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Chapter 14: Problem 21

Nitrogen oxides play important roles in air pollution. Write expressions for \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) for the following reactions involving nitrogen oxides. a. \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)\) b. \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g)\) c. \(2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\)

Short Answer

Expert verified
Question: Write the expressions for the equilibrium constants \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) for the following reactions involving nitrogen oxides: a. \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)\) b. \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g)\) c. \(2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\) Answer: a. \(K_{\mathrm{c}} = \frac{[\mathrm{N}_{2}\mathrm{O}_{4}]}{[\mathrm{N}_{2}][\mathrm{O}_{2}]^2}\) and \(K_{\mathrm{p}} = \frac{P_{\mathrm{N}_{2}\mathrm{O}_{4}}}{P_{\mathrm{N}_{2}}P_{\mathrm{O}_{2}}^2}\) b. \(K_{\mathrm{c}} = \frac{[\mathrm{NO}_{2}][\mathrm{N}_{2}\mathrm{O}]}{[\mathrm{NO}]^3}\) and \(K_{\mathrm{p}} = \frac{P_{\mathrm{NO}_{2}}P_{\mathrm{N}_{2}\mathrm{O}}}{P_{\mathrm{NO}}^3}\) c. \(K_{\mathrm{c}} = \frac{[\mathrm{N}_{2}]^2[\mathrm{O}_{2}]}{[\mathrm{N}_{2}\mathrm{O}]^2}\) and \(K_{\mathrm{p}} = \frac{P_{\mathrm{N}_{2}}^2P_{\mathrm{O}_{2}}}{P_{\mathrm{N}_{2}\mathrm{O}}^2}\)

Step by step solution

01

Calculate expression for \(K_{\mathrm{c}}\)

The equilibrium constant, \(K_{\mathrm{c}}\), is defined as: \(K_{\mathrm{c}} = \frac{[\mathrm{N}_{2}\mathrm{O}_{4}]}{[\mathrm{N}_{2}][\mathrm{O}_{2}]^2}\)
02

Calculate expression for \(K_{\mathrm{p}}\)

The equilibrium constant, \(K_{\mathrm{p}}\), is defined as: \(K_{\mathrm{p}} = \frac{P_{\mathrm{N}_{2}\mathrm{O}_{4}}}{P_{\mathrm{N}_{2}}P_{\mathrm{O}_{2}}^2}\) #Reaction b.# 2. Nitrogen oxide reaction The reaction is \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g)\).
03

Calculate expression for \(K_{\mathrm{c}}\)

The equilibrium constant, \(K_{\mathrm{c}}\), is defined as: \(K_{\mathrm{c}} = \frac{[\mathrm{NO}_{2}][\mathrm{N}_{2}\mathrm{O}]}{[\mathrm{NO}]^3}\)
04

Calculate expression for \(K_{\mathrm{p}}\)

The equilibrium constant, \(K_{\mathrm{p}}\), is defined as: \(K_{\mathrm{p}} = \frac{P_{\mathrm{NO}_{2}}P_{\mathrm{N}_{2}\mathrm{O}}}{P_{\mathrm{NO}}^3}\) #Reaction c.# 3. Nitrogen oxide reaction The reaction is \(2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\).
05

Calculate expression for \(K_{\mathrm{c}}\)

The equilibrium constant, \(K_{\mathrm{c}}\), is defined as: \(K_{\mathrm{c}} = \frac{[\mathrm{N}_{2}]^2[\mathrm{O}_{2}]}{[\mathrm{N}_{2}\mathrm{O}]^2}\)
06

Calculate expression for \(K_{\mathrm{p}}\)

The equilibrium constant, \(K_{\mathrm{p}}\), is defined as: \(K_{\mathrm{p}} = \frac{P_{\mathrm{N}_{2}}^2P_{\mathrm{O}_{2}}}{P_{\mathrm{N}_{2}\mathrm{O}}^2}\)

