Using the van der Waals equation, calculate the pressure (in atmospheres) exerted by 91.14 g of Cl2 at 91.11 °C in a 1.00 L container. The van der Waals constants for Cl2 are a = 6.490 L2*atm/mol2 and b = 0.05620 L/mol.
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To calculate the pressure exerted by Cl2 using the van der Waals equation, we need to follow these steps:
Step 1: Convert the given mass of Cl2 to moles.
Use the molar mass of Cl2 to convert grams to moles.
Molar mass of Cl2 = 35.453 g/mol
91.14 g of Cl2 × (1 mol/35.453 g) = 2.5723 mol
Step 2: Convert the given temperature from °C to Kelvin.
The van der Waals equation requires temperature in Kelvin.
91.11 °C + 273.15 = 364.26 K
Step 3: Substitute the values into the van der Waals equation.
PV = nRT become (P + n^2a/V^2)(V-nb) = nRT
P = (nRT)/(V - nb) - (n^2a/V^2)
P = (2.5723 mol × 0.0821 L*atm/(mol*K) × 364.26 K) / (1.00 L - (2.5723 mol × 0.05620 L/mol)) - ((2.5723 mol)^2 × 6.490 L^2*atm/mol^2 / (1.00 L)^2)
Simplifying the above equation gives:
P = 3.584 atm (rounded to three decimal places)
Therefore, the pressure exerted by 91.14 g of Cl2 at 91.11 °C in a 1.00 L container is approximately 3.584 atm.