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Chapter 12: Problem 17

Explain the difference between \(K, K_{\mathrm{p}},\) and \(Q\).

Short Answer

Expert verified
\(K\) is the equilibrium constant, which describes the relationship between the concentration of reactants and products in a chemical reaction at equilibrium. \(K_\mathrm{p}\) is the equilibrium constant for reactions involving gases, expressed in terms of partial pressures instead of concentrations. \(Q\) is the reaction quotient, calculated using the concentrations or partial pressures at any given point during the reaction and used to determine the reaction's direction when compared to the appropriate equilibrium constant (\(K\) or \(K_\mathrm{p}\)).

Step by step solution

01

What is K?

\(K\) is the equilibrium constant. It is a dimensionless quantity that describes the relationship between the concentration of reactants and products in a chemical reaction at equilibrium. The expression for the equilibrium constant, \(K\), can be written as: \[K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] where: - \([A]\), \([B]\), \([C]\), and \([D]\) represent the equilibrium concentration of species A, B, C, and D, respectively. - \(a\), \(b\), \(c\), and \(d\) represent the stoichiometric coefficients of the balanced chemical equation.
02

What is K_p?

\(K_\mathrm{p}\) is the equilibrium constant for a reaction involving gases, expressed in terms of partial pressures instead of concentrations. The expression for \(K_\mathrm{p}\) can be written as: \[K_\mathrm{p} = \frac{P_C^c P_D^d}{P_A^a P_B^b}\] where: - \(P_A\), \(P_B\), \(P_C\), and \(P_D\) represent the equilibrium partial pressure of the gaseous species A, B, C, and D, respectively. - \(a\), \(b\), \(c\), and \(d\) represent the stoichiometric coefficients of the balanced chemical equation. Note that for a reaction involving only gases, you can convert between \(K\) and \(K_\mathrm{p}\) using the following equation: \[K_\mathrm{p} = K(RT)^{\Delta n}\] where: - \(R\) is the ideal gas constant - \(T\) is the temperature in Kelvin - \(\Delta n\) is the change in the number of moles of gas in the reaction, given by \(\Delta n = (c + d) - (a + b)\).
03

What is Q?

Q is the reaction quotient, which is calculated similarly to the equilibrium constant but using the concentrations or partial pressures at any given point during the reaction (not necessarily at equilibrium). The equation for the reaction quotient can be written as: \[Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] if the species are in the solution, or \[Q = \frac{P_C^c P_D^d}{P_A^a P_B^b}\] if the species are in the gas phase. Comparing the value of \(Q\) to the value of the appropriate equilibrium constant (\(K\) or \(K_\mathrm{p}\)) can help determine the direction in which a reaction will proceed. Specifically: - If \(Q < K\) (or \(Q < K_\mathrm{p}\), if the reaction involves gases), the reaction will proceed in the forward direction, converting more reactants into products. - If \(Q > K\) (or \(Q > K_\mathrm{p}\)), the reaction will proceed in the reverse direction, converting more products into reactants. - If \(Q = K\) (or \(Q = K_\mathrm{p}\)), the system is at equilibrium, and there will be no net change in the concentrations or partial pressures of the species in the reaction.

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Key Concepts

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

Chemical Equilibrium
Chemical equilibrium refers to a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. At this point, a reaction has reached a stable balance, although both reactions continue to occur. It's crucial to understand that equilibrium does not mean the reactants and products are in equal concentrations, but rather that their concentrations have stabilized at a constant ratio.

This ratio is described by the equilibrium constant, denoted as \(K\), which provides insight into the proportions of reactants to products in the equilibrium state. The value of \(K\) is specific to each reaction and varies with temperature; it remains constant as long as temperature is constant. Knowing the equilibrium constant helps predict the extent of a reaction and gives us an idea of whether the equilibrium lies in favor of the reactants or the products.
Reaction Quotient (Q)
The reaction quotient, or \(Q\), is a measure that tells us how far a system is from equilibrium at any given moment during a reaction. It is calculated using the same formula as the equilibrium constant but with the current concentrations or partial pressures of the reacting species, rather than those at equilibrium.

The value of \(Q\) is used to predict the direction in which a reaction must shift to reach equilibrium. If \(Q < K\), this indicates that the reaction will proceed in the forward direction to produce more products. Conversely, if \(Q > K\), the reaction will move in the reverse direction to produce more reactants. When \(Q = K\), the system is at equilibrium, and there will be no further change in the composition of the reaction mixture.
Partial Pressure (Kp)
In gas-phase reactions, the equilibrium constant can be expressed in terms of partial pressures, known as \(K_\mathrm{p}\). The partial pressure of a gas is the pressure that the gas would exert if it alone occupied the entire volume of the mixture at a given temperature.

