13) *A solution is prepared having these initial...

13) *A solution is prepared having these initial concentrations: ( left[mathrm{Fe}^{3+} ight]=left[mathrm{Hg}_{2}{ }^{2+} ight]=0.5000 ) ( mathrm{M} ;left[mathrm{Fe}^{2+} ight]=left[mathrm{Hg}^{2+} ight]=0.03000 mathrm{M} ). The following reaction occurs among the ions at 25 ( { }^{circ} mathrm{C} ). What will be the ion concentrations at equilibrium? (5P) [ egin{aligned} 2 mathrm{Fe}^{3+}(mathrm{aq})+mathrm{Hg}_{2}{ }^{2+}(mathrm{aq}) ightleftharpoons 2 mathrm{Fe}^{2+}(mathrm{aq}) & +2 mathrm{Hg}^{2+}(mathrm{aq}) \ K_{mathrm{c}} & =9.14 imes 10^{-6} end{aligned} ]

Transcript

00:01 They've given us the balanced chemical reaction from which we can write the k value.

00:06 The k value, kc, will be equal to the concentrations of the products raised to their coefficients divided by the concentrations of the reactants raised to their coefficients.

00:19 And they give us this numerical value as 9 .14 times 10 to the negative 6.

00:26 So if we start initially with 0 .5 of f3 +, and 0 .5 of hg2 2 +, and additionally 0 .03 of fe 2 +, and 0 .03 of hg 2+.

01:07 Because this value is so small, we shouldn't have hardly any reactant at equilibrium, i'm sorry, product at equilibrium.

01:17 We do have a fair amount.

01:19 We have about 1 tenth of what we started with, but with this being 10 to the negative 6, we should have much less than that.

01:27 So that means the reaction needs to shift to the left to establish equilibrium, increasing this by 2x, increasing this by x, and decreasing each of these by 2x.

01:41 So at equilibrium, the new concentrations will be 0 .500 plus 2x, 0 .500 plus x, 0 .3000 minus 2x, and 0 .300 minus 2x.

02:03 If we plug these expressions, equilibrium expressions, for each concentration into our kc expression, then we can solve for x.

02:15 Kc, which is 9 .14 times 10 to the negative 6, is going to be equal to 0 .0300 minus 2x squared multiplied by 0 .0300 minus 2x also squared.

02:43 Squared.

02:45 We then divide that by 0 .500 plus 2x squared and 0 .500 plus x...

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