A reaction in which A, B, and C react to form products is zero order in A, one-half order in B, and second order in C.

a. Write a rate Jaw for the reaction.

b. What is the overall order of the reaction?

c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant )?

d. By what factor does the reaction rate change if [B] is doub led (and the other reactant co ncen trati ons are held consta nt )?

e. By what factor does the reaction rate change if [C] is doubled (and the other reactant concen trations are held constant)?

f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled?

[tex]\sqrt[n]{x} \frac{r_f}{r_i}=\frac{[2B]^{(1/2)} [C]^2}{[B]^{(1/2)}[C]^2} \\\\\frac{r_f}{r_i}=\frac{[2B]^{(1/2)}}{[B]^{(1/2)}}\\\\\frac{r_f}{r_i}=(\frac{2}{1})^{1/2}\\\\r_f=\sqrt{2} r_i[/tex]

It means that the rate increases by a factor of [tex]\sqrt{2}[/tex].

e. In this case, if the concentration of C is doubled, such term in the equation shows:

[tex]\frac{r_f}{r_i}=\frac{[B]^{(1/2)}[2C]^2}{[B]^{(1/2)}[C]^2} \\\\\frac{r_f}{r_i}=(\frac{[2C]}{[C]})^{2}\\\\\frac{r_f}{r_i}=(\frac{2}{1})^{2}\\\\r_f=4r_i[/tex]

It means that the rate increases by a factor of 4.

f. In this case, if the concentration of both B and C are doubled, such terms in the equation shows:

[tex]\frac{r_f}{r_i}=\frac{[2B]^{(1/2)}[2C]^2}{[B]^{(1/2)}[C]^2} \\\\\frac{r_f}{r_i}=\frac{2^{(1/2)}2^2}{1^{(1/2)}1^2} \\\\\frac{r_f}{r_i}=4\sqrt{2} \\\\r_f=4\sqrt{2} r_i[/tex]

It means that the rate increases by a factor of 4[tex]\sqrt{2}[/tex].

Best regards.