Lead is a toxic metal. The U.S. Environmental Protection Agency limits the concentration of lead ions in drinking water to less than 5 $\times$ 10^-8 M. Assess the feasibility of monitoring of lead in drinking water using a voltaic cell based on the following half-reactions. $~~~~~~~~$E $\circ$ = -0.762 V $~~~~~~~~$E $\circ$ = -0.126 V If the zinc ion concentration were 0.100 M, what lead ion concentration at 298 K would decrease the cell potential by 10 mV from the standard cell potential?

Question

Quizplus · Accepted Answer

The Nernst equation relates the cell potential to the concentration of species involved in the half-reactions. At 298 K, the Nernst equation for this cell is:

E = E° - (RT/nF) ln (Q)

where E° is the standard potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient.

For the given cell, the reaction quotient is:

Q = [Pb2+] / [Zn2+] = x / 0.100

where x is the concentration of lead ions that we want to find.

We want the cell potential to decrease by 10 mV (0.010 V) from the standard potential. So we can rearrange the Nernst equation:

ln (Q) = (E° - E) nF / RT

ln (x/0.100) = (0.762 - 0.010) 2 (-1) (96500) / (8.314) (298)

ln (x/0.100) = -4.688

x/0.100 = e^(-4.688)

x = 0.0456 M

Therefore, the lead ion concentration that would decrease the cell potential by 10 mV from the standard potential is 0.046 M, which is closest to choice C.

Lead Is a Toxic Metal ×\times× 10-8 M ~~~~~~~~ E ∘\circ∘ = -0

Lead Is a Toxic Metal $\times$ 10^-8 M $~~~~~~~~$ E^$\circ$ = -0