A 225 g sample of xenon is placed in a 15.6 L stainless steel vessel at 27.0°C.
a. What is the pressure in the vessel?
b. If the temperature is raised to 200°C, what is the pressure in the vessel?
c. The air pressure outside the vessel is 1.00 atm. If the vessel is opened to release the pressure to the air, what is the new pressure in the vessel?
a. use PV=nRT
b. either use PV=nRT again or
P1/T1=P2/T2
c. 1.00 atm
To answer these questions, we will 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
Step 1: Calculate the number of moles of xenon (Xe) using the molar mass of Xe (131.29 g/mol).
Given mass of Xe = 225 g
Number of moles (n) = mass / molar mass
n = 225 g / 131.29 g/mol
n = 1.71 mol (approx.)
a. To find the pressure in the vessel at 27.0°C:
Given:
V = 15.6 L
T = 27.0°C + 273.15 = 300.15 K
Step 2: Plug the values into the ideal gas law equation to find the pressure (P).
PV = nRT
P = nRT / V
P = (1.71 mol) * (0.0821 L · atm/(mol · K)) * (300.15 K) / 15.6 L
P = 8.35 atm (approx.)
b. To find the pressure in the vessel at 200°C:
Given:
V = 15.6 L
T = 200°C + 273.15 = 473.15 K
Step 2: Plug the values into the ideal gas law equation to find the pressure (P).
PV = nRT
P = nRT / V
P = (1.71 mol) * (0.0821 L · atm/(mol · K)) * (473.15 K) / 15.6 L
P = 25.5 atm (approx.)
c. When the vessel is opened to release the pressure to the air, the new pressure in the vessel will equalize with the air pressure outside. So the new pressure will be 1.00 atm.
To find the answers to these questions, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the container
n = Number of moles of gas
R = Gas constant (0.0821 L.atm/mol.K)
T = Temperature in Kelvin
To solve for the pressure (P), we will rearrange the equation to:
P = (nRT) / V
Now, let's solve each question step by step:
a. What is the pressure in the vessel?
First, we need to convert the temperature from Celsius to Kelvin.
T = 27.0°C + 273.15 = 300.15 K
Next, we need to convert the mass of xenon (given in grams) to moles.
molar mass of xenon (Xe) = 131.29 g/mol
n = mass / molar mass
n = 225 g / 131.29 g/mol = 1.714 mol
Now, plug in the values into the ideal gas law equation:
P = (nRT) / V
P = (1.714 mol * 0.0821 L.atm/mol.K * 300.15 K) / 15.6 L
P ≈ 8.47 atm
Therefore, the pressure in the vessel is approximately 8.47 atm.
b. If the temperature is raised to 200°C, what is the pressure in the vessel?
Again, we convert the temperature to Kelvin.
T = 200°C + 273.15 = 473.15 K
Now we can calculate the pressure using the ideal gas law equation:
P = (nRT) / V
P = (1.714 mol * 0.0821 L.atm/mol.K * 473.15 K) / 15.6 L
P ≈ 28.09 atm
Therefore, the pressure in the vessel is approximately 28.09 atm.
c. The air pressure outside the vessel is 1.00 atm. If the vessel is opened to release the pressure to the air, what is the new pressure in the vessel?
If the vessel is opened and the pressure is released, the pressure inside the vessel will equalize with the pressure outside the vessel, which is 1.00 atm.
Therefore, the new pressure in the vessel, after release, will be 1.00 atm.