au The internal pressure of a gas, π = av), is a measure of intermolecular forces, because it indicates a change in internal energy as the molecules get closer or further apart, without temperature changing. au = a Calculate the change in internal Vm 2. T i) Using the van der Waals equation of state, T = energy, AU, when 1.5 mols of acetone (a 1 = 16 l²atm/mol²), expands from 2 liters to 5 liters at a constant temperature. ii) Would this change in internal energy be greater or smaller for an ideal gas? Why?

Chemistry: The Molecular Science
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Chapter4: Energy And Chemical Reactions
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The internal pressure of a gas, \( \pi_T = \left(\frac{\partial U}{\partial V}\right)_T \), is a measure of intermolecular forces, because it indicates a change in internal energy as the molecules get closer or further apart, without temperature changing.

i) Using the van der Waals equation of state, \( \pi_T = \left(\frac{\partial U}{\partial V}\right)_T = a \frac{1}{V_m^2} \). Calculate the change in internal energy, \( \Delta U \), when 1.5 mols of acetone (a = 16 \( l^2 \, atm / mol^2 \)), expands from 2 liters to 5 liters at a constant temperature.

ii) Would this change in internal energy be greater or smaller for an ideal gas? Why?
Transcribed Image Text:The internal pressure of a gas, \( \pi_T = \left(\frac{\partial U}{\partial V}\right)_T \), is a measure of intermolecular forces, because it indicates a change in internal energy as the molecules get closer or further apart, without temperature changing. i) Using the van der Waals equation of state, \( \pi_T = \left(\frac{\partial U}{\partial V}\right)_T = a \frac{1}{V_m^2} \). Calculate the change in internal energy, \( \Delta U \), when 1.5 mols of acetone (a = 16 \( l^2 \, atm / mol^2 \)), expands from 2 liters to 5 liters at a constant temperature. ii) Would this change in internal energy be greater or smaller for an ideal gas? Why?
Expert Solution
Step 1

The internal pressure of a gas is expressed as:

πT=(UV)T

For a real gas or van der Waals gas, the internal pressure is supposed to have the following expression:

πT=aVm2

In order to find the total internal energy change during a particular range of volume change, we need to integrate the expression.

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