Question

Give four related expressions for the rate of the reaction

\(2\;{H_2}CO\left( g \right)\; + \;{O_2}\left( g \right)\;\; \to \;2\;C{O_2}\left( g \right)\; + \;2\;{H_2}O\left( g \right)\)

assuming that the concentrations of any intermediates are constant and that the volume of the reaction vessel does not change.

Short answer

The rate expression is given as

\(rate\; = \; - \dfrac{{d\left( {{H_2}CO} \right)}}{{dt}}\; = \; - \dfrac{{d\left( {{O_2}} \right)}}{{dt}}\; = \;\dfrac{1}{2}\dfrac{{\;d\left( {C{O_2}} \right)}}{{dt}}\; = \;\dfrac{1}{2}\dfrac{{d\left( {{H_2}0} \right)}}{{dt}}\)

Step-by-step solution

STEP-1:   Finding the rate expression for the given equation

For a chemical reaction rate expression can be defined as rate of change of concendration of every molecule or species with respect to time in an equation.

As the concendration of reactents decreases with time the reactents are represented by negative sign,whereas positive sign is represented in the products side as the concendration of products increases.

For the reaction

\(2\;{H_2}CO\left( g \right)\; + \;{O_2}\left( g \right)\;\; \to \;2\;C{O_2}\left( g \right)\; + \;2\;{H_2}O\left( g \right)\)

Rate expression is given as

\(rate\; = \; - \dfrac{1}{2}\dfrac{{d\left( {{H_2}CO} \right)}}{{dt}}\; = \; - \dfrac{{d\left( {{O_2}} \right)}}{{dt}}\; = \;\dfrac{1}{2}\dfrac{{\;d\left( {C{O_2}} \right)}}{{dt}}\; = \;\dfrac{1}{2}\dfrac{{d\left( {{H_2}0} \right)}}{{dt}}\)