The relationship between \(K_\mathrm{p}\) and \(K\) involves the ideal gas constant \(R\) and temperature \(T\). The conversion factor \((RT)^{\Delta n}\) accounts for the change in the number of moles of gaseous reactants and products, known as \(\Delta n\). This factor stems from the ideal gas law, which relates pressure, volume, and temperature for a gas. For reactions involving both gases and solutions or when all reactants and products are in gaseous form, understanding \(K_\mathrm{p}\) is essential in predicting the behavior of the reaction under varying pressure conditions.
Equilibrium Concentration
Equilibrium concentration is the specific amount of reactants and products present when a chemical reaction is at equilibrium. Unlike initial concentrations, which can vary widely, equilibrium concentrations are fixed values when temperature remains constant and are directly related to the equilibrium constant \(K\).

To calculate equilibrium concentrations, a table commonly known as an ICE table (Initial, Change, Equilibrium) is often used. This involves setting up an expression for the equilibrium constant based on the balanced chemical equation and solving for the unknown concentrations. Understanding these concentrations allows chemists to accurately predict the outcomes of reactions and to design processes that optimize the yield of desired products.

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Most popular questions from this chapter

Given \(K=3.50\) at \(45^{\circ} \mathrm{C}\) for the reaction $$\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)$$ and \(K=7.10\) at \(45^{\circ} \mathrm{C}\) for the reaction $$2 \mathrm{A}(g)+\mathrm{D}(g) \rightleftharpoons \mathrm{C}(g)$$what is the value of \(K\) at the same temperature for the reaction $$ \mathrm{C}(g)+\mathrm{D}(g) \rightleftharpoons 2 \mathrm{B}(g)$$.What is the value of \(K_{\mathrm{p}}\) at \(45^{\circ} \mathrm{C}\) for the reaction? Starting with 1.50 atm partial pressures of both \(\mathrm{C}\) and \(\mathrm{D},\) what is the mole fraction of B once equilibrium is reached?

Which of the following statements is(are) true? Correct the false statement(s). a. When a reactant is added to a system at equilibrium at a given temperature, the reaction will shift right to reestablish equilibrium. b. When a product is added to a system at equilibrium at a given temperature, the value of \(K\) for the reaction will increase when equilibrium is reestablished. c. When temperature is increased for a reaction at equilibrium, the value of \(K\) for the reaction will increase. d. When the volume of a reaction container is increased for a system at equilibrium at a given temperature, the reaction will shift left to reestablish equilibrium. e. Addition of a catalyst (a substance that increases the speed of the reaction) has no effect on the equilibrium position.

At a particular temperature, \(K=1.00 \times 10^{2}\) for the reaction$$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$.In an experiment, 1.00 mole of \(\mathrm{H}_{2}, 1.00\) mole of \(\mathrm{I}_{2}\), and 1.00 mole of HI are introduced into a 1.00 -L container. Calculate the concentrations of all species when equilibrium is reached.

The following equilibrium pressures at a certain temperature were observed for the reaction $$\begin{aligned}2 \mathrm{NO}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \\\P_{\mathrm{NO}_{2}} &=0.55 \mathrm{atm} \\\P_{\mathrm{NO}} &=6.5 \times 10^{-5} \mathrm{atm} \\\P_{\mathrm{O}_{2}} &=4.5 \times 10^{-5} \mathrm{atm}\end{aligned}$$. Calculate the value for the equilibrium constant \(K_{\mathrm{p}}\) at this temperature.

A \(4.72-\mathrm{g}\) sample of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) was placed in an otherwise empty 1.00 -L flask and heated to \(250 .^{\circ} \mathrm{C}\) to vaporize the methanol. Over time, the methanol vapor decomposed by the \(10=\) following reaction:$$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$.After the system has reached equilibrium, a tiny hole is drilled in the side of the flask allowing gaseous compounds to effuse out of the flask. Measurements of the effusing gas show that it contains 33.0 times as much \(\mathrm{H}_{2}(g)\) as \(\mathrm{CH}_{3} \mathrm{OH}(g) .\) Calculate \(K\) for this reaction at \(250 .^{\circ} \mathrm{C}\).
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