In the laboratory, a general chemistry student measured the pH of a 0.486 M aqueous solution of triethanolamine, C6H15O3N to be 10.740. Use the information she obtained to determine the Kb for this base.

Kb = 6.22x10⁻⁷

Explanation:

Triethanolamine, C₆H₁₅O₃N, is in equilibrium with water:

C₆H₁₅O₃N(aq) + H₂O(l) ⇄ C₆H₁₅O₃NH⁺(aq) + OH⁻(aq)

Kb is defined from concentrations in equilibrium, thus:

Kb = [C₆H₁₅O₃NH⁺] [OH⁻] / [C₆H₁₅O₃N]

The equilibrium concentration of these compounds could be written as:

[C₆H₁₅O₃N] = 0.486M - X

[C₆H₁₅O₃NH⁺] = X

[OH⁻] = X

pH is -log [H⁺], thus, [H⁺] = 10^-pH = 1.820x10⁻¹¹M

Also, Kw = [OH⁻] ₓ [H⁺];

1x10⁻¹⁴ = [OH⁻] ₓ [H⁺]

1x10⁻¹⁴ = [OH⁻] ₓ [1.820x10⁻¹¹M]

5.495x10⁻⁴M = [OH⁻], that means X = 5.495x10⁻⁴M

Replacing in Kb formula:

Kb = [5.495x10⁻⁴M] [5.495x10⁻⁴M] / [0.486M-5.495x10⁻⁴M]

Kb = 6.22x10⁻⁷

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.