# A solution of formic acid (HCOOH, K a = 1.8 × 10 −4 ) has a pH of 2.70. Calculate the initial concentration of formic acid in this solution.

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 13, Problem 79E
Textbook Problem
683 views

## A solution of formic acid (HCOOH, Ka = 1.8 × 10−4) has a pH of 2.70. Calculate the initial concentration of formic acid in this solution.

Interpretation Introduction

Interpretation: The pH of a solution of formic acid (HCOOH) and its Ka value is given. The initial concentration of formic acid is to be calculated.

Concept introduction: The pH of a solution is define as a figure that expresses the acidity of the alkalinity of a given solution.

The pH of a solution is calculated by the formula, pH=log[H+]

At equilibrium, the equilibrium constant expression is expressed by the formula,

Ka=ConcentrationofproductsConcentrationofreactants

### Explanation of Solution

Explanation

To determine: The initial concentration of formic acid.

The [H+] for formic acid is 1.99×10-3M_ .

Given

The pH of the given concentration of formic acid is 2.70 .

The pH of a solution is calculated by the formula,

pH=log[H+]

Rearrange the above expression to obtain the value of [H+] .

[H+]=10pH

Substitute the pH value of formic acid in the above expression.

[H+]=102.70=1.99×10-3M_

The equilibrium constant expression for the dissociation reaction of formic acid is,

Ka=[H+][HCOO][HCOOH]

HCOOH is a comparatively stronger acid than H2O .

The dominant equilibrium reaction for the given case is,

HCOOH(aq)H+(aq)+HCOO(aq)

At equilibrium, the equilibrium constant expression is expressed by the formula,

Ka=ConcentrationofproductsConcentrationofreactants

Where,

• Ka is the acid dissociation constant.

The equilibrium constant expression for the given reaction is,

Ka=[H+][HCOO][HCOOH] (1)

The initial concentration of HCOOH is 0.024M_ .

The initial concentration of HCOOH is assumed to be x .

The [H+] for formic acid is 1.99×103M .

The ICE table for the stated reaction is,

HCOOH(aq)H+(aq)+HCOO(aq)Inititialconcentrationx00Change1

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