The compound CH3F has van der Waals constants a = 5.009 atm•L2
/mol
2
and b = 0.0562 L/mol.
Using both the ideal gas law and van der Waals’s equation, calculate the pressure expected for 25 mol of
CH3F gas in a 5.00-L container at 75 °C.
no idea how to even start this one...
Of course you do. Look in your text, find the van der waals equation, substitute the numbers and solve for P.
Then in a separate calculate, use PV = nRT and calculate P.
Post your work if you get stuck. This just some algebra to go through.
To solve this problem, we can use both the ideal gas law and van der Waals equation to calculate the expected pressure for 25 mol of CH3F gas in a 5.00-L container at 75 °C.
First, let's start by using the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = gas constant (0.0821 L•atm/(mol•K))
T = temperature in Kelvin (75 °C = 75 + 273 = 348 K)
Substituting the given values, we have:
P * 5.00 L = 25 mol * 0.0821 L•atm/(mol•K) * 348 K
Simplifying the equation:
P * 5.00 L = 711.15 L•atm
Solving for P:
P = 711.15 L•atm / 5.00 L
P ≈ 142.23 atm
Now, let's use van der Waals equation to calculate the corrected pressure:
(P + a * (n/V)²) * (V - nb) = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = gas constant (0.0821 L•atm/(mol•K))
T = temperature in Kelvin (75 °C = 75 + 273 = 348 K)
a = van der Waals constant for attraction (5.009 atm•L²/mol²)
b = van der Waals constant for volume correction (0.0562 L/mol)
Substituting the given values, we have:
(P + 5.009 atm•L²/mol² * (25 mol / 5.00 L)²) * (5.00 L - 0.0562 L/mol * 25 mol) = 25 mol * 0.0821 L•atm/(mol•K) * 348 K
Simplifying the equation:
(P + 5.009 atm•L²/mol² * 25²/5.00²) * (5.00 L - 0.0562 L/mol * 25 mol) = 711.15 L•atm
Solving for P:
P + 5.009 atm•L²/mol² * 25²/5.00² * (5.00 L - 0.0562 L/mol * 25 mol) = 711.15 L•atm
P + 5.009 atm•L²/mol² * 25²/5.00² * (5.00 L - 0.0562 L/mol * 25 mol) = 711.15 L•atm
P ≈ 139.44 atm
Therefore, using both the ideal gas law and van der Waals equation, the pressure expected for 25 mol of CH3F gas in a 5.00-L container at 75 °C is approximately 139.44 atm.