One of the few industrial-scale processes that produce organic compounds electrochemically is used by the Monsanto Company to produce 1,4-dicyanobutane. The reduction reaction is $$2 \mathrm{CH}_{2}=\mathrm{CHCN}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{NC}-\left(\mathrm{CH}_{2}\right)_{4}-\mathrm{CN}$$ The \(\mathrm{NC}-\left(\mathrm{CH}_{2}\right)_{4}-\mathrm{CN}\) is then chemically reduced using hydrogen gas to $\mathrm{H}_{2} \mathrm{N}-\left(\mathrm{CH}_{2}\right)_{6}-\mathrm{NH}_{2},$ which is used to produce production of nylon. What current must be used to produce \(150 . \mathrm{kg} \mathrm{NC}-\left(\mathrm{CH}_{2}\right)_{4}-\mathrm{CN}\) per hour?

Step by step solution

01

Calculate moles of NC-(CH2)4-CN

First, we need to find the molar mass of NC-(CH2)4-CN. This can be done by adding the molar masses of each constituent element: N: 14 g/mol, C: 12 g/mol, H: 1 g/mol Molar mass of NC-(CH2)4-CN = 2 * 14 + 12 * 6 + 1 * 8 = 104 g/mol Now, we can find the moles of NC-(CH2)4-CN in 150 kg (or 150,000 g): Moles of NC-(CH2)4-CN = (150,000 g) / (104 g/mol) = 1442.31 mol

02

Calculate moles of electrons needed

Based on the balanced reduction reaction, we can see that 2 moles of electrons are required for 1 mole of NC-(CH2)4-CN. Therefore: Moles of electrons = 2 * Moles of NC-(CH2)4-CN = 2 * 1442.31 mol = 2884.62 mol

03

Calculate the total charge

One mole of electrons has a charge of Faraday's constant (F), which is approximately 96485 Coulombs/mol. Therefore: Total charge = Moles of electrons * F = 2884.62 mol * 96485 C/mol ≈ 278144724.7 C

04

Calculate the current

The problem asks for the current needed to produce 150 kg of NC-(CH2)4-CN per hour. Since current is defined as charge per unit time (I = Q/t), and we want the time to be one hour: Current = Total charge / Time = 278144724.7 C / (1 hour * 3600 s/hour) ≈ 77262.4 A Thus, at a current of approximately 77,263 A (rounded to the nearest integer), 150 kg of NC-(CH2)4-CN can be produced per hour.

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