Explanation

Step 1: Write the equilibrium constant expression.

For the reaction:

$$ X_2 + Y_2 \rightleftharpoons 2Z $$

$$ K_c = \frac{[Z]^2}{[X_2][Y_2]} $$

Step 2: Calculate the equilibrium constant using given equilibrium moles.

Since volume = 1 L, molarity = number of moles.

$$ [X_2] = 3,\quad [Y_2] = 3,\quad [Z] = 9 $$

$$ K_c = \frac{9^2}{3 \times 3} = \frac{81}{9} = 9 $$

Step 3: Add 10 mol of Z(g).

Immediately after addition:

$$ [X_2] = 3,\quad [Y_2] = 3,\quad [Z] = 19 $$

Step 4: Let the reaction shift backward by x mol to re-establish equilibrium.

Change in moles:

$$ X_2: +x,\quad Y_2: +x,\quad Z: -2x $$

New equilibrium moles:

$$ [X_2] = 3 + x $$

$$ [Y_2] = 3 + x $$

$$ [Z] = 19 - 2x $$

Step 5: Apply equilibrium constant again.

$$ K_c = \frac{(19 - 2x)^2}{(3 + x)(3 + x)} = 9 $$

Taking square root on both sides:

$$ \frac{19 - 2x}{3 + x} = 3 $$

$$ 19 - 2x = 9 + 3x $$

$$ 5x = 10 \Rightarrow x = 2 $$

Step 6: Calculate final moles of Z.

$$ Z = 19 - 2(2) = 15 $$

Hence, the number of moles of Z(g) at new equilibrium is 15.

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