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Answer :
Carbon dioxide gas (880 g) at 100 °C occupies 35.6 dm3 at 3.8 x 104 mmHg pressure, thevalue of the pressure (atm) using Van der Waals equation is A) 16.47
To calculate the pressure (in atm) using the Van der Waals equation, we need to use the formula: (P + a(n/V)^2) (V - nb) = nRT
Given:
Mass of carbon dioxide gas (m) = 880 g
Temperature (T) = 100 °C = 373 K
Volume (V) = 35.6 dm^3
Pressure (P) = 3.8 x 10^4 mmHg = 5.03 atm (converted)
Van der Waals constants:
a = 3.61 L^2 atm mol^(-2)
b = 0.0428 L mol^(-1)
First, we need to convert the mass of carbon dioxide to moles using the molar mass of CO2 (44 g/mol): n = m / M = 880 g / 44 g/mol = 20 mol
Next, substitute the values into the equation and solve for P: (5.03 atm) + (3.61 L^2 atm mol^(-2) * (20 mol / 35.6 dm^3)^2) * (35.6 dm^3 - (0.0428 L mol^(-1) * 20 mol)) = 20 mol * (0.0821 L atm K^(-1) mol^(-1)) * 373 K
Simplifying the equation gives: 5.03 + (3.61 * (20 / 35.6)^2) * (35.6 - (0.0428 * 20)) = 20 * (0.0821 * 373)
Calculating the left side of the equation: 5.03 + (3.61 * (0.561)^2) * (35.6 - 0.856) = 20 * 30.824
Simplifying further gives: 5.03 + (3.61 * 0.314) * 34.744 = 616.48
Solving for P gives: P = (616.48 - (3.61 * 0.314 * 34.744)) / 34.744 = 16.47 atm
Therefore, the calculated value of the pressure (in atm) using the Van der Waals equation is A. 16.47.
Learn more about Van der Waals at:
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