對於任意可逆反應：
\[a\text{A}\left( \text{g} \right)\ +\ b\text{B}\left( \text{g} \right)\ \rightleftharpoons \ c\text{C}\left( \text{g} \right)\ +\ d\text{D}\left( \text{g} \right)\]在一定溫度下，向體積為 \(\text{V}\ \text{d}{{\text{m}}^{\text{3}}}\) 的密閉容器內通入 \(p\ \text{mol}\ \text{A}\left( \text{g} \right)\) 和 \(q\ \text{mol}\ \text{B}\left( \text{g} \right)\)。達至平衡後，測得生成物 \(\text{C}\left( \text{g} \right)\) 的摩爾數是 \(y\ \text{mol}\)。根據指引推演在此條件下，該反應的平衡常數 \({{K}_{\text{c}}}\) 的表達式。
| \(a\text{A}\left( \text{g} \right)\ + \) | \( b\text{B}\left( \text{g} \right)\ \) | \(\rightleftharpoons \) | \( c\text{C}\left( \text{g} \right)\ + \) | \( d\text{D}\left( \text{g} \right)\) | ||
|---|---|---|---|---|---|---|
| 起始摩爾數 \(\left( \text{mol} \right)\) | \(p\) | \(q\) | \(0\) | \(0\) | ||
| 摩爾數改變 \(\left( \text{mol} \right)\) |
\(\displaystyle{-\frac{a}{c}y}\)
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\(\displaystyle{-\frac{b}{c}y}\)
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\(+y\)
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\(\displaystyle{+\frac{d}{c}y}\)
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| 平衡摩爾數 \(\left( \text{mol} \right)\) |
\(\displaystyle{p\ -\frac{a}{c}y}\)
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\(\displaystyle{q\ -\frac{b}{c}y}\)
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\(y\)
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\(\displaystyle{\frac{d}{c}y}\)
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| 平衡濃度 \(\left( \text{mol}\ \text{d}{{\text{m}}^{-3}} \right)\) |
\(\displaystyle{\frac{p\ -\ \displaystyle{\frac{a}{c}y}}{\text{V}}}\)
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\(\displaystyle{\frac{q\ -\ \displaystyle{\frac{b}{c}y}}{\text{V}}}\)
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\(\displaystyle{\frac{y}{\text{V}}}\)
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\(\displaystyle{\frac{\displaystyle{\frac{d}{c}y}}{\text{V}}}\)
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| 平衡常數 |
\[\displaystyle{{{K}_{\text{c}}}\ =\ \frac{{{\left( \displaystyle{\frac{y}{\text{V}}} \right)}^{c}}{{\left( \displaystyle{\frac{\displaystyle{\frac{d}{c}y}}{\text{V}}} \right)}^{d}}}{{{\left( \displaystyle{\frac{p\ -\ \displaystyle{\frac{a}{c}y}}{\text{V}}} \right)}^{a}}{{\left( \displaystyle{\frac{q\ -\ \displaystyle{\frac{b}{c}y}}{\text{V}}} \right)}^{b}}}}\]
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