Chapter 17.2, Problem 17.3CYU

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Use the Henderson-Hasselbalch equation to calculate the pH of 1.00 L of a buffer solution containing 15.0 g of NaHCO3 and 18.0 g of Na2CO3. (Consider this buffer as a solution of the weak acid HCO3− and its conjugate base, CO32−.)

Interpretation Introduction

Interpretation:

The value of pH for the solution containing 15.0g of sodium bicarbonate and 18.0g of sodium carbonate were dissolved in 1litre of water is to be calculated by using Henderson-Hasselbalch equation.

Concept introduction:

The Henderson-Hasselbalch equation relates pH of a buffer with pKa of acid, concentration of conjugate base and concentration of acid. The expression is written as,

pH=pKa+log[conjugatebase][acid] (1)

This equation shows that pH of buffer solution is controlled by two major factors. First, is strength of the acid which can be expressed on terms of pKa and second, the relative concentration of acid and its conjugate base at equilibrium.

Explanation

The equilibrium between HCO3âˆ’ and its conjugate base CO32âˆ’ is written as follows;

HCO3âˆ’(aq)+H2O(l)â‡ŒH3O+(aq)+CO32âˆ’(aq)(acid)â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(conjugateâ€‰base)

The calculation of pH is done by using Henderson-Hasselbalch equation is given below.

Given:

Refer to table no. 16.2 in the textbook for the value of Ka.

The value of Ka for hydrogen carbonate ion is 4.8Ã—10âˆ’11.

Negative logarithm of the Ka value gives the pKa value of the acid.

pKa=âˆ’log(Ka)=âˆ’log(4.8Ã—10âˆ’11)=10.31

Therefore, pKa value for the hydrogen carbonate ion is 10.31.

The 15.0â€‰g of sodium bicarbonate (NaHCO3) is dissolved in 1â€‰litre of H2O.

Molar mass of sodium bicarbonate (NaHCO3) is 84.0â€‰gâ‹…molâˆ’1.

The 18.0â€‰g of sodium carbonate (Na2CO3) is dissolved in 1â€‰litre of H2O.

Molar mass of sodium carbonate is 105.98â€‰gâ‹…molâˆ’1.

The concentration of sodium bicarbonate is calculated as follows;

Molarity=Numberâ€‰ofâ€‰moles1â€‰LÂ ofÂ solvent (2)

Numberâ€‰ofâ€‰moles are calculated by using expression.

Numberâ€‰ofâ€‰moles=weightmolarâ€‰mass

Substitute 15.0â€‰g for weight and 84.0â€‰gâ‹…molâˆ’1 for molarâ€‰mass for sodium bicarbonate (NaHCO3)

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