1. Given reaction and equilibrium constant

For the reaction $A + B \rightleftharpoons C + D$ we have $K_c = 100$

At the start: $[A]_0 = [B]_0 = [C]_0 = [D]_0 = 1\,\text{M}$

We need the equilibrium concentration of $D$.

2. Check the reaction quotient initially

The initial reaction quotient is $Q_c = \frac{[C][D]}{[A][B]} = \frac{(1)(1)}{(1)(1)} = 1$

Since $Q_c < K_c$ that is, $1 < 100$ so the reaction will proceed in the forward direction.

3. Let the forward change be $x$

Then at equilibrium:

$[A] = 1 - x$ $[B] = 1 - x$ $[C] = 1 + x$ $[D] = 1 + x$

Using the equilibrium constant expression: $K_c = \frac{[C][D]}{[A][B]} = \frac{(1+x)(1+x)}{(1-x)(1-x)} = 100$

So, $\left(\frac{1+x}{1-x}\right)^2 = 100$

Taking positive square root: $\frac{1+x}{1-x} = 10$

4. Solve for $x$

$1 + x = 10(1 - x)$ $1 + x = 10 - 10x$ $11x = 9$ $x = \frac{9}{11}$

Thus, $[D]_{eq} = 1 + x = 1 + \frac{9}{11} = \frac{20}{11}$

So, $[D]_{eq} = 1.81818\ldots\,\text{M}$

5. Express in the required form

We need $[D]_{eq} = \underline{\hspace{2cm}} \times 10^{-2}\,\text{M}$

Now, $1.81818\,\text{M} = 181.818\times 10^{-2}\,\text{M}$

Nearest integer $= 182$.

6. Comparison with stored answer

Our derived answer is 182, which matches the stored correct answer.