4 The van der Waals equation of state was designed to predict the relationship b

Question

4 The van der Waals equation of state was designed to predict the relationship between pressure p, volume V and temperature T for gases better than the Ideal Gas Law: The van der Waals equation of state. R stands for the gas constant and n for the moles of gas pta- (V-nb) = nRT The van der Waals parameters a and b have to be determined for each gas by comparing to experimental data Consider the hypothetical gases X, Y and Z listed in the table below. Use the information provided to decide the relative size of the van der Waals parameters a and b heat of vaporization particle diameter gas kJ/mol size of a size of b (Choose one) (Choose one) (Choose one) (Choose one) (Choose one) (Choose one) 6.4 237 187 13.9 217 1 (lowest) 3 (highest)

Explanation / Answer

The van der Waals equation of state is given as (P + an2/V2) (V - nb) = RT

Where a is the measure internal pressure and b is the measure of effective volume

Basic facts: As the heat of vaporization increases, the internal pressure decreases.

As the particle diameter increases, the effective volume decreases due to high volume, where b is neglected.

According to the given data: Heats of vaporizations increase in the order: X < Y < Z

Hence, the decreasing order of van der Waals coefficient (a): X > Y > Z, i.e. the value of 'a' is the highest for the gas X, and it's the least for the gas Z.

Now, the particle diameters increase in the order: Y < Z < X

Hence, the decreasing order of van der Waals coefficient (b): Y > Z > X, i.e. the value of 'b' is the highest for the gas Y, and it's the least for the gas X.

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