This problem is providing the rate of the given reaction as 0.840 M/s and asks for the relative rate of change of each species. At the end, the results turned out to be -0.840 M/s, 0.210 M/s and 0.420 M/s for A, B and C respectively.
In chemical kinetics, when chemical reactions take place, it turns out possible for us to quantify in what extent a reaction is proceeding over time, by overseeing the change in the concentration as the time goes by.
In such a way, when given the rate of reaction, one can calculate the relative rate of change of each species by using the following equation, involving their stoichiometric coefficients in the reaction:
[tex]r_A=\frac{r}{-1} \\\\r_B=\frac{r}{-4} \\\\r_C=\frac{r}{2}[/tex]
Where these coefficients are negative for reactants and positive for products. In such a way, one can plug in the given rate of reaction to obtain each species' as follows:
[tex]r_A=\frac{0.840M/s}{-1} =-0.840M/s\\\\r_B=\frac{0.840M/s}{-4} =0.210M/s\\\\r_C=\frac{0.840M/s}{2}=0.420M/s[/tex]
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