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 \(\text{A}\left( \text{g} \right)\) 的轉化率是 \(x\)。根據指引，完成下表中的計算，並總結平衡常數 \({{K}_{\text{c}}}\) 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 \(\left( \text{mol} \right)\) |
\(-px\)
|
\(\displaystyle{-\frac{b}{a}px}\)
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\(\displaystyle{+\frac{c}{a}px}\)
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\(\displaystyle{+\frac{d}{a}px}\)
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||
| 平衡摩爾數 \(\left( \text{mol} \right)\) |
\(p\left( 1-x \right)\)
|
\(\displaystyle{q\ -\frac{b}{a}px}\)
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\(\displaystyle{\frac{c}{a}px}\)
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\(\displaystyle{\frac{d}{a}px}\)
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| 平衡濃度 \(\left( \text{mol}\ \text{d}{{\text{m}}^{-3}} \right)\) |
\(\displaystyle{\frac{p\left( 1-x \right)}{\text{V}}}\)
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\(\displaystyle{\frac{q\ -\ \displaystyle{\frac{b}{a}px}}{\text{V}}}\)
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\(\displaystyle{\frac{\displaystyle{\frac{c}{a}px}}{\text{V}}}\)
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\(\displaystyle{\frac{\displaystyle{\frac{d}{a}px}}{\text{V}}}\)
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| 平衡常數 |
\[\displaystyle{{{K}_{\text{c}}}\ =\ \frac{{{\left( \displaystyle{\frac{\displaystyle{\frac{c}{a}px}}{\text{V}}} \right)}^{c}}{{\left( \displaystyle{\frac{\displaystyle{\frac{d}{a}px}}{\text{V}}} \right)}^{d}}}{{{\left[ \displaystyle{\frac{p\left( 1-x \right)}{\text{V}}} \right]}^{a}}{{\left( \displaystyle{\frac{q-\displaystyle{\frac{b}{a}px}}{\text{V}}} \right)}^{b}}}}\]
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