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Chapter 11: Problem 26

WEB When boron trifluoride reacts with ammonia, the following \(T\) reaction occurs: for $$\mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{BF}_{3} \mathrm{NH}_{3}(g)$$ The following data are obtained at a particular temperature: $$\begin{array}{cccc}\hline \text { Expt. } & {\left[\mathrm{BF}_{3}\right]} & {\left[\mathrm{NH}_{3}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\\\\hline 1 & 0.100 & 0.100 & 0.0341 \\ 2 & 0.200 & 0.233 & 0.159 \\ 3 & 0.200 & 0.0750 & 0.0512 \\ 4 & 0.300 & 0.100 & 0.102 \\\\\hline\end{array}$$

Short Answer

Expert verified
Based on the given experimental data, the rate law for the reaction between boron trifluoride (BF3) and ammonia (NH3) is: $$Rate = (3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1})([\mathrm{BF}_{3}])([\mathrm{NH}_{3}])$$ with both reactants having a reaction order of 1 and the rate constant (k) being 3.41 L·mol⁻¹·s⁻¹.

Step by step solution

01

Find the reaction order with respect to the reactants

Compare Experiments 1 and 3 to find the reaction order for BF3: Initial rate exp. 3 = \(\frac {1}{2}\) (Initial rate exp. 1) \(\frac{0.0512}{0.0341} = \frac{2^x}{1^x} \implies 1.5 = 2^x \implies x = 0.58496\) We can approximate this value as the reaction order for BF3 to 1. Now, let's find the reaction order for NH3 by comparing Experiments 1 and 4: Initial rate exp. 4 = \(3\) (Initial rate exp. 1) \(\frac{0.102}{0.0341} = \frac{1^x}{3^y} \implies 2.99 \approx 3^y\) We can approximate the reaction order for NH3 to 1 as well.
02

Calculate the Rate Constant

Now that we have both reaction orders, let's use any of the given experiment data to determine the rate constant (k): Using Experiment 1 data to calculate the rate constant: $$Rate = k[\mathrm{BF}_{3}]^1[\mathrm{NH}_{3}]^1$$ $$0.0341 = k(0.100)(0.100) \implies k = 3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1}$$
03

Write the Rate Law based on Reaction Orders and Rate Constant

We will now write the rate law using the reaction orders for both reactants and the rate constant k: $$Rate = (3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1})([\mathrm{BF}_{3}])([\mathrm{NH}_{3}])$$ This expression represents the rate law for the given reaction.

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Most popular questions from this chapter

For the reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z} \quad \Delta H=+295 \mathrm{~kJ},$$ draw a reaction-energy diagram for the reaction if its activation energy is \(378 \mathrm{~kJ} .\)

For the reaction $$2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)$$ the rate constant is \(0.066 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{min}\) at \(565^{\circ} \mathrm{C}\) and \(22.8 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{min}\) at \(728^{\circ} \mathrm{C} .\) (a) What is the activation energy of the reaction? (b) What is \(k\) at \(485^{\circ} \mathrm{C}\) ? (c) At what temperature is \(k\), the rate constant, equal to \(11.6 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{min} ?\)

The following gas-phase reaction is second-order. $$2 \mathrm{C}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{C}_{4} \mathrm{H}_{8}(g)$$ Its half-life is \(1.51\) min when \(\left[\mathrm{C}_{2} \mathrm{H}_{4}\right]\) is \(0.250 \mathrm{M}\) (a) What is \(k\) for the reaction? (b) How long will it take to go from \(0.187 M\) to \(0.0915 \mathrm{M}\) ? (c) What is the rate of the reaction when \(\left[\mathrm{C}_{2} \mathrm{H}_{4}\right]\) is \(0.335 \mathrm{M} ?\)

For the reaction $$5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}$$ it was found that at a particular instant bromine was being formed at the rate of \(0.039 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). At that instant, at what rate is (a) water being formed? (b) bromide ion being oxidized? (c) \(\mathrm{H}^{+}\) being consumed?

Write the rate expression for each of the following elementary steps: (a) \(\mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}\) (b) \(\mathrm{I}_{2} \longrightarrow 2 \mathrm{I}\) (c) \(\mathrm{NO}+\mathrm{O}_{2} \longrightarrow \mathrm{NO}_{3}\)
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