1) Given this data in a study on how the rate of a reaction was affected by the concentration of the reactants
Initial Rate,
RUN # (A), M (B), M (C), M mol L-1 s-1
1 0.200 0.100 0.600 5.00
2 0.200 0.400 0.400 80.0
3 0.600 0.100 0.200 15.0
4 0.200 0.100 0.200 5.00
5 0.200 0.200 0.400 20.0
The rate constant for this reaction (all in the same units) is?
I am not sure where to start since there are so many numbers given.
You start by finding a set of two reactions in which A changes concn but B and C do not. Compare the concn changes and rate changes to find the order with respect to A. Do the same with B and C.
To find the rate constant for the reaction, you need to use the rate equation that relates the rate of the reaction to the concentration of the reactants. The rate equation generally takes the form:
Rate = k[A]^x[B]^y[C]^z
Where:
- Rate is the rate of the reaction
- k is the rate constant
- [A], [B], and [C] are the concentrations of reactants A, B, and C, respectively
- x, y, and z are the reaction orders with respect to A, B, and C, respectively
In this case, the reaction is given as:
Rate = k[A]^x[B]^y[C]^z
To determine the rate constant, you need to compare two runs, where the concentrations of the reactants change. Dividing these two run's equations will allow the reactants' concentration terms to cancel out, leaving only the rate constants left.
Taking run 1 and run 2 as an example:
Run 1:
Rate1 = k[A1]^x[B1]^y[C1]^z
Run 2:
Rate2 = k[A2]^x[B2]^y[C2]^z
Divide Run 2 equation by Run 1 equation:
Rate2/Rate1 = (k[A2]^x[B2]^y[C2]^z) / (k[A1]^x[B1]^y[C1]^z)
The concentration terms [A], [B], and [C] will cancel out, leaving only the rate constants:
Rate2/Rate1 = (A2/A1)^x(B2/B1)^y(C2/C1)^z = (0.200 / 0.200)^x(0.400 / 0.100)^y(0.400 / 0.600)^z
Simplifying, we can substitute the given values:
Rate2/Rate1 = (1)^x(4)^y(2/3)^z
Now, by comparing the rates given in the table, we find:
Rate2/Rate1 = 80.0 / 5.00
Now, solve the equation for (1)^x(4)^y(2/3)^z:
(1)^x(4)^y(2/3)^z = 80.0 / 5.00
Simplify further by taking logarithms:
log((1)^x(4)^y(2/3)^z) = log(80.0 / 5.00)
This will give you a system of equations involving logarithms that you can solve to find the values of x, y, and z. Once you have the values of x, y, and z, you can substitute them back into one of the rate equations (e.g., Run 1) to find the rate constant (k).