Name: equilibrium concentrations from an ice table
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 5 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

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Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating Equilibrium Concentrations

Nieznane stężenia równowagowe można wyznaczyć na podstawie początkowego stężenia reagentów i stałej równowagi K dla reakcji.
Rozważmy reakcję, w której 0,30 molowego azotu i 0,40 molowego tlenu gazowego reagują, tworząc gazowy tlenek azotu i gdzie K wynosi 0,10. Aby obliczyć stężenia równowagowe, znane wartości są zestawione w tabeli ICE.
W przypadku zmiany stężenia, wzrost lub spadek odpowiednio dla każdego produktu lub reagenta jest oznaczony przez x razy jego współczynnik stechiometryczny. Suma lub różnica służy do znalezienia stężeń równowagi, które są następnie podstawiane do wyrażenia równowagi.
Aby rozwiązać dla x, wyrażenie jest rozwijane, a wszystkie terminy są umieszczane po jednej stronie, aby przekształcić je w postać: ax2 + bx + c. Równanie to można rozwiązać za pomocą wzoru kwadratowego.
Rozwiązywanie daje dwie wartości dla x: 0,047 i −0,065. Ponieważ ujemne stężenie substancji jest niemożliwe, wartość może zostać odrzucona.
Używając 0,047 dla x, stężenia równowagowe azotu, tlenu i tlenku azotu wynoszą odpowiednio 0,25, 0,35 i 0,094 mola.
Idealny warunek kwadratowy to jedna z sytuacji, w której można użyć skrótu, aby uniknąć formuły kwadratowej.
Na przykład, jeśli początkowe stężenia azotu i tlenu w powyższej reakcji wynosiły po 0,30 mola, równanie staje się idealnym kwadratem. W takich przypadkach równanie można uprościć, biorąc pierwiastek kwadratowy z obu stron, aby rozwiązać x.

<ol>
	<li>Lim, Kieran F. "Korzystanie z kalkulatorów graficznych i arkuszy kalkulacyjnych w chemii: rozwiązywanie problemów równowagi." Journal of Chemical Education 85, nr 10 (2008): 1347. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed085p1347">https://pubs.acs.org/doi/pdf/10.1021/ed085p1347</a></li>
</ol>

obliczanie stężeń równowagowych

Możliwość obliczenia stężeń równowagowych jest niezbędna w wielu obszarach nauki i technologii — na przykład przy formułowaniu i dozowaniu produktów farmaceutycznych. Po spożyciu lub wstrzyknięciu leku zwykle zachodzi kilka reakcji chemicznych, które wpływają na jego ostateczne stężenie w danym układzie organizmu. Aby obliczyć wielkość dawki, która zapewni pożądany efekt terapeutyczny, wymagana jest znajomość równowagi ilości substancji.

Bardziej wymagającym rodzajem obliczenia równowagi może być taki, w którym stężenia równowagowe wyprowadza się ze stężeń początkowych i stałej równowagi. W przypadku tych obliczeń zazwyczaj przydatne jest podejście składające się z czterech etapów:

<ol>
	<li>Określenie kierunku, w którym reakcja będzie przebiegać, aż do osiągnięcia równowagi.</li>
	<li>Opracowanie tabeli ICE.</li>
	<li>Obliczenie zmiany stężeń, a następnie stężenia równowagowego.</li>
	<li>Potwierdzenie obliczonych stężeń równowagowych.</li>
</ol>

Obliczenie stężeń równowagowych

W pewnych warunkach stała równowagi Kc rozkładu PCl5(g) na PCl3(g) i Cl2(g) wynosi 0,0211. Powyższą procedurę można zastosować do określenia stężeń równowagowych PCl5, PCl3 i Cl2 w mieszaninie, która początkowo zawierała tylko PCl5 w stężeniu 1,00 M.

Krok 1. Określenie kierunku przebiegu reakcji.

