If the current is used, find the time taken for 5.5g of gold to be deposited(Au=197, 1F=96500C)
To find the time taken for gold to be deposited, we need to use Faraday's constant and the formula for calculating the time taken for electroplating.
The formula to calculate the time taken for electroplating is:
t = (m * M) / (z * F * I)
Where:
t = time taken for electroplating (in seconds)
m = mass of the substance being deposited (in grams)
M = molar mass of the substance being deposited (in grams per mole)
z = number of electrons transferred per mole of substance being deposited (based on the balanced chemical equation)
F = Faraday's constant (96500 C)
I = current (in amperes)
Given:
m = 5.5g (mass of gold)
M = 197g/mol (molar mass of gold)
z = 1 (1 electron transferred per mole of gold)
F = 96500 C (Faraday's constant)
Now, we need to find the current (I). The current is the rate of flow of charge, and it can be calculated using the formula:
I = Q / t
where Q is the charge (in coulombs) and t is the time (in seconds).
We are not given the charge Q, but we know that 1 Faraday (1F) is equal to 96500 Coulombs. So, if we have 1F of charge passing through a point in 1 second, the current at that point will be 1 Ampere (1A).
Now, let's calculate the charge (Q) for the given mass of gold:
Charge (Q) = (m / M) * (z * F)
Q = (5.5g / 197g/mol) * (1 * 96500 C)
Q = (0.02791 mol) * (96500 C)
Q = 2697.11 C
Now, we can calculate the current (I):
I = Q / t
1A = 2697.11 C / t
t = 2697.11 C / 1A
t = 2697.11 seconds
Therefore, the time taken for 5.5g of gold to be deposited is approximately 2697.11 seconds.