Chapter 12, Problem 12.108PAE

12.108 A nuclear engineer is considering the effect of discharging waste heat from a power plant into a lake and estimates that this may warm the water locally to 25 °C. One question to be considered is the effect of this temperature change on the uptake of CO₂ by the water. The equilibrium constant for the reaction ${\text{CO}}_2+{\text{H}}_{\text{2}}\text{O}\rightleftarrows {\text{H}}_{\text{2}}{\text{CO}}_3$ ; is $K=1.7\times {10}^{-3}$ at 25 °C. Because bonds form, the reaction is exothermic.

(a) Will this reaction progress further toward products at higher temperatures near the water discharge with its warmer water than it would in the cooler lake water? Explain your reasoning.

(b) Carbonic acid has a K_aof $2.5\times {10}^{-4}$ at 25 °C. What

is the equilibrium constant for the ${\text{CO}}_2+2{\text{H}}_{\text{2}}\text{O}\rightleftarrows {\text{HCO}}_3{}^{-}+{\text{H}}_3{\text{O}}^{+}?$

(c) What additional factor should the engineer be considering about CO₂ gas, probably before considering this reaction chemistry?