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[OUTPUT]

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system
Calculate the volumetric fraction $X$ in a mixture after the reaction.

In an aqueous solution of $\mathrm{NH}_{4} \mathrm{OH}$ dissociates into ions:

$$
\mathrm{NH}_{4} \mathrm{OH} \leftrightarrow \mathrm{NH}_{4}^{+}+\mathrm{OH}^{-}
$$

The degree of ionization $\alpha$ is calculated as:

$$
\alpha = \frac{\mathrm{C}_{\text {ion}}}{\mathrm{C}_{\text {total}}}
$$

Substituting the numerical values:

$$
1.33 \cdot 10^{-2} = \frac{\mathrm{C}_{\text{ion}}}{0.1}, \quad\left[\mathrm{OH}^{-}\right] = \mathrm{C}_{\text{ion}} = 1.33 \cdot 10^{-3} \text{ (mol/L)}
$$

Substitute into the expression for $K_{\text {ion}}$:

$$
K_{\text {ion}} = \frac{\left[\mathrm{NH}^{4+}\right] \cdot \left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_{4} \mathrm{OH}\right]}
$$

$$
K_{\text {ion}} = \frac{1.33 \cdot 10^{-3} \cdot 1.33 \cdot 10^{-3}}{0.1} = 1.76 \cdot 10^{-5}
$$

Present the answer in LaTex format: \boxed{Your answer}
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