Sulfur dioxide emissions in power plant stack gases may react with carbon monoxide as follows: SO_2 (g) + 3CO(g) rightarrow 2CO_2 + COS(g) Write an equation relating each of the following pairs of rates:

a. The rate of formation of CO_2 to the rate of consumption of CO

b. The rate of formation of COS to the rate of consumption of SO_2

c. The rate of consumption of CO to the rate of consumption of SO_2

The middle one is proportional

a.

[tex]\frac{1}{2} \frac{dC_{CO_2}}{dt} =-\frac{1}{3} \frac{dC_{CO}}{dt}[/tex]

b.

[tex]\frac{dC_{COS}}{dt}=- \frac{dC_{SO_2}}{dt}[/tex]

c.

[tex]-\frac{1}{3} \frac{dC_{CO}}{dt}=\frac{dC_{SO_2}}{dt}[/tex]

Explanation:

Hello,

In this case, the undergoing chemical reaction is:

[tex]SO_2 (g) + 3CO(g) \rightarrow 2CO_2 + COS(g)[/tex]

For which rates of consumption are related as follows, taking into account the change in the concentration with respect to the time and each species stoichiometric coefficient:

[tex]-\frac{1}{3} \frac{dC_{CO}}{dt}=- \frac{dC_{SO_2}}{dt}=\frac{1}{2} \frac{dC_{CO_2}}{dt} =\frac{dC_{COS}}{dt}[/tex]

For the given requirements, each rate of formation turns out as shown below:

a.

[tex]\frac{1}{2} \frac{dC_{CO_2}}{dt} =-\frac{1}{3} \frac{dC_{CO}}{dt}[/tex]

b.

[tex]\frac{dC_{COS}}{dt}=- \frac{dC_{SO_2}}{dt}[/tex]

c.

[tex]-\frac{1}{3} \frac{dC_{CO}}{dt}=\frac{dC_{SO_2}}{dt}[/tex]

Best regards.