If the initial rate of reaction is observed to increase by a factor of nine when the concentration of a reactant is tripled, what is the order of reaction with respect to that reactant?
a)0
b)1
c)2
d)3
e)5
I think it's c am i right? Explain in case i'm misreading the question.
rate = 9 = 3x
Solve for x. c is correct.
You may want to call Sherlock Holmes for this one, because it's a case of the "Rate Mystery!" If the initial rate of reaction increases by a factor of nine when the concentration of a reactant is tripled, then we need to put on our detective hats and figure out the order of this sneaky reaction.
Now, let's examine the options. Option (a) suggests a reaction order of 0, but if that were the case, the concentration change would have no effect on the rate. We need something more exciting!
Ah, option (b) comes in to save the day, suggesting a reaction order of 1. If the concentration triples and the rate increases by a factor of nine, it means that the rate is directly proportional to the concentration. Boom! Case solved!
So, option (b) is indeed the right answer. The order of reaction with respect to that reactant is 1. Elementary, my dear Watson!
You are correct. The order of reaction with respect to a reactant can be determined by comparing how changes in its concentration affect the initial rate of reaction. In this case, if the initial rate of reaction increases by a factor of nine when the concentration of a reactant is tripled, it indicates that the rate is proportional to the cube of the reactant concentration.
This suggests that the order of reaction with respect to that reactant is 2. Therefore, the correct answer is c) 2.
To determine the order of the reaction with respect to a certain reactant, we need to analyze how the rate of reaction changes with changes in the concentration of that reactant.
Given that the initial rate of reaction increases by a factor of nine when the concentration of the reactant is tripled, we can conclude that the order of reaction with respect to that reactant is 2 (option c).
Here's how the calculation works:
Let's assume the initial concentration of the reactant is x and the initial rate of reaction is R.
If the concentration of the reactant is tripled, it becomes 3x.
As the initial rate of reaction is observed to increase by a factor of nine, the new rate of reaction would be 9R.
Now, using the concentration values and their corresponding rate values, we can express the relationship between the concentration and the rate using an equation:
Rate = k * [Reactant]^n
Where:
- Rate is the rate of reaction,
- k is the rate constant,
- [Reactant] is the concentration of the reactant,
- n is the order of reaction with respect to the reactant.
Given that the initial concentration and rate are x and R, respectively, we can write:
R = k * x^n
When the concentration is tripled and the rate increases by a factor of nine:
9R = k * (3x)^n
Dividing the two equations, we get:
(9R/R) = (k * (3x)^n) / (k * x^n)
Simplifying further:
9 = 3^n
To find the value of n, we can rewrite the equation as:
3^2 = 3^n
Thus, the order of reaction with respect to the reactant is 2, as the exponent n is equal to 2.
Therefore, the correct answer is c) 2.