A current of 3.94 A is pass through a Pb(NO3)2 solution. How long (in hours) would this current have to be applied to plate out 5.40 g of lead?
To determine how long the current needs to be applied, we can use the equation:
\( \text{Charge} = \text{Current} \times \text{Time} \)
Since we know the current and we want to find the time, we need to rearrange the equation to solve for time:
\( \text{Time} = \frac{\text{Charge}}{\text{Current}} \)
Now let's calculate the charge needed to plate out 5.40 g of lead. We can use the formula:
\( \text{Charge} = \text{Moles} \times \text{Faraday's Constant} \)
First, calculate the moles of lead using the molar mass of Pb (lead):
\( \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \)
The molar mass of Pb is 207.2 g/mol, so:
\( \text{Moles} = \frac{5.40 \, \text{g}}{207.2 \, \text{g/mol}} \)
Now, calculate the charge using Faraday's constant, which is 96485 C/mol:
\( \text{Charge} = \text{Moles} \times 96485 \, \text{C/mol} \)
Finally, substitute the known values into the equation to find the time:
\( \text{Time} = \frac{\text{Charge}}{\text{Current}} \)
\( \text{Time} = \frac{\text{Moles} \times 96485 \, \text{C/mol}}{3.94 \, \text{A}} \)
Simplify the equation to find the time in hours. Remember that 1 hour is equal to 3600 seconds:
\( \text{Time} = \frac{\text{Moles} \times 96485 \, \text{C/mol}}{3.94 \, \text{A}} \times \frac{1 \, \text{hr}}{3600 \, \text{s}} \)
Calculate the value to find the time in hours.
3.94 x seconds = coulombs
You want to know seconds (and convert to hours).
96,485 coulombs will plate out 207.2/2 = 103.6g Pb.
So how many coulombs do you need? That's 96,485 x 5.40/193.6 = ?
Substitute that ? into coulombs above, solve for seconds and convert to hours.