Consider the system: A (aq) rightarrow B (aq) at 259 K where Delta G degree_form

Question

Consider the system: A (aq) rightarrow B (aq) at 259 K where Delta G degree_form A = -18.1 kJ/mol and Delta G degree_form B = -13.7 kJ/mol. Calculate the concentration of B at equilibrium when 2.09 mol of A and 1.87 mol of B are mixed in water to form exactly one liter of solution. 0.09 m Remember, something is always gaining heat and something is always losing heat. Start by determining what is gaining and losing heat and then set the appropriate q = -q expression. For q_rxn, the chemical equation tells us q for one mol of salt. Do we have one mole of salt? Finally, remember that q = m c Delta T.

Explanation / Answer

given

G0rxn = G0products - G0reactant

G0rxn = -13.7 - (-18.1) = 4.4 KJ / mole

Also

G0rxn =-RTln Keq

4.4 X 10^3 = -8.314 X 259 X ln Keq

-2.04 = lnKeq

Keq = 0.13

Initial concentrations are

[A] = 2.09 moles / L

[B] = 1.87 moles / L

let change in concentration of [A] = -x

So the change in concentration of [B] = +x

Keq = (1.87+x) / (2.09-x)

0.13 X 2.09 - 0.13x = 1.87 + x

0.272 - 1.87 = 1.13 x

-1.143 = 1.13 x

x = -1.011

[B] at equilibrium = 1.87 - 1.011 = 0.859 M

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