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The equation that represents the water-gas shift reaction is:
A. \[CO(g){\rm{ }} + {\rm{ }}{H_2}O(g){\rm{ }} \xrightarrow[673 K]{Catalyst}
{\rm{ }}C{O_2}(g){\rm{ }} + {\rm{ }}{H_2}(g)\]
B. \[2C(s){\rm{ + }}{{\rm{O}}_2}(g) \overset{1273 K}{\rightarrow} {\rm{2CO(g) + 4N}}{}_2(g)\]
C. \[C(s){\rm{ + }}{{\rm{H}}_2}O(g) \overset{1270 K}{\rightarrow} {\rm{CO(g) + }}{{\rm{H}}_2}(g)\]
D. \[{\rm{C}}{{\rm{H}}_4}(g){\rm{ + }}{{\rm{H}}_2}O(g) \xrightarrow[Ni]{1270 K} {\rm{CO(g) + 3}}{{\rm{H}}_2}(g)\]

Answer
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Hint: The water-gas shift reaction refers to the reaction of Carbon monoxide gas with water (in the form of steam) to produce Carbon dioxide and Hydrogen gas. This reaction is a very important one industrially since it can produce Hydrogen gas in a very pure form.

Complete Step by Step Solution:
The reaction between Carbon monoxide (\[CO\]) of syngas with water (in the form of steam) in the presence of a catalyst to produce Carbon dioxide (\[C{O_2}\]) and Hydrogen gas \[H{ & _2}\]) is called a water-gas shift reaction. The equation of this reaction is given below:
\[CO(g){\rm{ }} + {\rm{ }}{H_2}O(g){\rm{ }} \xrightarrow[673 K]{Catalyst}
{\rm{ }}C{O_2}(g){\rm{ }} + {\rm{ }}{H_2}(g)\]

Since this reaction is moderately exothermic, its equilibrium shifts to the right (favouring Hydrogen gas production) at lower temperatures. Although increasing the temperature will increase the rate of the reaction, Hydrogen gas production will become thermodynamically unfavourable.

Industrially, this reaction is run in two adiabatic stages which consist of a high-temperature shift followed by a low-temperature shift. The high-temperature shift (HTS) part of the process takes advantage of the elevated reaction rate at high temperature at the cost of incomplete conversion of Carbon monoxide into Hydrogen gas. The HTS part of the reaction runs in a temperature range of 310 \[^\circ C\] to 450 \[^\circ C\]. The subsequent low-temperature shift (LTS) part of the process converts all the remaining Carbon monoxide into Hydrogen gas.

The catalyst for LTS is copper based. An example of a LTS catalyst has the composition of 32% Cupric oxide (\[CuO\]), 34% Zinc oxide (\[ZnO\]) and 15% Aluminium oxide (\[A{l_2}{O_3}\]) with \[CuO\] being the active ingredient. Catalysts for HTS are based on Iron and Chromium oxides. The composition of a typical HTS catalyst is 74.2% Ferric oxide (\[F{e_2}{O_3}\]), 10% Chromic oxide (\[C{r_2}{O_3}\]) and 0.2% Magnesium oxide (\[MgO\]).
Thus, the correct option is A.

Additional Information: The water-gas shift reaction is very valuable industrially because the Hydrogen gas produced by this reaction is further used in processes such as the Haber-Bosch process to produce ammonia (\[N{H_3}\]). This reaction is also used in the production of methanol and other hydrocarbons.

Note: The reaction given in option C is the coal gasification reaction which is closely related to the water-gas shift reaction. Therefore, sometimes the two can get confused. It is worth keeping in mind that although both reactions produce Hydrogen gas, the coal gasification reaction produces Carbon monoxide as a by-product whereas the water-gas shift reaction produces Carbon dioxide as a by-product.