2P(s) + 3Cl2(g) --> 4PCl3(l)
What is the vapor pressure of PCl3 at 298K? Show Calculations.
To determine the vapor pressure of PCl3 at 298K, you can use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvin)
In this case, we want to find the pressure (P), so we rearrange the equation to solve for P:
P = (nRT) / V
To use this equation, we need to know the moles of PCl3 and the volume of the gas. However, since in the given reaction the liquid PCl3 is produced, we need to consider only the vapor pressure of the liquid.
Given that the chemical equation is balanced as 2P(s) + 3Cl2(g) -> 4PCl3(l), we know that the balanced stoichiometry relates the moles of Cl2 to moles of PCl3 in a 1:4 ratio. Therefore, we can assume that the number of moles of PCl3 is (3/2) times the number of moles of Cl2.
Next, we need to find the volume (V) of the gas. The volume of the gas can be approximated as the volume of the container, given that the vapor pressure is usually measured under conditions where the gas is in equilibrium with its liquid phase.
Assuming the container volume is 1 liter, we can substitute the values into the equation:
P = ((3/2) * nRT) / 1
Now, let's calculate the vapor pressure of PCl3 at 298K.
Step 1: Calculate the number of moles of Cl2.
Since we don't know the amount of Cl2, we cannot directly determine the number of moles. However, if we know the initial and final amounts of Cl2 in the reaction, we can determine the moles used:
Initial moles of Cl2 = 3 moles (given)
Step 2: Calculate moles of PCl3.
Moles of PCl3 = (3/2) * (moles of Cl2 used)
= (3/2) * 3
= 4.5 moles
Step 3: Calculate the vapor pressure using the ideal gas law.
P = ((3/2) * nRT) / V
= ((3/2) * 4.5 * 0.0821 * 298) / 1
≈ 184.6 atm
Therefore, the vapor pressure of PCl3 at 298K is approximately 184.6 atm.