Consider the following elementary reaction $$M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }M _ { s ol } ^ { 2 + } + 2 e ^ { - }$$

where M is metal and
$$M _ { \text {sol } } ^ { 2 + }$$
is metal ion in solution, F denotes Faraday constant. The net faradaic current density due to metal dissolution is
A) $$2 F \left( k _ { 1 } \left[ M _ { s d } ^ { + } \right] - k _ { - 1 } \right)$$
B) $$2 F \left\{ k _ { 1 } - k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$
C) $$F \left\{ k _ { 1 } - k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$
D) $$2 F \left\{ k _ { 1 } + k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$

Question

Consider the following elementary reaction $$M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }M _ { s ol } ^ { 2 + } + 2 e ^ { - }$$
 
 where M is metal and 
 $$M _ { \text {sol } } ^ { 2 + }$$ 
is metal ion in solution, F denotes Faraday constant. The net faradaic current density due to metal dissolution is
A) $$2 F \left( k _ { 1 } \left[ M _ { s d } ^ { + } \right] - k _ { - 1 } \right)$$
B) $$2 F \left\{ k _ { 1 } - k _ { - 1 } \left[  M _ { s o l } ^ { 2 + } \right] \right\}$$
C) $$F \left\{ k _ { 1 } - k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$
D) $$2 F \left\{ k _ { 1 } + k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$

Quizplus · Accepted Answer

The net faradaic current density for the dissolution of metal M into $M_{sol}^{2+}$ and 2 electrons involves the rate of the forward reaction (metal dissolution) minus the rate of the backward reaction (metal deposition). The forward reaction rate is proportional to the rate constant $k_1$ and the backward reaction rate is proportional to the rate constant $k_{-1}$ and the concentration of $M_{sol}^{2+}$. Since 2 electrons are involved in the reaction, the current density is multiplied by $2F$, where $F$ is the Faraday constant. Therefore, the correct expression is $2F\{k_1 - k_{-1}[M_{sol}^{2+}]\}$.

Consider the Following Elementary Reaction M⇄k1k−1Msol2++2e−M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }M _ { s ol } ^ { 2 + } + 2 e ^ { - }Mk−1​⇄k1​​​Msol2+​+2e−

Consider the Following Elementary Reaction $M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }M _ { s ol } ^ { 2 + } + 2 e ^ { - }$