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Chapter 15: Problem 19

Can the equilibrium constant ever be a negative number? Explain.

Short Answer

Expert verified
The equilibrium constant (K) can never be a negative number because it represents the ratio of positive concentrations of products to positive concentrations of reactants, with positive stoichiometric coefficients as powers. This implies that K will always be a positive number or equal to 1 when the concentrations of products and reactants are equal at equilibrium.

Step by step solution

01

Definition of the Equilibrium Constant

The equilibrium constant (K) is a measure of the extent of a reversible chemical reaction when it reaches a state of equilibrium. It is the ratio of the concentrations of products to the concentrations of reactants, each raised to the power of their respective stoichiometric coefficients. The equilibrium constant only depends on the temperature of the system.
02

Formula of the Equilibrium Constant

The equilibrium constant is expressed using the following formula: \[ K = \frac{[\text{Products}]}{[\text{Reactants}]} \] Here, the brackets represent the concentrations of products and reactants at equilibrium, and the stoichiometric coefficients are used as powers. Remember that gases and aqueous solutions are included in the equilibrium constant expression, while pure solids and pure liquids are not.
03

Sign of the Equilibrium Constant

The concentrations of products and reactants in the equilibrium constant expression are always expressed in positive values, usually as molar concentrations or partial pressures. Since we are taking the ratio of positive values with positive stoichiometric coefficients as powers, the equilibrium constant will always be a positive number. It can also be equal to 1, which indicates that the concentrations of products and reactants are equal at equilibrium.
04

Conclusion

The equilibrium constant can never be a negative number because it is the ratio of positive concentrations of products to positive concentrations of reactants, with positive stoichiometric coefficients as powers.

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Key Concepts

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

Chemical Equilibrium
Chemical equilibrium is a crucial concept in understanding reversible reactions. It represents the state in a chemical system where the concentrations of reactants and products remain constant over time, despite ongoing activity at the molecular level. This happens because the forward and reverse reactions occur at equal rates. Thus, there is no net change in the concentration of reactants and products.

- **Dynamic Nature:** Unlike static equilibrium, chemical equilibrium is dynamic, meaning that reactions continue to occur, but there is no observable change in the overall composition.
- **Dependence on Temperature:** The position of equilibrium and the equilibrium constant are influenced only by changes in temperature. When the temperature changes, the equilibrium will shift to accommodate this change as described by Le Chatelier's Principle.
- **No Temporal Change:** At equilibrium, the concentrations of reactants and products do not necessarily mean they are equal; rather, they remain consistent over time.

Understanding how chemical equilibrium is achieved and maintained is fundamental in predicting how different conditions affect reaction rates and equilibrium positions.
Reversible Reactions
Reversible reactions are those chemical reactions where products can revert to the original reactants. This two-way process is represented by a double-headed arrow (鈬�) in chemical equations.

- **Bidirectional Nature:** In these reactions, product formation and reactant formation are possible concurrently, transforming the reactants into products and vice versa.
- **Equilibrium Achievement:** Once the rate of the forward reaction equals the rate of the reverse reaction, the system is at equilibrium. At this point, the quantities of reactants and products cease changing, highlighting the dynamic nature of reversible reactions.

These reactions are widespread and crucial in both natural processes and industrial applications. They offer a deeper understanding of how concentration changes impact the direction and extent of reactions.
Stoichiometry
Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It is essential for calculating exactly how much product will form from given quantities of reactants.

- **Balanced Equations:** A key stoichiometric principle is that chemical equations must be balanced to reflect the conservation of mass. Each element must have the same number of atoms on both the reactant and product sides.
- **Mole Ratios:** Stoichiometric coefficients in balanced chemical equations give the ratio of moles of reactants to moles of products. These ratios are used to determine how much of one reactant is needed to react with a given amount of another reactant, or how much product will be produced.
- **Applications:** Stoichiometry is used extensively in laboratory settings to prepare solutions with precise concentrations, and in industrial processes where reaction yields must be optimized.

Understanding stoichiometry is vital for predicting reaction outcomes and for efficiently designing chemical processes.

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Most popular questions from this chapter

The following graph represents the yield of the compound \(\mathrm{AB}\) at equilibrium in the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g)\) at two different pressures, \(x\) and \(y\), as a function of temperature. (a) Is this reaction exothermic or endothermic? (b) Is \(P=x\) greater or smaller than $P=y ?

A mixture of \(0.10 \mathrm{~mol}\) of \(\mathrm{NO}, 0.050 \mathrm{~mol}\) of \(\mathrm{H}_{2},\) and \(0.10 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) is placed in a \(1.0-\mathrm{L}\) vessel at \(300 \mathrm{~K}\). The following equilibrium is established: $$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ At equilibrium \([\mathrm{NO}]=0.062 \mathrm{M}\). (a) Calculate the equilibrium concentrations of \(\mathrm{H}_{2}, \mathrm{~N}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\). (b) Calculate \(K_{c}\)

How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant (b) removal of a product, (c) decrease in the volume, (d) decrease in the temperature, (e) addition of a catalyst?

Which of the following reactions lies to the right, favoring the formation of products, and which lies to the left, favoring formation of reactants? (a) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) ; K_{p}=5.0 \times 10^{12}\) (b) \(2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) ; K_{c}=5.8 \times 10^{-18}\)

Consider the following equilibrium between oxides of nitrogen $$3 \mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g)$$ (a) Use data in Appendix \(\mathrm{C}\) to calculate \(\Delta H^{\circ}\) for this reaction. (b) Will the equilibrium constant for the reaction increase or decrease with increasing temperature? Explain. (c) At constant temperature, would a change in the volume of the container affect the fraction of products in the equilibrium mixture?
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