Zbilansowane równanie rozkładu PCl5 to:

<img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />

Ponieważ początkowo obecny jest tylko reagent, Qc = 0, a reakcja będzie przebiegać w prawo.

Krok 2. Opracowanie tabeli ICE.

<div class="overflow">
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;">     PCl5 (g)     </td>
			<td style="color: black; border: 1px solid black; text-align: center;">  PCl3 (g)   </td>
			<td style="color: black; border: 1px solid black; text-align: center;">  Cl2 (g)  </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Stężenie początkowe (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Zmień (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">−x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Stężenie równowagowe (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 − x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
		</tr>
	</tbody>
</table>
</div>

Krok 3. Obliczenie zmianęy i stężenia równowagowego.

Podstawienie stężeń równowagowych do równania stałej równowagi daje

<img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />

Równanie w postaci ax2 + bx + c = 0 można przekształcić tak, aby obliczyć x:

<img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />

W tym przypadku a = 1, b = 0,0211 i c = −0,0211. Podstawiając odpowiednie wartości a, b i c otrzymujemy:

<img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />

Zatem dwa pierwiastki kwadratu to:

<img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />

W tym scenariuszu tylko pierwiastek dodatni ma znaczenie fizyczne (stężenia są albo zerowe, albo dodatnie), a więc x = 0,135 M. Stężenia równowagowe to

<img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />

Krok 4. Potwierdzenie obliczonych stężeń równowagowych.

Podstawienie do wyrażenia Kc (w celu sprawdzenia obliczenia) daje

<img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />

Stała równowagi obliczona ze stężeń równowagowych jest równa podanej w zadaniu wartości Kc (po zaokrągleniu do odpowiedniej liczby cyfr znaczących).

Obliczanie stężeń równowagowych

Umiejętność obliczania stężeń równowagowych jest niezbędna w wielu dziedzinach nauki i techniki - na przykład w formułowaniu i dozowaniu ...

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Kluczowe terminy i pojęcia

equilibrium concentrations from an ice table

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic effect.

A common approach is needed when equilibrium concentrations must be derived from starting values and a known Kc. The first step is to decide which way the reaction will move to reach equilibrium. Next, an ICE table is set up. ICE stands for initial, change, and equilibrium. After that, the concentration changes are solved and used to find the equilibrium concentrations. The final step is to check the answer.

The decomposition of PCl5(g) into PCl3(g) and Cl2(g) shows how this works. In the example, Kc is 0.0211, and the mixture starts with only PCl5 at 1.00 M. Because only the reactant is present at the start, Qc equals 0, so the reaction moves to the right. The ICE table gives an initial concentration of 1.00 M for PCl5 and 0 for the products, with changes of -x, +x, and +x.

Substituting the equilibrium values into the Kc expression leads to a quadratic equation. Solving it gives two roots, but only the positive root is physically meaningful because concentrations cannot be negative. In this case, x = 0.135 M. The equilibrium concentrations are then found for PCl5, PCl3, and Cl2. A final substitution into the Kc expression confirms that the calculated value matches the given equilibrium constant when rounded correctly.

Equilibrium Concentrations from an ICE Table

equilibrium-concentrations-from-an-ice-table

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Chemical Equilibrium and Kc Rules

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calculating equilibrium concentrations

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic...

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Estimating Equilibrium with Small Changes

A small equilibrium constant can make equilibrium calculations easier. In these reactions, the equilibrium position favors the reactants. When the initial reactant concentration is high and the Kc value is small, the change in concentration may be negligible. In that case, the equilibrium concentration is close to the initial concentration. This idea helps simplify weak acid and weak base problems. Chemists can assume that some equilibrium concentrations are equal to the initial concentrations.

key terms and concepts

Learn how to find equilibrium concentrations with an ICE table, use Kc, and check answers with a PCl5 decomposition example for high school chemistry.

Equilibrium Concentrations from an ICE Table | JoVE K12

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Equilibrium Concentrations from an ICE Table

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