Calculating the Equilibrium Constant, \(K\) for a System The graphing calculator can run a program that calculates \(K\) for a system, given the concentrations of the products and the concentrations of the reactants. Given the balanced chemical equation $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightarrow 2 \mathrm{HI}(g)$$ and the equilibrium mixture at \(425^{\circ} \mathrm{C},\) you can calculate the equilibrium constant for the system. Then you can use the program to make calculations. Go to Appendix \(\mathbf{C}\) If you are using a TI- \(-83\) Plus, you can download the program CONSTANT and data and run the application as directed. If you are using another calculator, your teacher will provide you with key- strokes and data sets to use. After you have graphed the data, answer the questions below. a. What is the equilibrium constant given the following equilibrium concentrations: 0.012840 \(\mathrm{mol} / \mathrm{L}\) of \(\mathrm{H}_{2}, 0.006437 \mathrm{mol} / \mathrm{L}\) of \(\mathrm{I}_{2},\) and 0.066807 \(\mathrm{mol} / \mathrm{L}\) of \(\mathrm{HI}\) ? b. What is the equilibrium constant given the following equilibrium concentrations: 0.000105 \(\mathrm{mol} / \mathrm{L}\) of \(\mathrm{H}_{2}, 0.000107 \mathrm{mol} / \mathrm{L}\) of \(\mathrm{I}_{2},\) and 0.000779 \(\mathrm{mol} / \mathrm{L}\) of \(\mathrm{HI}\) ? c. What is the equilibrium constant given the following equilibrium concentrations: 0.000527 \(\mathrm{mol} / \mathrm{L}\) of \(\mathrm{H}_{2}, 0.000496 \mathrm{mol} / \mathrm{L}\) of \(\mathrm{I}_{2},\) and 0.003757 \(\mathrm{mol} / \mathrm{L}\) of HI?

Step by step solution

01

Understand the Law of Mass Action

The law of mass action states that the ratio of the concentrations of the products to the reactants, raised to their stoichiometric coefficients, at equilibrium is a constant (the equilibrium constant, \(K\)). This is represented as \(K = \dfrac{[Products]}{[Reactants]}\) in a general sense.

02

Calculate \(K\) for case a

Given the balanced chemical equation \(H_{2} + I_{2} \rightarrow 2HI\), and the equilibrium concentrations of \(H_{2}\) and \(I_{2}\) to be 0.012840, 0.006437 and of \(HI\) to be 0.066807 respectively, we can calculate \(K = \dfrac{[HI]^{2}}{[H_{2}][I_{2}]}\) \n Thus, \(K = \dfrac{(0.066807)^{2}}{0.012840 \times 0.006437} = 68.48\)

03

Calculate \(K\) for case b

Given the equilibrium concentrations of \(H_{2}\) and \(I_{2}\) to be 0.000105, 0.000107 and of \(HI\) to be 0.000779 respectively, we can calculate \(K = \dfrac{[HI]^{2}}{[H_{2}][I_{2}]}\) \n Thus, \(K = \dfrac{(0.000779)^{2}}{0.000105 \times 0.000107} = 57.41\)

04

Calculate \(K\) for case c

Given the equilibrium concentrations of \(H_{2}\) and \(I_{2}\) to be 0.000527, 0.000496 and of \(HI\) to be 0.003757 respectively, we can calculate \(K = \dfrac{[HI]^{2}}{[H_{2}][I_{2}]}\) \n Thus, \(K = \dfrac{(0.003757)^{2}}{0.000527 \times 0.000496} = 53.72\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Law of Mass Action

The Law of Mass Action is a foundational principle in chemical equilibrium, one that reveals how the concentrations of reactants and products influence the state of a reaction. At its core, it asserts that at a constant temperature, the rate at which a reaction proceeds is determined by the concentrations of the reacting substances, each raised to the power of its stoichiometric coefficient.
For the reaction \[aA + bB \leftrightarrow cC + dD\], the equilibrium constant ( \(K\)) can be expressed mathematically as: \[ K = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}} \]
Here, \([A]\) and \([B]\) denote the molar concentrations of reactants, while \([C]\) and \([D]\) represent the concentrations of the products. The exponents \(a\), \(b\), \(c\), and \(d\) correspond to the stoichiometric coefficients from the balanced chemical equation. This law is critical in chemistry because it allows for the prediction of the direction of the reaction and the calculation of the equilibrium concentrations of reactants and products.

Chemical Equilibrium

Chemical Equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to an unchanging, or dynamic, system. When equilibrium is achieved, the concentrations of the reactants and products remain constant over time, but not necessarily equal. This state is essential in understanding how reactions behave under different conditions and is often visualized with a double arrow (\(\leftrightarrow\)) in chemical equations to indicate that the forward and reverse reactions are ongoing.
Although the system is in a state of balance, it is not static. The forward and reverse reactions continue to happen but do so at an equal rate, meaning there is no net change in the concentrations of either reactants or products. At this point, the ratio of these concentrations will always remain constant and is denoted as the equilibrium constant, \(K\), for a given reaction at a specific temperature.
The process of reaching equilibrium can be influenced by factors such as temperature, pressure, and concentration changes, and can also be predicted and manipulated using Le Chatelier's principle. Understanding equilibrium is not only crucial for grasping how reactions occur but also for applications in industry, where reaching and maintaining a specific equilibrium state can be essential to the desired production output.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is rooted in the conservation of mass and the concept of the mole, a unit that facilitates the comparison of amounts of different substances. Stoichiometry is the tool that allows chemists to predict the quantities of substances consumed and produced in a given reaction.
By using the balanced chemical equation, one can determine the proportion of molecules involved. For example, in the reaction between hydrogen gas (\(H_{2}\)) and iodine (\(I_{2}\)), which produces hydrogen iodide (\(HI\)), the balanced equation \(H_{2} + I_{2} \rightarrow 2HI\) communicates that one mole of \(H_{2}\) reacts with one mole of \(I_{2}\) to form two moles of \(HI\). These ratios are the foundation of stoichiometric calculations and are directly applied when determining the equilibrium constant. As seen in the exercise provided, using these stoichiometric relationships, you can perform calculations to find the equilibrium constant, ensuring a deep understanding of how much product can be formed from given amounts of reactants in a chemical equilibrium scenario.
Stoichiometry also extends to include the calculation of theoretical yields, limiting reagents, and percent yield, making it a comprehensive approach to quantitative analysis in chemistry.