Using the van der Waals equation, determine the pressure of 436.0g of SO2(g) in a 7.30-L vessel at 725k.?
For SO2(g), a=6.865L^2•atm/mol^2 and b=0.05679L/mol. (R=0.0821L•atm/(K•mol))
What's your problem. You substitute the numbers and turn the crank.
52.6 atm
To determine the pressure of the SO2(g) using the van der Waals equation, you need to substitute the given values into the equation and solve for P.
The van der Waals equation is given by:
[P + a(n/V)^2] * (V - nb) = nRT
Where:
P is the pressure
a is a constant for intermolecular attractions
n is the number of moles
V is the volume
b is a constant for molecular volume
R is the ideal gas constant
T is the temperature
Let's calculate step by step:
1. Convert the given mass of SO2(g) into moles using the molar mass of SO2.
Molar mass of SO2 = 32.06 g/mol (Sulfur: 32.06 g/mol, Oxygen: 16.00 g/mol × 2)
moles = mass / molar mass
moles = 436.0g / 32.06g/mol
2. Convert the given volume of the vessel into liters.
The volume of the vessel is already given as 7.30 L.
3. Substitute the known values into the van der Waals equation.
[P + a(n/V)^2] * (V - nb) = nRT
[P + (6.865 L^2•atm/mol^2) * (moles / V)^2] * (V - (0.05679 L/mol) * moles) = moles * (0.0821 L•atm/(K•mol)) * 725 K
Substitute the values from the given data:
[P + (6.865 L^2•atm/mol^2) * (moles / 7.30 L)^2] * (7.30 L - (0.05679 L/mol) * moles) = moles * (0.0821 L•atm/(K•mol)) * 725 K
4. Solve the equation for P.
Rearrange the equation to solve for P:
P = [moles * (0.0821 L•atm/(K•mol)) * 725 K - (6.865 L^2•atm/mol^2) * (moles / 7.3 L)^2] / [7.3 L - (0.05679 L/mol) * moles]
Substitute the calculated moles:
P = [(moles * (0.0821 L•atm/(K•mol)) * 725 K) - (6.865 L^2•atm/mol^2) * (436.0g / 32.06g/mol) / (7.3 L)^2] / [7.3 L - (0.05679 L/mol) * (436.0g / 32.06g/mol)]
5. Calculate P using a calculator.
Substitute the values and use the calculator to determine the final value for P.
Please note that the above calculations are for illustrative purposes, and you need to substitute the appropriate values and units into the equation to get the accurate result.