SME
General Chemistry II · Problem type
Electrolysis: mass plated by a current
Use this for “A current of 2.50 A runs for 45 min through copper(II) sulfate. What mass of copper plates onto the cathode?”, or the time or current a mass needs.
Diagram
Each
Cu²⁺
takes
2
electrons
from
the
cathode,
so
the
metal
is
the
electrons
counted
z
.
F = 96,485 C per mole of electrons.
This is an example. Type your own values to start a new problem.
I
Current
example · A
t
Time
example
Q
Charge
calculated · C
n(e⁻)
Moles of electrons
calculated · mol
z
Electrons per ion
example
n
Moles of metal
calculated · mol
M
Molar mass of the metal
example · g/mol
m
Mass plated
calculated · g
Formulas
Q
=
I
×
t
6,750 = 2.5 × 2,700
n
(e⁻)
=
Q
96,485
0.07
=
6,750
96,485
n
=
n
(e⁻)
z
0.035
=
0.07
2
m
=
n
×
M
2.22 = 0.035 × 63.55
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
Every electron that flows reduces one share of the metal’s ion (100% current efficiency), so the charge counts the metal plated.
•
F = 96,485 C is the charge of one mole of electrons.
•
z is the charge on the metal’s ion: Cu²⁺ takes 2 electrons per atom, Ag⁺ takes 1.
•
The time goes into seconds (minutes × 60), since 1 A for 1 s is 1 C.
Step-by-step
WE KNOW
I = 2.5 A, t = 45 min, z = 2, M = 63.55 g/mol
FIND
charge (Q), moles of electrons (n(e⁻)), moles of metal (n), mass plated (m)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to s).
t = 45 min = 2,700 s (1 min = 60 s)
Step 2 · Find charge (Q)
Use Q = I × t
Multiply the current by the time in seconds: one ampere for one second is one coulomb.
Q
=
2.5
×
2,700
Q
=
6,750
C
Step 3 · Find moles of electrons (n(e⁻))
Use n(e⁻) = Q ÷ 96,485
Divide the charge by F, the charge of one mole of electrons.
n
(e⁻)
=
6,750
96,485
n
(e⁻)
=
0.07
mol
Step 4 · Find moles of metal (n)
Use n = n(e⁻) ÷ z
Each
ion
takes
z
electrons
to
become
a
metal
atom,
so
divide
the
moles
of
electrons
by
z
.
n
=
0.07
2
n
=
0.035
mol
Step 5 · Find mass plated (m)
Use m = n × M
Multiply the moles of metal by its molar mass.
m
=
0.035
×
63.55
m
=
2.22
g
Check
Put the numbers back in. Both sides should match.
6,750 = 2.5 × 2,700 ✓
0.07
=
6,750
96,485
✓
0.035
=
0.07
2
✓
2.22 = 0.035 × 63.55 ✓
← Previous lesson
Free energy and K from a cell potential
Next lesson →
Voltage of a concentration cell
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Electrochemistry
Main lesson
Free energy and K from a cell potential
Use this for “A cell has E° = 0.462 V and moves 2 electrons. Find ΔG° and K at 25 °C.”
Voltage of a concentration cell
Use this for “One silver electrode sits in 0.0050 M Ag⁺ and another in 0.80 M Ag⁺, joined by a salt bridge. Find the cell’s voltage at 25 °C.”