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Chapter 22: Problem 28

When the conjugate acid of aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\), reacts with the acetate ion, the following reaction takes place: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}(a q)+\mathrm{CH}_{3} \mathrm{COO}^{-}(a q) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}(a q)+\mathrm{CH}_{3} \mathrm{COOH}(a q)\) If \(K_{\mathrm{a}}\) for \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\) is \(1.35 \times 10^{-5}\) and \(K_{\mathrm{a}}\) for \(\mathrm{CH}_{3} \mathrm{COOH}\) is \(1.86 \times 10^{-5}\) what is \(K\) for the reaction?

Short Answer

Expert verified
Answer: The equilibrium constant (K) for the reaction between aniline and acetic acid is approximately 1.38.

Step by step solution

01

Identify the Ka values provided

We are given that: \(K_{a}\)(C6H5NH3+) = \(1.35 \times 10^{-5}\), this is for the conjugate acid of aniline \(K_{a}\)(CH3COOH) = \(1.86 \times 10^{-5}\), this is for the acetic acid
02

Apply the relationship to find the equilibrium constant of the reaction

We know that \(K_{reaction} = \frac{K_{a \space acid}}{K_{a \space conjugate \space acid}}\). In this case, our reaction involves the acid CH3COOH and the conjugate acid C6H5NH3+. So, we can plug in the given Ka values to find the equilibrium constant: \(K = \frac{K_{a \space (CH3COOH)}}{K_{a \space (C6H5NH3+)}}\) \(K = \frac{1.86 \times 10^{-5}}{1.35 \times 10^{-5}}\)
03

Calculate the equilibrium constant K

Now divide the given values to find the equilibrium constant K: \(K \approx \frac{1.86}{1.35}\) \(K \approx 1.38\) Thus, the equilibrium constant K for the reaction is approximately 1.38.

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Most popular questions from this chapter

When aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\left(K_{\mathrm{b}}=7.4 \times 10^{-10}\right)\), reacts with a strong acid, its conjugate acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\), is formed. Calculate the \(\mathrm{pH}\) of a \(0.100 \mathrm{M}\) solution of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\) and compare it with the \(\mathrm{pH}\) of acetic acid \(\left(K_{\mathrm{a}}=\right.\) \(\left.1.86 \times 10^{-5}\right)\)

Write the structural formulas of all the esters that can be formed by ethylene glycol with formic and acetic acids. (One or both of the - OH groups of ethylene glycol can react.)

Write the formula for (a) an alkyne with 16 hydrogen atoms. (b) an alkene with 44 hydrogen atoms. (c) an alkane with ten carbon atoms.

The \(K_{\mathrm{b}}\) for ethylamine \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\) is \(4.3 \times 10^{-4}\). What is the \(\mathrm{pH}\) of a \(0.250 \mathrm{M}\) solution of ethylamine? Compare with the \(\mathrm{pH}\) of a \(0.250 \mathrm{M}\) solution of ammonia \(\left(K_{b}=1.86 \times 10^{-5}\right)\).

There are three compounds with the formula \(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}_{3}\) in which three of the hydrogen atoms of the benzene molecule have been replaced by chlorine atoms. Draw structures for these compounds.
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