   Chapter 17.6, Problem 2.2ACP

Chapter
Section
Textbook Problem

A typical total phosphate concentration in a cell, [HPO42−] + [H2PO4−], is 2.0 × 10−2 M. What are the concentrations of HPO42− and HPO4− at pH 7.40?

Interpretation Introduction

Interpretation:

The concentration of [H2PO4] and [HPO42] at pH7.40 has to be calculated.

Concept introduction:

The pH value of the body is maintanined in the range of 6.97.4 by buffer system. The two important buffer system present in the biological system are bicarbonate/carbonic acid system and phosphate system.

The pH is related to the concentration of conjugate base and acid as follows,

pH=pKa+log([conjugate base][weak acid])

This equation is known as Handerson-Hasselbalch equation.

Explanation

The concentration of  [H2PO4] and [HPO42] at pH7.40 is calculated below.

Given:

The total phosphate concentration ([H2PO4]+[HPO42]) is 2.0×102 M.

The pKa value for weak acid H2PO4 is 7.2.

The pH of system is 7.40.

The phosphate equilibria is given as,

H2PO4(aq)+H2O(aq)H3O+(aq)+HPO42(aq)

HPO42 is the conjugate base of weak acid H2PO4.

The pH is related to the concentration of conjugate base, HPO42 and acid, H2PO4 as follows,

pH=pKa+log([HPO42][H2PO4])

Rearrange for [HPO42]/[H2PO4].

[HPO42][H2PO4]=10(pHpKa)

Substitute the values to calculate the value of ratio of [HPO42]/[H2PO4].

[HPO42][H2PO4]=10(7

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