The pressure of a nitrogen gas, N2, cylinder is measured at 250 K and found to be 4.0 atm. What is the pressure of the same cylinder at room temperature, 293 K?
To solve this problem, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
Since we are looking for the final pressure at room temperature, we can write the equation as:
P1V1/T1 = P2V2/T2
Given:
P1 = 4.0 atm
V1 = unknown (since it does not change)
T1 = 250 K
P2 = unknown
V2 = unknown (since it does not change)
T2 = 293 K
We can rearrange the equation to solve for P2:
P2 = P1 * (T2 / T1)
Substitute the given values into the equation:
P2 = 4.0 atm * (293 K / 250 K)
P2 = 4.0 atm * 1.172
P2 = 4.688 atm
Therefore, the pressure of the same nitrogen gas cylinder at room temperature (293 K) would be 4.688 atm.