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Chapter 6: Problem 20

Calculate the work done in joules when 1.0 mole of water vaporizes at 1.0 atm and \(100^{\circ} \mathrm{C}\). Assume that the volume of liquid water is negligible compared with that of steam at \(100^{\circ} \mathrm{C}\), and ideal gas behavior.

Short Answer

Expert verified
The work done, when 1 mole of water is vaporized at 1.0 atm and \(100^{\circ} \mathrm{C}\), is approximately -3.0 x \(10^{3}\) J.

Step by step solution

01

Find the volume of 1 mole of steam

First, use the ideal gas law to find the volume of 1 mole of steam at the boiling point of water. Using ideal gas law \(PV=nRT\), with \(P=1.0 atm\), \(n=1.0 mol\), \(R=0.0821 L atm/K mol\), \(T=373 \mathrm{K}\), one can calculate volume \(V\).
02

Calculate the Work

After finding the volume of steam after vaporization, calculate the work done. As stated before, work done during expansion of gas against an external pressure is \(W_{\text{gas}} = -P_{\text{ext}}dV\). Here \(P_{\text{ext}}\) is 1.0 atm and \(dV\) is the volume of 1 mol of water vapor. Remember that the work is negative as the system does work on the surroundings.
03

Conversion of the Work to Joules

The work calculated in the previous step will be in liters-atm. One must convert this to Joules by using the conversion factor 101.3 J = 1 L atm. Multiply the calculated work in liters-atm by 101.3 to get the work in Joules.

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Most popular questions from this chapter

Describe how chemists use Hess's law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

State Hess's law. Explain, with one example, the usefulness of Hess's law in thermochemistry.

(a) A snowmaking machine contains a mixture of compressed air and water vapor at about 20 atm. When the mixture is sprayed into the atmosphere it expands so rapidly that, as a good approximation, no heat exchange occurs between the system (air and water) and its surroundings. (In thermodynamics, such a process is called an adiabatic process.) Do a first law of thermodynamics analysis to show how snow is formed under these conditions. (b) If you have ever pumped air into a bicycle tire, you probably noticed a warming effect at the valve stem. The action of the pump compresses the air inside the pump and the tire. The process is rapid enough to be treated as an adiabatic process. Apply the first law of thermodynamics to account for the warming effect. (c) A driver's manual states that the stopping distance quadruples as the speed doubles; that is, if it takes \(30 \mathrm{ft}\) to stop a car traveling at \(25 \mathrm{mph}\) then it would take \(120 \mathrm{ft}\) to stop a car moving at 50 mph. Justify this statement by using the first law of thermodynamics. Assume that when a car is stopped, its kinetic energy \(\left(\frac{1}{2} m u^{2}\right)\) is totally converted to heat.

Consider the following data: $$ \begin{array}{lcc} \text { Metal } & \text { Al } & \text { Cu } \\ \hline \text { Mass (g) } & 10 & 30 \\ \text { Specific heat }\left(\mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) & 0.900 & 0.385 \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & 40 & 60 \end{array} $$ When these two metals are placed in contact, which of the following will take place? (a) Heat will flow from Al to Cu because Al has a larger specific heat. (b) Heat will flow from Cu to Al because Cu has a larger mass. (c) Heat will flow from Cu to Al because Cu has a larger heat capacity. (d) Heat will flow from Cu to Al because Cu is at a higher temperature. (e) No heat will flow in either direction.

Predict the value of \(\Delta H_{\mathrm{f}}^{\circ}\) (greater than, less than, or equal to zero) for these elements at \(25^{\circ} \mathrm{C}\) : (a) \(\mathrm{Br}_{2}(g)\) and \(\mathrm{Br}_{2}(l)\) (b) \(\mathrm{I}_{2}(g)\) and \(\mathrm{I}_{2}(s)\)
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