Question

At ${25}^{o}C$, for the reaction $2A\left(aq\right)\to B\left(aq\right)+C\left(aq\right),$ the equilibrium constant is 1.95. If the concentration of B(aq) was 0.368 M and the concentration of C(aq) was 0.488 M, what would be the minimum concentration of A(aq) necessary in order to make this reaction spontaneous under these conditions?

• A. Greater than 0.303 M
• B. Greater than0.092 M
• C. (a) and (b) above.
• D. None of the above

Answer 1

The correct option is A Greater than 0.303 M

To predict whether a reaction will be spontaneous or not, the reaction quotient (Q) must be less than the Keq. The Q of the reaction is the ratio of the concentrations of the product and the reactants. The formula for Q is the same for Keq. The only difference is that for Q, the actual concentrations of the reactants and products are used.
First, we can determine the concentration of A at equilibtium where Q = Keq. This is solved as follows:
$Keq=\frac{\left[B\right]\left[C\right]}{[A{]}^2}$
$1.95=\frac{\left(0.368M\right)\left(0.488M\right)}{[A{]}^2}$
$[A{]}^2=\frac{0.180M^2}{1.95}$
$[A{]}^2=0.092M^2$
$[A{]}^{=}0.303M$
At this concentration, the reaction is in equilibrium. For it to be spontaneous, Q should be less than Keq and that would happen when the concentration of A is greater than 0.303 M.