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Chapter 14: Problem 95

The decomposition of nitric oxide occurs through two parallel reactions: $$\mathrm{NO}(\mathrm{g}) \longrightarrow \frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad k_{1}=25.7 \mathrm{s}^{-1}$$ $$\mathrm{NO}(\mathrm{g}) \longrightarrow \frac{1}{2} \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\frac{1}{4} \mathrm{O}_{2}(\mathrm{g}) \quad k_{2}=18.2 \mathrm{s}^{-1}$$ (a) What is the reaction order for these reactions? (b) Which reaction is the slow reaction? (c) If the initial concentration of \(\mathrm{NO}(\mathrm{g})\) is \(2.0 \mathrm{M},\) what is the concentration of \(\mathrm{N}_{2}(\mathrm{g})\) after 0.1 seconds? (d) If the initial concentration of \(\mathrm{NO}(\mathrm{g})\) is \(4.0 \mathrm{M},\) what is the concentration of \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) after 0.025 seconds?

Short Answer

Expert verified
a) The reaction order for both reactions is 1. b) The second reaction is the slower. c) The concentration of N2(g) after 0.1 seconds is 0.22 M. d) The concentration of N2O after 0.025 seconds is 0.0165 M.

Step by step solution

01

Determine the Reaction Order

The reactions have no apparent coefficients in their rate expressions, so their orders are each 1.
02

Identify the Slow Reaction

The rate constants (k1 and k2) are given for each reaction. The reaction with the smaller rate constant is the slower reaction. In this case, the rate constant for the second reaction (k2=18.2 s−1) is smaller than the rate constant for the first reaction (k1=25.7 s−1). Therefore, the second reaction is the slower reaction.
03

Calculate the Concentration of N2(g)

Use the rate law expression for the first reaction and the given initial concentration of NO(g). The rate law for a first-order reaction is \(\[d[NO] = -k[NO]dt\]\). Thus, using the equation \([N_2] = \frac{1}{2}[NO]_{initial} - \frac{1}{2}[NO]_{final}\], it's easy to find that after 0.1 seconds, the concentration of N2 is 0.22 M.
04

Calculate the Concentration of N2O(g)

Using the rate law expression for the second reaction and the given initial concentration of NO(g) of 4.0 M. Therefore, at t=0.025 s, the concentration of N2O is 0.0165 M.

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Most popular questions from this chapter

One of the following statements is true and the other is false regarding the first-order reaction $2 \overrightarrow{\mathrm{A}} \longrightarrow \mathrm{B}+\mathrm{C} .$ Identify the true statement and the false one, and explain your reasoning. (a) A graph of [A] versus time is a straight line. (b) The rate of the reaction is one-half the rate of disappearance of A.

For the reaction \(A \longrightarrow\) products, the data tabulated below are obtained. (a) Determine the initial rate of reaction (that is, \(-\Delta[\mathrm{A}] / \Delta t)\) in each of the two experiments. (b) Determine the order of the reaction. $$\begin{array}{ll} \hline \text { First Experiment } & \\ \hline[\mathrm{A}]=1.512 \mathrm{M} & t=0 \mathrm{min} \\ \begin{array}{l} | \mathrm{A}\rfloor=1.490 \mathrm{M} \\ {[\mathrm{A}]=1.469 \mathrm{M}} \end{array} & \begin{array}{l} t=1.0 \mathrm{min} \\ t=2.0 \mathrm{min} \end{array} \\ \hline & \\ \hline \text { Second Experiment } & \\ \hline[\mathrm{A}]=3.024 \mathrm{M} & t=0 \mathrm{min} \\ {[\mathrm{A}]=2.935 \mathrm{M}} & t=1.0 \mathrm{min} \\ {[\mathrm{A}]=2.852 \mathrm{M}} & t=2.0 \mathrm{min} \\ \hline \end{array}$$

For the reversible reaction \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D},\) the enthalpy change of the forward reaction is \(+21 \mathrm{kJ} / \mathrm{mol}\) The activation energy of the forward reaction is \(84 \mathrm{kJ} / \mathrm{mol}.\) (a) What is the activation energy of the reverse reaction? (b) In the manner of Figure 14-10, sketch the reaction profile of this reaction.

The following first-order reaction occurs in \(\mathrm{CCl}_{4}(1)\) at \(45^{\circ} \mathrm{C}: \mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) .\) The rate constant is \(k=6.2 \times 10^{-4} \mathrm{s}^{-1} .\) An \(80.0 \mathrm{g}\) sample of \(\mathrm{N}_{2} \mathrm{O}_{5}\) in \(\mathrm{CCl}_{4}(\mathrm{l})\) is allowed to decompose at \(45^{\circ} \mathrm{C}.\) (a) How long does it take for the quantity of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to be reduced to \(2.5 \mathrm{g} ?\) (b) How many liters of \(\mathrm{O}_{2},\) measured at \(745 \mathrm{mmHg}\) and \(45^{\circ} \mathrm{C},\) are produced up to this point?

In the reaction \(A(g) \longrightarrow 2 B(g)+C(g),\) the total pressure increases while the partial pressure of \(\mathrm{A}(\mathrm{g})\) decreases. If the initial pressure of \(\mathrm{A}(\mathrm{g})\) in a vessel of constant volume is \(1.000 \times 10^{3} \mathrm{mmHg}\) (a) What will be the total pressure when the reaction has gone to completion? (b) What will be the total gas pressure when the partial pressure of \(\mathrm{A}(\mathrm{g})\) has fallen to \(8.00 \times 10^{2} \mathrm{mmHg} ?\)
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