   Chapter 18, Problem 103E

Chapter
Section
Textbook Problem

# It took 2.30 min using a current of 2.00 A to plate out all the silver from 0.250 L of a solution containing Ag+ What was the original concentration of Ag+ in the solution?

Interpretation Introduction

Interpretation:

The plating out of Ag from the solution of Ag+ when a given amount of current is passed for a given period of time. The original concentration of Ag+ in the solution is to be calculated.

Concept introduction:

The non-spontaneous reaction takes place in an electrolytic cell in which there occurs conversion of electrical energy into chemical energy and this is used for the electrolysis of a metal.

The charge generated in the cell is calculated as,

Q=It

When electricity is passed through an electrolytic cell, at that time the amount of the substance that is liberated at an electrode is given by,

W=ZQ=ZIt

The value of Z is given as,

Z=Molarmassn×96,485

To determine: The original concentration of Ag+ in the solution.

Explanation

Given information

The given current is 2.0A .

The given time is 2.30min .

The volume of solution containing Ag+ is 0.250L

The current in seconds is given as,

1min=60s2.30min=2.30×60s=138s

The molar mass of Silver is 107.87g/mol .

The reaction Ag+ undergoes during plating out of Ag is,

Ag++e-Ag

The value of Z is given as,

Z=Molarmassn×96,485=E96,485

Where,

• n is the number of electrons exchanged.
• E is the equivalent weight.
• Z is the electrochemical equivalent.

Substitute the values of atomic mass and n to obtain the value of the electrochemical equivalent of Ag+ .

Z=107.87gmol1e-×96,485Cmole-Z=107.87gmole-96,485Cmole-=1.1×10-3g/C

When electricity is passed through an electrolytic cell, at that time the amount of the substance that is liberated at an electrode is given by,

W=ZQ=ZIt

Where,

• Q is the charge carried into the cell.
• I is the current in amperes.
• t is the time for which current is passed through the cell

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