To calculate the time required to deposit 80g of copper (\(m\)) on a copper plate using the electrochemical equivalent (\(E\)) and current (\(I\)), you can use the formula:
\[m = E \times I \times t\]
Where:
\(m = 80g\) (mass of copper to be deposited)
\(E = 3.3 \times 10^{-3} \, \text{g/C}\) (electrochemical equivalent of copper)
\(I = 2A\) (current in the cell)
\(t\) is the time in seconds (which we need to find)
Substituting the given values into the formula:
\[80g = (3.3 \times 10^{-3} \, \text{g/C}) \times (2A) \times t\]
Solving for \(t\):
\[t = \frac{80g}{(3.3 \times 10^{-3} \, \text{g/C}) \times (2A)}\]
\[t \approx \frac{80}{(3.3 \times 10^{-3}) \times 2} \, \text{seconds}\]
\[t \approx \frac{80}{6.6 \times 10^{-3}} \, \text{seconds}\]
\[t \approx 12121.21 \, \text{seconds}\]
It will take approximately \(12121.21\) seconds to deposit \(80g\) of copper on the copper plate under the given conditions. To convert this to hours, divide by the number of seconds in an hour (3600 seconds):
\[t \approx \frac{12121.21 \, \text{seconds}}{3600 \, \text{seconds/hour}} \approx 3.37 \, \text{hours}\]