Consider the reaction given by $$\begin{array} { l }
M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \
\
M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }
\end{array}$$ .
-In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by
A) $$\theta _ { s s } = \frac { k _ { 1 \dot { dc } } } { k _ { 1 \dot {dc } } + k _ { 2 dc } }$$
B) $$\theta _ { s s } = \frac { k _ { 1 \dot {dc } } } { k _ { \mathrm { dc } } + k _ { 2 \dot { dc } } + k _ { - 2 \dot {dc } } }$$
C) $$\theta _ { s s } = \frac { k _ { 1dc } + k _ { - 2dc } C _ { M _ { sol} ^ {+2} } } { k _ { 1dc } + k _ { 2 dc } + k _ {- 2 dc} C _ { M _ {sol} ^ { +2 }} }$$
D) $$\theta _ { s s } = \frac { k _ { 1dc } - k _ { - 2dc} C _ { M _ { s ol } ^ { +2 } } } { k _ { 1 dc} + k _ { 2dc} + k _ { - 2dc } C _ { M _ {sol} ^ { +2 } } }$$

Question

Consider the reaction given by $$\begin{array} { l } 
M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \
\
M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }
\end{array}$$ .
-In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by
A) $$\theta _ { s s } = \frac { k _ { 1 \dot { dc } } } { k _ { 1 \dot {dc } } + k _ { 2 dc } }$$
B) $$\theta _ { s s } = \frac { k _ { 1 \dot {dc } } } { k _ { \mathrm { dc } } + k _ { 2 \dot { dc } } + k _ { - 2 \dot {dc } } }$$
C) $$\theta _ { s s } = \frac { k _ { 1dc } + k _ { - 2dc } C _ { M _ { sol} ^ {+2} } } { k _ { 1dc } + k _ { 2 dc } + k _ {- 2 dc} C _ { M _ {sol} ^ { +2  }} }$$
D) $$\theta _ { s s } = \frac { k _ { 1dc } - k _ { - 2dc} C _ { M _ { s ol } ^ { +2 } } } { k _ { 1 dc} + k _ { 2dc} + k _ { - 2dc } C _ { M _ {sol} ^ { +2 } } }$$

Quizplus · Accepted Answer

The correct expression for the steady-state fractional surface coverage ($\theta_{ss}$) in a reaction mechanism involving adsorption, desorption, and further reaction steps typically accounts for the rates of these processes. The given expression in choice C correctly incorporates the rates of adsorption ($k_{1dc}$), desorption ($k_{-2dc} C_{M_{sol}^{+2}}$), and further reaction ($k_{2dc}$) to calculate the fractional surface coverage. It balances the forward adsorption and the combined effects of desorption and further reaction of the adsorbed species, considering the concentration of $M_{sol}^{+2}$ in the desorption term.

Consider the Reaction Given By -In the Same Mechanism, the Steady-State Fractional Surface Coverage

Consider the Reaction Given By
-In the Same Mechanism, the Steady-State Fractional Surface Coverage