Question 17.11: CALCULATING THE CURRENT REQUIRED TO PRODUCE A GIVEN AMOUNT O...
CALCULATING THE CURRENT REQUIRED TO PRODUCE A GIVEN AMOUNT OF PRODUCT IN A GIVEN TIME
How many amperes must be passed through a Downs cell to produce sodium metal at a rate of 30.0 kg/h?
STRATEGY
Proceed through a sequence of conversions similar to that in Worked Example 17.10, but in reverse order.
Because the molar mass of sodium is 23.0 g/mol, the number of moles of sodium produced per hour is
Moles of Na = (30.0 kg Na)\left(\frac{1000 g}{1 kg}\right)\left(\frac{1 mol Na}{23.0 g Na}\right) = 1.30 × 10^{3} mol Na
To produce each mole of sodium, 1 mol of electrons must be passed through the cell:
Na^{+}(l) + e^{-} → Na(l)
Therefore, the charge passed per hour is
Charge = (1.30 × 10³ mol Na)\left(\frac{1 mol e^{-}}{1 mol Na}\right)\left(\frac{96,500 C}{mol e^{-}}\right) = 1.25 × 10^{8} C
Since there are 3600 s in 1 h, the current required is
Current = \frac{1.25 × 10^{8} C}{3600 s} = 3.47 × 10^{4} C/s = 34,700 A