Step-by-step explanation:
A + B + C → D
Given rate law of the reaction :
![R=k[A]^2[B]](https://img.qammunity.org/2021/formulas/social-studies/middle-school/n3sqdzbge8t4lxrmu2gso26hlvq0d38wqd.png)
a) Rate of the reaction if [A] is doubled = R'
![R'=k[2A]^2[B]=4k[A]^2[B]](https://img.qammunity.org/2021/formulas/social-studies/middle-school/w4c2xioy1oiifs05b4qgyhpo6i72m5yjjk.png)
R' = 4 × R
The rate of the reaction will change by factor of 4.
b) Rate of the reaction if [B] is reduced to quarter = R'
![R'=k[A]^2[(B)/(4)]=0.25k[A]^2[B]](https://img.qammunity.org/2021/formulas/social-studies/middle-school/bak7mlzgbjx0i8c36fztnnoi7abx298van.png)
R' = 0.25 × R
The rate of the reaction will change by factor of 0.25.
c) Rate of the reaction if [C] is increased by 3 times= R'
Rate law of the reaction :
![R'=k[A]^2[B]](https://img.qammunity.org/2021/formulas/social-studies/middle-school/6qrffjo7lspi7g7wy51cq4yra8xs1b6guo.png)
As we can see that [C] does not appears in rate law of the reaction, which means that rte of the reaction is independent of [C].
R' = R
The rate of the reaction will remain the same.
The expected rate constant value for this experiment:
![R=k[A]^2[B]](https://img.qammunity.org/2021/formulas/social-studies/middle-school/n3sqdzbge8t4lxrmu2gso26hlvq0d38wqd.png)
![k=(R)/([A]^2[B])](https://img.qammunity.org/2021/formulas/social-studies/middle-school/a6qwt3v84f918sbf3tbsxy0ayrm50nig37.png)