A 38 L gas tank at 35 Celsius has nitrogen at a pressure of 4.65 atm. The contents of the tank are transferred without loss to an evacuated 55.0L tank in a cold room where the temperature is 4 Celsius. What is the pressure of the tank??
(P1V1)/T1 = (P2V2)/T2
Don't forget to change T to Kelvin.
p=2.89atm
To find the final pressure of the tank, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to convert the initial temperature of 35 Celsius to Kelvin:
T1 = 35 + 273.15 = 308.15 K
Next, we need to calculate the number of moles of nitrogen in the initial tank using the ideal gas law equation:
n1 = PV/RT
where P1 is the initial pressure, V1 is the initial volume, and R is the ideal gas constant.
Given:
P1 = 4.65 atm
V1 = 38 L
R = 0.0821 L·atm/(mol·K)
n1 = (4.65 atm * 38 L) / (0.0821 L·atm/(mol·K) * 308.15 K)
= 60.23 mol
Now, we can use the values of n1, V2, R, and T2 to calculate the final pressure, P2, in the empty tank:
V2 = 55.0 L
T2 = 4 + 273.15 = 277.15 K
P2 = (n1 * R * T2) / V2
P2 = (60.23 mol * 0.0821 L·atm/(mol·K) * 277.15 K) / 55.0 L
= 18.36 atm
Therefore, the pressure of the tank after the transfer is approximately 18.36 atm.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin for both the initial and final states.
Initial temperature (T1) = 35 Celsius + 273.15 = 308.15 K
Final temperature (T2) = 4 Celsius + 273.15 = 277.15 K
Now, let's solve for the number of moles (n) in the initial state using the ideal gas law equation:
P1V1 = nRT1
Since the volume (V1) is given as 38 L, the pressure (P1) is given as 4.65 atm, and the constant R is known, we can rearrange the equation to solve for n:
n = (P1V1) / (RT1)
n = (4.65 atm * 38 L) / (0.0821 L·atm/mol·K * 308.15 K)
n ≈ 0.7122 mol
Now that we know the initial number of moles (n), we can use the ideal gas law again to find the pressure (P2) in the final state:
P2V2 = nRT2
Since the volume (V2) is given as 55.0 L, the number of moles (n) is known from the initial state, and the constant R is the same, we can rearrange the equation to solve for P2:
P2 = (nRT2) / V2
P2 = (0.7122 mol * 0.0821 L·atm/mol·K * 277.15 K) / 55.0 L
P2 ≈ 1.952 atm
Therefore, the pressure of the 55.0L tank in the cold room is approximately 1.952 atm.