Question

The negative Zn pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemical equivalent of Zn and Cu are 32.5 and 31.5 respectively, the increase in the mass of the positive Cu pole in this time is
A. 0.242 g
B. 0.190 g
C. 0.141 g
D. 0.126 g

Answer 1

Hint: To determine the mass of copper cation we will use the relation which is given by the faraday equation (faraday’s law of electrolysis). According to the faraday’s law of electrolysis, the mass of substance increases or decreases on any particular electrode is proportional to the current passed through the electrochemical cell (containing two beakers and each containing one electrode of different substance) such as
\[\text{M }\propto \text{ }Q\]
or
\[\text{M }=\text{ }ZQ\] or \[\text{M }=\text{ }Z\text{ }\left( it \right)\]
where Z is electrochemical equivalent, I is current and t is time.

Complete Step by Step Answer:
The Daniell cell is an example of an electrochemical cell or galvanic cell or voltaic cell (chemical energy to electric energy so there is no battery present in between wires). Like the galvanic cell, the Daniell cell also contains two beakers.

In the beaker on the left side, the electrode of zinc is present on which oxidation takes place (release of electrons on electrode) so, it said to be anode and on right side of beaker copper electrode is present at which reduction will take place (gain of an electron at electrode) so, it termed as the cathode. Both these electrodes are connected with conducting wire. Also, a salt bridge is present which is a connection between the two solutions.

In the given question, it is given that the mass of the zinc electrode decreases (oxidation) by 0.13 g and now we need to find the increase in mass of copper on the other hand.

As per Faraday's law of electrolysis, the mass which decreases or increases on a particular electrode is directly proportional to the charge which is supplied (as there is no charge supply so Q will not change). For a zinc electrode at which mass decreased by 0.13 g (\[{{m}_{1}}\]) then it will be equal to
\[{{m}_{1}}\text{ }\propto \text{ }Q\]
\[{{m}_{1}}\text{ }=\text{ }ZQ\] where Z is ECE (electrochemical equivalent, constant)
As in the question, the electrochemical equivalent of zinc is given, 32.5 so the relation of it with the decreased mass of zinc is given as
\[{{m}_{1}}\text{ }\propto \text{ }Z\]
\[0.13\text{ }=\text{ }32.5\]
Now for copper electrode whose mass (\[{{m}_{2}}\]) should be increased as at copper electrode reduction will take place and electrons are gained by \[C{{u}^{2+}}\]cations can be determined by the same method applied above such as
\[{{\text{m}}_{2}}\text{ }=\text{ }31.5\]
Finding the ratio of \[{{m}_{1}}\] by \[{{m}_{2}}\]we will get
\[\frac{{{m}_{1}}}{{{m}_{2}}}\text{ }=\text{ }\frac{32.5}{31.5}\]
\[{{\text{m}}_{2}}\text{ =}\frac{{{m}_{1}}\times 31.5}{32.5}\]
\[{{\text{m}}_{2}}\text{ =}\frac{0.13\times 31.5}{32.5}\]
\[{{m}_{2}}\text{ }=\text{ }0.126\text{ }g\]
Thus, the correct option is D.

Note: As we noticed that mass is directly proportional to charge and charge is given as current in time. But in question, we had asked that when zinc mass decreased by 0.13 g at same point of time how much mass of copper increased so we have taken time a constant also we do not provide charge so Q is taken as constant.