Answer:
a. ![r=k[B]^{1/2}[C]^2](https://tex.z-dn.net/?f=r%3Dk%5BB%5D%5E%7B1%2F2%7D%5BC%5D%5E2)
b. ![Order=3.5](https://tex.z-dn.net/?f=Order%3D3.5)
c. It does not affect the rate.
d.
.
e. 4.
f. 4
.
Explanation:
Hello,
In this case, considering the given information, we have:
a. ![r=k[B]^{1/2}[C]^2](https://tex.z-dn.net/?f=r%3Dk%5BB%5D%5E%7B1%2F2%7D%5BC%5D%5E2)
b. By adding 1/2 and 2 (powers for B and C), the overall order is:
![Order=\frac{1}{2} +2\\\\Order=3.5](https://tex.z-dn.net/?f=Order%3D%5Cfrac%7B1%7D%7B2%7D%20%2B2%5C%5C%5C%5COrder%3D3.5)
c. It is not changed, since the concentration of A is not affecting the rate due to its specific zeroth-order.
d. In this case, if the concentration of B is doubled, such term in the equation shows:
![\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](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%5Cfrac%7Br_f%7D%7Br_i%7D%3D%5Cfrac%7B%5B2B%5D%5E%7B%281%2F2%29%7D%20%5BC%5D%5E2%7D%7B%5BB%5D%5E%7B%281%2F2%29%7D%5BC%5D%5E2%7D%20%20%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D%5Cfrac%7B%5B2B%5D%5E%7B%281%2F2%29%7D%7D%7B%5BB%5D%5E%7B%281%2F2%29%7D%7D%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D%28%5Cfrac%7B2%7D%7B1%7D%29%5E%7B1%2F2%7D%5C%5C%5C%5Cr_f%3D%5Csqrt%7B2%7D%20r_i)
It means that the rate increases by a factor of
.
e. In this case, if the concentration of C is doubled, such term in the equation shows:
![\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](https://tex.z-dn.net/?f=%5Cfrac%7Br_f%7D%7Br_i%7D%3D%5Cfrac%7B%5BB%5D%5E%7B%281%2F2%29%7D%5B2C%5D%5E2%7D%7B%5BB%5D%5E%7B%281%2F2%29%7D%5BC%5D%5E2%7D%20%20%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D%28%5Cfrac%7B%5B2C%5D%7D%7B%5BC%5D%7D%29%5E%7B2%7D%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D%28%5Cfrac%7B2%7D%7B1%7D%29%5E%7B2%7D%5C%5C%5C%5Cr_f%3D4r_i)
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:
![\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](https://tex.z-dn.net/?f=%5Cfrac%7Br_f%7D%7Br_i%7D%3D%5Cfrac%7B%5B2B%5D%5E%7B%281%2F2%29%7D%5B2C%5D%5E2%7D%7B%5BB%5D%5E%7B%281%2F2%29%7D%5BC%5D%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D%5Cfrac%7B2%5E%7B%281%2F2%29%7D2%5E2%7D%7B1%5E%7B%281%2F2%29%7D1%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Br_f%7D%7Br_i%7D%3D4%5Csqrt%7B2%7D%20%20%5C%5C%5C%5Cr_f%3D4%5Csqrt%7B2%7D%20r_i)
It means that the rate increases by a factor of 4
.
Best regards.