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Chapter 14: Problem 79

A solution of formic acid \(\left(\mathrm{HCOOH}, K_{\mathrm{a}}=1.8 \times 10^{-4}\right)\) has a \(\mathrm{pH}\) of \(2.70 .\) Calculate the initial concentration of formic acid in this solution.

Short Answer

Expert verified
The initial concentration of formic acid in the solution is approximately \(0.0221 \, M\).

Step by step solution

01

Write the dissociation equation for formic acid and Ka expression.

The chemical equation for the dissociation of formic acid into its ions can be written as: \(HCOOH \rightleftharpoons H^+ + HCOO^-\) And the Ka expression for this reaction is: \(K_a = \frac{[H^+][HCOO^-]}{[HCOOH]}\)
02

Calculate the concentration of hydrogen ions, H+.

We can use the given pH value to find the concentration of H+ in the solution, since pH is the negative logarithm of the concentration of hydrogen ions: \(pH = -\log[H^+]\) We'll rearrange this equation to solve for the concentration of hydrogen ions: \( [H^+] = 10^{-pH}\) Plugging in the given pH value, we'll have: \( [H^+] = 10^{-2.70} ≈ 1.995 \times 10^{-3} \, M\)
03

Write the reaction in terms of an initial concentration.

We'll call the initial concentration of formic acid "C." After dissociation, we'll have: [HCOOH] = C - x [H+] = x [HCOO-] = x Since formic acid is a weak acid, we can assume that x is very small compared to C, so C - x ≈ C.
04

Substitute the concentrations into the Ka expression and solve for C.

With our simplified assumptions, we can substitute the values back into the Ka expression: \(K_a = \frac{[H^+][HCOO^-]}{[HCOOH]}\) Simplifying to: \(1.8 \times 10^{-4} = \frac{(1.995 \times 10^{-3})^2}{C}\) Now, we need to solve for "C": \(C = \frac{(1.995 \times 10^{-3})^2}{1.8 \times 10^{-4}} ≈ 0.0221 \, M\)
05

Report the initial concentration of formic acid.

The initial concentration of formic acid in the solution is approximately 0.0221 M.

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Most popular questions from this chapter

Write the reaction and the corresponding \(K_{\mathrm{b}}\) equilibrium expression for each of the following substances acting as bases in water. a. \(\mathrm{NH}_{3}\) b. \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\)

Consider \(0.10 M\) solutions of the following compounds: \(\mathrm{AlCl}_{3}\) \(\mathrm{NaCN}, \mathrm{KOH}, \mathrm{CsClO}_{4}\), and NaF. Place these solutions in order of increasing \(\mathrm{pH}\).

An acid HX is \(25 \%\) dissociated in water. If the equilibrium concentration of \(\mathrm{HX}\) is \(0.30 \mathrm{M}\), calculate the \(K_{\mathrm{a}}\) value for \(\mathrm{HX}\).

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Consider a \(0.60-M\) solution of \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\), lactic acid \(\left(K_{\mathrm{a}}=\right.\) \(\left.1.4 \times 10^{-4}\right)\) a. Which of the following are major species in the solution? i. \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\) ii. \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) iii. \(\mathrm{H}^{+}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) v. \(\mathrm{OH}^{-}\) b. Complete the following ICE table in terms of \(x\), the amount \((\mathrm{mol} / \mathrm{L})\) of lactic acid that dissociates to reach equilibrium. c. What is the equilibrium concentration for \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) ? d. Calculate the \(\mathrm{pH}\) of the solution.
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