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Key Concepts

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

Nitrogen Oxides
Nitrogen oxides are a group of gases that are composed of nitrogen and oxygen. They are commonly referred to as NOx gases and mainly include nitric oxide (NO) and nitrogen dioxide (NO鈧�). These gases play a significant role in air pollution due to their participation in atmospheric reactions.
  • Nitric oxide (NO) is a colorless gas that reacts with oxygen to form nitrogen dioxide (NO鈧�).
  • Nitrogen dioxide (NO鈧�) is a brown gas with a distinct sharp smell and is highly reactive.
Nitrogen oxides are considered pollutants because they contribute to the formation of smog and acid rain. They also facilitate the production of tropospheric ozone, a major component of urban smog. More importantly, they are involved in various chemical reactions that can shift equilibrium states, as seen in the gaseous reactions of these oxides.
Chemical Equilibrium
Chemical equilibrium is a state in a chemical reaction where there is no net change in the concentration of reactants and products over time. During equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction.
The equilibrium constant, denoted as either \(K_c\) or \(K_p\), is used to express the ratio of concentrations (or partial pressures) of products to reactants at equilibrium.
  • For a reaction involving concentrations, equilibrium is expressed as \(K_c\).
  • For gaseous reactions involving pressures, it is expressed as \(K_p\).
These constants provide insight into the position of equilibrium. A large value of \(K\) suggests that the reaction favors the formation of products, whereas a small \(K\) indicates that reactants are favored at equilibrium. It is important to note that equilibrium does not mean that reactants and products are equal in concentration, but rather that their rates of change are balanced.
Gaseous Reactions
Gaseous reactions are chemical reactions where the reactants and products are in the gaseous state. Such reactions are influenced by changes in temperature, pressure, and concentration.
There are important concepts to understand in gaseous reactions, especially when dealing with equilibrium.
  • The reaction direction can shift if external conditions such as pressure or temperature change. For example, increasing pressure will favor the side of a reaction with fewer moles of gas.
  • Le Chatelier鈥檚 Principle is a key guide, stating that a system at equilibrium will adjust to offset changes in conditions.
When writing the expressions for \(K_c\) and \(K_p\) for gaseous reactions, it is crucial to account for the coefficients from the balanced chemical equations. These coefficients determine the powers to which the concentration or pressure terms are raised in the equilibrium expressions. This underscores the dynamic yet balanced nature of gaseous chemical reactions.

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Most popular questions from this chapter

The valuc of \(K_{p}\) for the water-gas shift reaction $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) $$ increases as the temperature decreases. Is the reaction exothermic or endothermic?

Bulletproof Glass Phosgene \(\left(\mathrm{COCl}_{2}\right)\) is used in the manufacture of foam rubber and bulletproof glass. It is formed from carbon monoxide and chlorine in the following reaction: $$ \mathrm{Cl}_{2}(g)+\mathrm{CO}(g) \rightleftharpoons \operatorname{COCl}_{2}(g) $$

If the value of \(K_{c}\) for the following reaction is \(5 \times 10^{5}\) at \(298 \mathrm{K},\) what is the value of \(K_{\mathrm{p}}\) at \(298 \mathrm{K} ?\) $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$

Flements of group 16 form hydrides with the generic formula \(\mathrm{H}_{2} \mathrm{X}\). When gaseous \(\mathrm{H}_{2} \mathrm{X}\) is bubbled through a solution containing \(0.3 M\) hydrochloric acid, the solution becomes saturated and \(\left[\mathrm{H}_{2} \mathrm{X}\right]=0.1 \mathrm{M} .\) The following equilibria exist in this solution: \(\mathrm{H}_{2} \mathrm{X}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{HX}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \quad K_{1}=8.3 \times 10^{-8}\) \(\mathrm{HX}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{X}^{2-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \quad K_{2}=1 \times 10^{-14}\) Calculate the concentration of \(\mathrm{X}^{2-}\) in the solution.

A mixture of \(^{13} \mathrm{CO},^{12} \mathrm{CO}_{2},\) and \(\mathrm{O}_{2}\) in a scaled reaction vessel was used to follow the reaction $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$ Analysis of the reaction mixture after 1 day revealed the presence of compounds with molar masses 28,29,32,44 and \(45 \mathrm{g} / \mathrm{mol}\). Identify the compounds and account for their presence.
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