Suppose a compound is involved in three
different reactions denoted R1, R2, and R3.
Tripling the concentration of this reactant in
all three reactions causes the rates of reaction
to increase by factors of 3, 9, and 1, respec-
tively. What is the order of each reaction with
respect to this reactant?
>>> I'm trying to make a guess because I don't understand. My guess is 1, 2, 0.
I think you are correct. For the first one,
R1 = k(A)x but we can ignore k since it will be a constant.
logR1 = x*log(A)
If A is tripled, then R1 is 3R1
log 3 = x*log 3
0.477 = x*0.477 and
x = 1 so that is first order.
If A is tripled, then R1 = 9R1
log 9 = x*log 9
0.954 = x*0.477
x = 0.954/0.477 = 2 or second order.
If A is tripled, then R1 = 1*R1
log 1 = x*log3
0 = x*0.477
x = 0/0.477 = 0 = zero order.
Your guess is close, but not entirely correct. Let's analyze the given information step by step to determine the order of each reaction with respect to the reactant.
1. The fact that tripling the concentration of the reactant in reaction R1 causes the rate to increase by a factor of 3 indicates that the reaction is first order with respect to the reactant. This means that R1 is represented by the reaction rate equation: Rate = k[R1]^1 (where k is the rate constant).
2. Tripling the concentration of the reactant in reaction R2 causes the rate to increase by a factor of 9. This suggests that the reaction is second order with respect to the reactant. Therefore, R2 is represented by the reaction rate equation: Rate = k[R2]^2.
3. Tripling the concentration of the reactant in reaction R3 only causes the rate to increase by a factor of 1. This indicates that the concentration of the reactant does not affect the rate of reaction in R3 (it has no effect). Hence, R3 is represented by the reaction rate equation: Rate = k[R3]^0 (which simplifies to Rate = k).
In summary, the order of each reaction with respect to the reactant is as follows:
- R1: First order (Rate = k[R1]^1)
- R2: Second order (Rate = k[R2]^2)
- R3: Zero order (Rate = k)
So, the correct answer is 1, 2, 0.
To determine the order of each reaction with respect to the reactant, we need to analyze the effect of changing the concentration on the rate of reaction for each reaction individually. Let's go step by step:
1. Start by determining the initial rate equation for each reaction:
For reaction R1:
Rate1 = k1[A]x[B]y[C]z
For reaction R2:
Rate2 = k2[A]m[B]n[C]p
For reaction R3:
Rate3 = k3[A]p[B]q[C]r
[A], [B], and [C] represent the concentrations of the reactants A, B, and C, respectively. k1, k2, and k3 are rate constants, and x, y, z, m, n, p, q, and r are the orders of the reactants.
2. Based on the given information, we know that tripling the concentration of the reactant in all three reactions causes the following changes in the rates:
For reaction R1: 3 times the concentration results in 3 times the rate.
For reaction R2: 3 times the concentration results in 9 times the rate.
For reaction R3: 3 times the concentration results in the same rate (factor of 1).
3. Now, let's apply these concentration changes to the rate equations:
For reaction R1:
Rate1' = k1[(3[A])x[B]y[C]z] = 3k1[A]x[B]y[C]z
So, the new rate is 3 times the original rate.
For reaction R2:
Rate2' = k2[(3[A])m[B]n[C]p] = 9k2[A]m[B]n[C]p
So, the new rate is 9 times the original rate.
For reaction R3:
Rate3' = k3[(3[A])p[B]q[C]r] = k3[A]p[B]q[C]r
So, the new rate is the same as the original rate.
4. Comparing the changes in rates with the changes in concentration, we can deduce the order of each reaction:
For reaction R1, tripling the concentration results in a tripling of the rate. Therefore, the order of reaction R1 with respect to the reactant is 1.
For reaction R2, tripling the concentration results in a 9-fold increase in the rate. Therefore, the order of reaction R2 with respect to the reactant is 2.
For reaction R3, tripling the concentration does not change the rate. Therefore, the order of reaction R3 with respect to the reactant is 0.
So, the order of each reaction with respect to the reactant is 1, 2, and 0 for R1, R2, and R3, respectively.