 1.0 atm and 25 degrees Celsius is compressed to 0.05 L and 5.0 atm. What is the temperature at this new set of conditions?
(P1V1/T1) = (P2V2/T2)
T must be in kelvin.
149 K
To find the temperature at the new set of conditions, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Let's plug in the given values and solve for T2.
Given:
P1 = 1.0 atm (initial pressure)
V1 = 5.0 L (initial volume)
T1 = 25 degrees Celsius = 25 + 273 = 298 K (initial temperature)
P2 = 5.0 atm (final pressure)
V2 = 0.05 L (final volume)
T2 = ? (final temperature, what we need to find)
The equation becomes:
(1.0 atm * 5.0 L) / (298 K) = (5.0 atm * 0.05 L) / T2
Now, let's solve for T2:
(5.0 atm * 0.05 L) / T2 = (1.0 atm * 5.0 L) / (298 K)
To simplify the equation, we can cross multiply:
(5.0 atm * 0.05 L * 298 K) = (1.0 atm * 5.0 L * T2)
Now, divide both sides by (1.0 atm * 5.0 L):
(5.0 atm * 0.05 L * 298 K) / (1.0 atm * 5.0 L) = T2
Simplify the equation further:
(0.25 L atm K) / (1 L) = T2
Finally, convert the units to Kelvin:
T2 ≈ 0.25 K
Therefore, the temperature at the new set of conditions is approximately 0.25 Kelvin.