The rate of a reaction A + 2B --> products is determined. When the concentration of A is 1.0 M, the rate of the reaction is 0.50 M/s. When the concentration of A is 0.50 M, the rate is 0.25 M/s. From this data, you can determine:
a.
that the reaction is second order in A.
b.
that the reaction is 0 order in A.
c.
that the reaction is 1/2 order in A.
d.
that the reaction is first order in A.
e.
nothing about the order of the reaction.
rate1 = k1(A)^x
---------------
rate2 = k1(A)^x
You know k1 and k2 are the same so they cancel.
rate1 = 0.50; (A) = 1.0M
rate2 = 0.25; (A) = 0.50
Substitute
0.50 = (1.0)^x
--------------
0.25 = (0.50)^x
Solve.
2 = 2^x
So x must be what?
1.7
To determine the order of the reaction, we need to examine how the rate of the reaction changes with respect to the concentration of reactant A.
At the given concentrations of A (1.0 M and 0.50 M), we have the corresponding rates of the reaction (0.50 M/s and 0.25 M/s).
Let's compare these values by calculating the rate ratios:
Rate ratio = (rate at 0.50 M A) / (rate at 1.0 M A)
Rate ratio = 0.25 M/s / 0.50 M/s
Rate ratio = 0.50
Now, let's examine the ratio between the concentration of A at 0.50 M and the concentration at 1.0 M:
Concentration ratio = (concentration at 0.50 M A) / (concentration at 1.0 M A)
Concentration ratio = 0.50 M / 1.0 M
Concentration ratio = 0.50
If the rate ratio is equal to the concentration ratio raised to some power, then we can determine the order of the reaction with respect to A. Let's calculate the power to check:
Rate ratio / Concentration ratio = 0.50 / 0.50
Rate ratio / Concentration ratio = 1
Since the rate ratio divided by the concentration ratio is equal to 1, it indicates that the reaction is first order in A. Therefore, the correct answer is:
d. that the reaction is first order in A.