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The following molecular scenes depict the aqueous reaction
Chapter 17, Problem 27P(choose chapter or problem)
The following molecular scenes depict the aqueous reaction \(2 \mathrm{D} \rightleftharpoons \mathrm{E}\), with \(\mathrm{D}\) red and \(\mathrm{E}\) blue. Each sphere represents \(0.0100 \mathrm{~mol}\), but the volume in scene \(A\) is \(1.00 \mathrm{~L}\), whereas in scenes \(B\) and \(\mathrm{C}\), it is \(0.500 \mathrm{~L}\).
(a) If the reaction in scene \(\mathrm{A}\) is at equilibrium, calculate \(K_{\mathrm{c}}\).
(b) Are the reactions in scenes \(B\) and \(C\) at equilibrium? Which, if either, is not, and in which direction will it proceed?
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QUESTION:
The following molecular scenes depict the aqueous reaction \(2 \mathrm{D} \rightleftharpoons \mathrm{E}\), with \(\mathrm{D}\) red and \(\mathrm{E}\) blue. Each sphere represents \(0.0100 \mathrm{~mol}\), but the volume in scene \(A\) is \(1.00 \mathrm{~L}\), whereas in scenes \(B\) and \(\mathrm{C}\), it is \(0.500 \mathrm{~L}\).
(a) If the reaction in scene \(\mathrm{A}\) is at equilibrium, calculate \(K_{\mathrm{c}}\).
(b) Are the reactions in scenes \(B\) and \(C\) at equilibrium? Which, if either, is not, and in which direction will it proceed?
ANSWER:Step 1 of 3
Here, we are going to calculate the KC for the given reaction.
Given that
The reaction is as follows:
\(\text{2D}\rightleftharpoons E\) —- (1)
Total No. of red spheres (D) in A vessel = 3
Total No. of blue spheres (E) in A vessel = 3
Concentration of each ball = 0.0100 mol
Therefore, the concentration of D is
\([D]=3\ \text{spheres}\times\frac{0.01\ \text{mol}}{1.0\ \text{sphere}}\times\frac{1}{1.0\ \text{Liter}}\)
\(= 0.03\ \text{mol/L} = 0.03\ \text{M}\)
Similarly, the concentration of E is
\([E] = 3\ \text{spheres}\times \frac{0.01\ \text{mol}}{1.0\ \text{sphere}}\times\frac{1}{1.0\ \text{Liter}}\)
\(= 0.03\ \text{mol/L} = 0.03\ \text{M}\)
We know that, the equilibrium constant is defined as
\(K_c=\frac{[E]}{[D]^2}\) —- (2)
\(\Rightarrow K_c=\frac{(0.03)}{(0.03)^2}\)
\(\Rightarrow K_c=33.33\)
Therefore, the \(K_c\) when the reaction in scene A is at equilibrium, is 33.33.
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