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Chapter 14: Problem 19

Consider the following reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ If the equilibrium partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and NO are 0.15 atm, 0.33 atm, and 0.050 atm, respectively, at \(2200^{\circ} \mathrm{C},\) what is \(K_{P} ?\)

Short Answer

Expert verified
The equilibrium constant (\( K_P\)) for the given reaction is approximately 0.050.

Step by step solution

01

Understanding the \(K_P\) Equation

First, it is important to understand the formula used to calculate the equilibrium constant, \(K_P\). For the given generic reaction: \(aA + bB \rightleftharpoons cC + dD\), \(K_P\) is defined as: \[K_P = \left( [C]^c [D]^d \right) / \left( [A]^a [B]^b \right)\] Where A, B, C, and D represent the reactants and products, 'a', 'b', 'c', and 'd' are their corresponding stoichiometric coefficients in the balanced chemical equation, and the brackets denote the partial pressure of the gases. Note that the pressures must be in the same units.
02

Substituting Given Values into the Equation

Given the reaction: \(N_2(g) + O_2(g) \rightleftharpoons 2 NO(g)\), we can apply the formula as: \[K_P = (P_{NO}^2) / (P_{N_2} * P_{O_2})\] Where \(P_{NO}\), \(P_{N_2}\), and \(P_{O_2}\) are the partial pressures of NO, N2, and O2 respectively. The given values can now be substituted into the equation: \[K_P = (0.050^2) / (0.15 * 0.33)\]
03

Calculating the Final Value

After substituting the given values into the formula, the final step is to calculate the value of \( K_P\). By computation, the resulting value of \( K_P\) is approximately 0.050.

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Most popular questions from this chapter

Pure nitrosyl chloride (NOCl) gas was heated to \(240^{\circ} \mathrm{C}\) in a \(1.00-\mathrm{L}\) container. At equilibrium the total pressure was 1.00 atm and the \(\mathrm{NOCl}\) pressure was 0.64 atm. $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$ (a) Calculate the partial pressures of \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) in the system. (b) Calculate the equilibrium constant \(K_{P}\).

A mixture of 0.47 mole of \(\mathrm{H}_{2}\) and 3.59 moles of \(\mathrm{HCl}\) is heated to \(2800^{\circ} \mathrm{C}\). Calculate the equilibrium partial pressures of \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) if the total pressure is 2.00 atm. For the reaction $$\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)$$ \(K_{P}\) is 193 at \(2800^{\circ} \mathrm{C}\)

Consider the equilibrium system \(3 \mathrm{~A} \rightleftharpoons \mathrm{B}\). Sketch the changes in the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) over time for the following situations: (a) Initially only A is present. (b) Initially only B is present. (c) Initially both A and B are present (with A in higher concentration). In each case, assume that the concentration of \(\mathrm{B}\) is higher than that of \(\mathrm{A}\) at equilibrium.

The vapor pressure of mercury is \(0.0020 \mathrm{mmHg}\) at \(26^{\circ} \mathrm{C}\). (a) Calculate \(K_{\mathrm{c}}\) and \(K_{P}\) for the process \(\mathrm{Hg}(l) \rightleftharpoons \mathrm{Hg}(g) .\) (b) A chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring \(6.1 \mathrm{~m}\) long, \(5.3 \mathrm{~m}\) wide, and \(3.1 \mathrm{~m}\) high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor in \(\mathrm{mg} / \mathrm{m}^{3}\). Does this concentration exceed the safety limit of \(0.05 \mathrm{mg} / \mathrm{m}^{3} ?\) (Ignore the volume of furniture and other objects in the laboratory.)

A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$$ Under these conditions, the average molar mass of the gases was \(35 \mathrm{~g} / \mathrm{mol}\). (a) Calculate the mole fractions of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\). (b) What is \(K_{P}\) if the total pressure is 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.
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