   # Many biochemical reactions that occur in cells require relatively high concentrations of potassium ion (K + ). The concentration of K + in muscle cells is about 0.l5 M. The concentration of K+ in blood plasma is about 0.0050 M. The high internal concentration in cells is maintained by pumping K + from the plasma. How much work must be done to transport 1.0 mole of K + from the blood to the inside of a muscle cell at 37°C, normal body temperature? When 1.0 mole of K + is transferred from blood to the cells, do any other ions have to be transported? Why or why not? ### Chemistry: An Atoms First Approach

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

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 16, Problem 88AE
Textbook Problem
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## Many biochemical reactions that occur in cells require relatively high concentrations of potassium ion (K+). The concentration of K + in muscle cells is about 0.l5 M. The concentration of K+ in blood plasma is about 0.0050 M. The high internal concentration in cells is maintained by pumping K+ from the plasma. How much work must be done to transport 1.0 mole of K+ from the blood to the inside of a muscle cell at 37°C, normal body temperature? When 1.0 mole of K+ is transferred from blood to the cells, do any other ions have to be transported? Why or why not?

Interpretation Introduction

Interpretation: The concentration of K+ in muscle cells and blood plasma is given. Work done to transport 1.0mol of K+ from blood to the inside of a muscle cell at a given temperature is to be calculated. It is to be identified that if any ion transported out when 1.0mol of K+ is transferred inside. The reason is to be given for this transportation.

ΔG°=RTln(K)

If equilibrium concentration, K , is expressed in terms of concentration, then it is expressed as X .

ΔG°=RTln(X)

### Explanation of Solution

Given

Concentration of K+ in muscle cells is 0.15M .

Concentration of K+ in blood plasma is 0.0050M .

Temperature is 37°C .

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence,

The conversion of 37°C into Kelvin is,

T(K)=T(°C)+37T(K)=(37+273)K=310K

Formula

Work done is calculated using the formula,

ΔG=ΔGmuscleΔGblood=RTln(X1)RTln(X2)=RT[ln(X1)ln(X2)]

Where,

• ΔG is the work done.
• X1 is the concentration of K+ in muscle cells.
• X2 is the concentration of K+ in blood plasma.
• R is the gas law constant (8

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