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Step-by-Step Solution
Step 1: Identify the relevant electrochemical formula
The mass of a metal deposited during electrolysis can be calculated using the formula:
$W = \dfrac{I\times E \times t}{96500}$
where
$W$ is the mass of metal deposited (in grams),
$I$ is the current (in amperes),
$E$ is the gram equivalent mass of the metal (in grams per equivalent),
$t$ is the time (in seconds), and
$96500$ coulombs corresponds to 1 Faraday of charge.
Step 2: Determine the equivalent mass of cobalt
For cobalt (Co) in the +2 oxidation state, the valence is 2.
Atomic mass of Co = 59 u
Gram equivalent mass $E = \dfrac{\text{Atomic mass}}{\text{Valence}} = \dfrac{59}{2} = 29.5$ grams/equivalent
Step 3: Convert all given parameters into consistent units
Current, $I = 10$ A
Time given = $109$ minutes. Convert minutes into seconds:
$109 \text{ min} \times 60 = 6540 \text{ seconds}$.
Faraday constant $= 96500 \text{ C mol}^{-1}$
Step 4: Substitute the values into the formula
Substituting into $W = \dfrac{I \times E \times t}{96500}$:
$
W = \dfrac{10 \times 29.5 \times 6540}{96500}
$
Step 5: Calculate the numerical value
Perform the multiplication and division:
$
W = \dfrac{10 \times 29.5 \times 6540}{96500}
$
First calculate the numerator:
$10 \times 29.5 \times 6540 = 10 \times (29.5 \times 6540)$.
$29.5 \times 6540 = 192,930$ (approximately).
So the numerator is $10 \times 192,930 = 1,929,300$.
Now divide by $96500$:
$
W = \dfrac{1,929,300}{96500} \approx 20
$
Step 6: Conclude the mass deposited
Hence, the mass of cobalt deposited is approximately 20 g.
