How would I do a calculation for an electroplating of solid metal onto the cathode in an electrolytic cell if, say, I am given current and the time that it took? What helps increase the mass yielded?
2 Answers
Here's my explanation
Explanation:
According to Ohm's law the current passed through a material is directly proportional to the voltage.
You can see the mathematical equation that describes this proportionality
Where
Where
and
The other equation
Where E is electric field at the given location
J is current density
σ (sigma) is a material-dependent parameter called the conductivity
R is the electrical resistance of a uniform specimen of the material
A is the cross-sectional area of the specimen
Simplifying
The resistance of a given material increases with length, but decreases with increasing cross-sectional area
If the
ρ depends on the conductor and is a constant
Here's a table of ρ of the conductor at
http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/rstiv.html
Note that ρ is different for conductors at different temperature
ρ increases as the temperature increases
ρ decreases as the temperature decreases
Where
ρ is resistivity
There are many version of the Ohm's law
Now lets come to the main problem.
Where Q is charge
PE is energy
By this you can understand that Voltage is proportional to charge which is proportional to coulombs
As
There is a relationship between V and C
As the V increases and the Q is thought to be constant the C increases. Means more voltage more coulombs
Now let me show you an example
Suppose that
The reaction
=
Net ionic reaction
Each mole of
Thus
The whole reaction
As 2C/s is applied for 2s
=
Use the Faraday's constant to calculate the moles of electrons lost and gained in total.
1 mole of
Thus moles of
Now see what happens if we apply more charge
Consider the charge as 3C/s for 2s
Do the same calculations
As 3C/s is applied for 2s
=
Thus more the current,voltage and coulomb the more the mol of copper formed thus more the mass of copper formmed
Plotting a graph
If my handwriting is too bad
y = mol of Cu formed from reduction of
x = mol of electrons used in the process
One can impart current to force a nonspontaneous chemical reaction, such as electroplating solid onto the cathode of an electrolytic cell. Increasing the voltage increases the mass plated by stoichiometry.
Here is a calculation example.
Suppose we have to plate
#"Cu"# , and we supply#"6.30 A"# of current through a#"Cu"("NO"_3)_2# solution for#"14.0 min"# . What mass is plated?
The preliminary calculation for
#14.0 cancel"min" xx (60 cancel"s")/cancel"1 min" xx (6.30 cancel"C")/cancel"s" xx cancel("1 mol e"^(-))/(96485 cancel"C") xx (2 cancel"mol Cu")/cancel("1 mol e"^(-)) xx "63.55 g Cu"/cancel"1 mol Cu"#
#=# #color(green)("6.97 g Cu")#
From Ohm's law, since
#V = IR# ,
where
Since voltage is directly proportional to the current supplied, a higher-voltage supply with the same resistance would increase the amount of mass plated.