Temperature Change on Adiabatic Mixing of an Acid and Water

Three moles of water and one mole of sulfuric acid, each at 0°C, are mixed adiabatically. Use the data in Fig. 8.1-1 and the information in Illustration 8.1-1 to estimate the final temperature of the mixture.

Question

Temperature Change on Adiabatic Mixing of an Acid and Water

Three moles of water and one mole of sulfuric acid, each at 0°C, are mixed adiabatically. Use the data in Fig. 8.1-1 and the information in Illustration 8.1-1 to estimate the final temperature of the mixture.

Accepted Answer

From the closed-system mass balance, we have

[latex]M^{f}=M_{ H _{2} O }+M_{ H _{2} SO _{4}}=3 imes 18.015+1 imes 98.078=152.12 g[/latex]

and from the energy balance, we have

[latex]U^{f}=H^{f}=H^{i}=M^{f} \hat{H}_{ mix }=M_{ H _{2} O } \hat{H}_{ H _{2} O }+M_{ H _{2} SO _{4}} \hat{H}_{ H _{2} SO _{4}}=3 imes 0+1 imes 0=0 kJ[/latex]

Thus finally we have a mixture of 64.5 wt % sulfuric acid that has an enthalpy of 0 kJ/kg. (Note that we have used the fact that for liquids and solids at low pressure, the internal energy and enthalpy are essentially equal.) From Fig. 8.1-1 we see that a mixture containing 64.5 wt % sulfuric acid has an enthalpy of 0 kJ/kg at about 150°C. Therefore, if water and sulfuric acid are adiabatically mixed in the ratio of 3:1, the mixture will achieve a temperature of 150°C, which is just below the boiling point of the mixture. This large temperature rise, and the fact that the mixture is just below its boiling point, makes mixing sulfuric acid and water an operation that must be done with extreme care.

Comment

If instead of starting with refrigerated sulfuric acid and water (at 0°C), one started with these components at 21.2°C and mixed them adiabatically, the resulting 3:1 mixture would be in the liquid + vapor region; that is, the mixture would boil (and splatter). Also note that because of the shape of the curves on the enthalpy-concentration diagram, adding sulfuric acid to water adiabatically (i.e., moving to the right from the pure water edge of the diagram) results in a more gradual temperature rise than adding water to sulfuric acid (i.e., moving to the left from the pure–sulfuric acid edge). Therefore, whenever possible, sulfuric acid should be added to water, and not vice versa.

Question 8.4.1: Temperature Change on Adiabatic Mixing of an Acid and Water ...

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