Question

A current of $1.70$ ampere is passed through $300ml$ of $0.130M$ solution of zinc sulphate for $230$ seconds with a current efficiency of $90\% $ . Find out the molarity of $Z{n^{2 + }}$ ions after the deposition of zinc. Assume the volume of the solution remains constant during electrolysis.

Answer 1

Hint: At first we will calculate the amount of charge passed in total given time. Since we have given the efficiency then we will calculate the total actual charge passed. Later on we will calculate the total mole of Zinc deposited by total charge passed. Once we get the moles we can find the molarity of the zinc.

Complete step by step answer:
Step1. At first we will write the data given in the question
The current given is $1.70A$
The volume of solution is $300ml$
The molarity of solution is $0.160M$
Time given is $230s$
The current efficiency is $90\% $ .
Step2. First task is to calculate the amount of charge passed. Total charge = $current \times time$
$ \Rightarrow 1.70 \times 230 = 391C$
The amount of charge that has actually passed= $efficiency \times ch\arg e$
$ \Rightarrow \dfrac{{90}}{{1000}} \times 391 = 351.9C$
Step3: Now we will calculate the no of moles of zinc deposited when the $351.9C$ charge is passed.
Moles= $\dfrac{{ch\arg e}}{{2 \times 96500}}$
$ \Rightarrow \dfrac{{351.9}}{{2 \times 96500}} = 0.000182$
So here we get $0.000182$ moles deposited of zinc.
Step4: Molarity of this deposited zinc will be
$molarity = \dfrac{{moles}}{{volume(l)}}$
$ \Rightarrow \dfrac{{0.000182 \times 1000}}{{300}}$
$ \Rightarrow 0.0060M$
Step5. The molarity of $Z{n^{2 + }}$ ion after deposition will be the initial molarity given in the question subtracted by the molarity of zinc deposited upon passing the current.
$ \Rightarrow 0.160 - 0.0060 = 0.154M$
Hence the molarity of $Z{n^{2 + }}$ ion is $0.154M$

Note:
Electrolysis is the process in which when the current is passed through a substance it affects the chemical changes in it. It is used for depositing metals on different other metal surfaces. Molarity is the concentration of solution in terms of mole per litre solution. To calculate molarity we divide the moles of solute by the total volume of solution which should be In litres.