At a temperature of 57oC, a gas inside a 5.30 L metal canister has a pressure of 4000 torr. If the temperature is decreased to 13oC (at constant volume), what is the new pressure of the gas?
(P1/T1) = (P2/T2)
I know how to set the problem up but when I go to solve I get the wrong answer can you help me please?
I know how to set the problem up but when I go to solve I get the wrong answer can you help me please?.
To find the new pressure of the gas inside the canister when the temperature is decreased to 13oC, we can use the combined gas law. The combined gas law relates the initial and final conditions of pressure, volume, and temperature for a gas.
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 (what we want to find)
V2 = final volume (constant volume in this case)
T2 = final temperature (13oC in this case)
We are given the following values:
P1 = 4000 torr
V1 = 5.30 L
T1 = 57oC
T2 = 13oC
V2 = V1 (constant volume)
Let's substitute these values into the equation and solve for P2:
(4000 torr * 5.30 L) / (57 + 273.15 K) = (P2 * 5.30 L) / (13 + 273.15 K)
First, we need to convert the temperatures to Kelvin by adding 273.15 to each temperature:
T1 = 57oC + 273.15 = 330.15 K
T2 = 13oC + 273.15 = 286.15 K
Now we can substitute the values into the equation:
(4000 torr * 5.30 L) / 330.15 K = (P2 * 5.30 L) / 286.15 K
We can cross multiply and solve for P2:
(4000 torr * 5.30 L) * 286.15 K = 330.15 K * (P2 * 5.30 L)
(4000 torr * 5.30 L * 286.15 K) / (330.15 K * 5.30 L) = P2
Now calculate:
P2 = (4000 torr * 286.15 K) / 330.15 K
P2 ≈ 3467.52 torr
Therefore, the new pressure of the gas inside the canister at a temperature of 13oC and constant volume is approximately 3467.52 torr.