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Chapter 7: Problem 115

When one mole of sodium carbonate decahydrate (washing soda) is gently warmed, \(155.3 \mathrm{kJ}\) of heat is absorbed, water vapor is formed, and sodium carbonate heptahydrate remains. On more vigorous heating, the heptahydrate absorbs \(320.1 \mathrm{kJ}\) of heat and loses more water vapor to give the monohydrate. Continued heating gives the anhydrous salt (soda ash) while \(57.3 \mathrm{kJ}\) of heat is absorbed. Calculate \(\Delta H\) for the conversion of one mole of washing soda into soda ash. Estimate \(\Delta U\) for this process. Why is the value of \(\Delta U\) only an estimate?

Short Answer

Expert verified
The enthalpy change for the given process is \(532.7 \, \mathrm{kJ}\). The estimated internal energy change (\(\Delta U\)) is also \(532.7 \, \mathrm{kJ}\) based on the assumptions of constant pressure and small changes in volume. The value of \(\Delta U\) is only an estimate because precise values of pressure and \(\Delta V\) were not provided in the question.

Step by step solution

01

Calculate the total heat absorbed

We can find the total heat absorbed (\(\Delta H\)) by summing up the heat absorbed in each step. This gives us: \(\Delta H = 155.3 \, \mathrm{kJ} + 320.1 \, \mathrm{kJ} + 57.3 \, \mathrm{kJ} = 532.7 \, \mathrm{kJ}\).
02

Estimate the internal energy change

We can estimate the internal energy change (\(\Delta U\)) using the equation \(\Delta U = \Delta H - P\Delta V\). But since both the pressure (P) and the change in volume (\(\Delta V\)) are not given in the problem, we can make an assumption that the pressure is relatively constant and that the change in volume is relatively small due both to the conversion happening in the solid state and the process happening at constant pressure. Given these assumptions, \(\Delta U \approx \Delta H = 532.7 \, \mathrm{kJ}\).
03

Explain why \(\Delta U\) is only estimated

The value of \(\Delta U\) is only an estimate because we do not have precise information of the pressure and the change in volume for the process. The formula used is an approximation under assumptions of constant pressure and small changes in volume. These assumptions will not always hold true and thus the value of \(\Delta U\) calculated is only an estimate.

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Most popular questions from this chapter

Construct a concept map to show the use of enthalpy for chemical reactions.

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