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Chapter 15: Problem 21

If \(K_{c}=0.013 \mathrm{~L} / \mathrm{mol}\) for $2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$ at \(1000 \mathrm{~K}\), what is the value of \(K_{p}\) for this reaction at this temperature?

Short Answer

Expert verified
The value of \(K_p\) for the reaction \(2 NO(g) + Br_2(g) \rightleftharpoons 2 NOBr(g)\) at 1000 K is approximately 0.125, given that \(K_c = 0.013 \mathrm{~L} / \mathrm{mol}\).

Step by step solution

01

Determine the value of ∆n

Using the balanced chemical equation, we can determine the change in the number of moles of gaseous products and reactants. \[2 NO (g) + Br_2 (g) \rightleftharpoons 2 NOBr (g)\] The number of moles of gaseous products is 2 (from 2 moles of NOBr), and the number of moles of gaseous reactants is also 2 (from 2 moles of NO and 1 mole of Br2). Thus, \[\Delta n = 2 - (2 + 1) = -1\]
02

Calculate Kp using the relationship between Kc and Kp

Now that we have the values of \(K_c\), \(\Delta n\), \(R\), and \(T\), we can calculate the value of \(K_p\). \[K_p = K_c(RT)^{\Delta n}\] \[K_p = (0.013)(0.0821 \times 1000)^{-1}\] Now, find the value of \(K_p\): \[K_p = (0.013)(8.21)^{-1}\] \[K_p ≈ 0.125\] Thus, the value of \(K_p\) for this reaction at 1000 K is approximately 0.125.

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Most popular questions from this chapter

True or false: When the temperature of an exothermic reaction increases, the rate constant of the forward reaction decreases, which leads to a decrease in the equilibrium constant, \(K_{c}\)

The equilibrium constant for the reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ is \(K_{c}=1.3 \times 10^{-2}\) at \(1000 \mathrm{~K}\). (a) At this temperature does the equilibrium favor \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\), or does it favor NOBr? (b) Calculate \(K_{c}\) for $2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) .$ (c) Calculate \(K_{c}\) for $\mathrm{NOBr}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)$.

Water molecules in the atmosphere can form hydrogenbonded dimers, \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} .\) The presence of these dimers is thought to be important in the nucleation of ice crystals in the atmosphere and in the formation of acid rain. (a) Using VSF.PR theory, draw the structure of a water dimer, using dashed lines to indicate intermolecular interactions. (b) What kind of intermolecular forces are involved in water dimer formation? (c) The \(K_{p}\) for water dimer formation in the gas phase is 0.050 at $300 \mathrm{~K}\( and 0.020 at \)350 \mathrm{~K}$. Is water dimer formation endothermic or exothermic?

For the equilibrium $$2 \operatorname{IBr}(g) \rightleftharpoons \mathrm{I}_{2}(g)+\operatorname{Br}_{2}(g)$$ \(K_{p}=8.5 \times 10^{-3}\) at \(150^{\circ} \mathrm{C}\). If \(5.07 \mathrm{kPa}\) of IBr is placed in a 10.0 -L container, what is the partial pressure of all substances after equilibrium is reached?

At \(2000^{\circ} \mathrm{C}\), the equilibrium constant for the reaction $2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$ is \(K_{c}=2.4 \times 10^{3} .\) If the initial concentration of NO is \(0.250 \mathrm{M}\), what are the equilibrium concentrations of \(\mathrm{NO}, \mathrm{N}_{2}\), and \(\mathrm{O}_{2}\) ?
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