Chapter 8, Problem 8.107P

One g-mole of pure liquid sulfuric acid at temperature T₀(°C) is mixed with r g-moles of liquid water, also at temperature T₀(°C), in an adiabatic container. The final solution temperature is T_s(°C). The heat capacities of the pure acid, pure water, and the product solution [J/(g·°C)] are C_pk, C_pw, and C_ps, respectively, all of which may be taken to be independent of temperature.

1. Without doing any calculations, sketch the plot of T_sversus r you would expect to obtain for r varying between 0 and oo. (Hint: Think first about what you would expect T_sto be at the extreme values of r.)
Use an energy balance to derive an expression for T _sin terms of the initial acid and water temperatures, the heat capacities, the water/acid mole ratio (r), and the heat of mixing, $\Delta {\hat{H}}_m\left(r,25°C\right)\left(kJ/mol{H}_{2}S{O}_4\right)$

A series of 1.00 mol samples of pure liquid sulfuric acid are added to 11 insulated flasks containing varying amounts of water. The quantities of water in the flasks and the mass heat capacities of the product solutions are tabulated below:

r (mol H2O)	0.5	1.0	1.5	2.0	3.0	4.0	5.0	10.0	25.0	50.0	100.0
Cp[J/(g·°C)]	1.58	1.85	1.89	1.94	2.10	2.27	2.43	3.03	3.56	3.84	4.00

The heat capacities of pure sulfuric acid and pure water may be determined from the molar heat capacities in Table B.2 evaluated at 25°C. All heat capacities should be taken to be independent of temperature.

Unfortunately, the laboratory air conditioner has been out of order for three weeks (Physical Plant promises they will get to it any day now) and the temperature on the July afternoon of the experiment (which also equals the initial acid and water temperatures) is an uncomfortable 40°C. Prepare a spreadsheet to generate a table and then a plot of T_s. the final temperature in each flask, versus r. the water/acid mole ratio of the solution in the flask. (Suggestion: Make the r axis logarithmic.) Assume that mixing is adiabatic.

The actual experimental plot of T, versus r would lie below the one determined in Part (c). Why?