To determine the overall order of the reaction given by the equation
2X+Y⟶A+B, we need to analyze how changes in the concentrations of reactants
[X] and
[Y] affect the initial rate of formation of
A.
The rate law for this reaction can be represented as:
Rate
=k[X]m[Y]nWhere:
k is the rate constant,
m is the order of the reaction with respect to
X,
n is the order of the reaction with respect to
Y,
the overall order of the reaction is
m+n.
From the data provided:
Experiment 1:
[X]=0.2,[Y]=0.2, Rate
=12.0×10−3Experiment 2:
[X]=0.6,[Y]=0.4, Rate
=14.4×10−2=144.0×10−3Experiment 3:
[X]=0.6,[Y]=0.8, Rate
=5.76×10−1=576.0×10−3Experiment 4:
[X]=0.8,[Y]=0.2, Rate
=48.0×10−3 To find
m (the order with respect to
X ):
Comparing Experiment 1 and Experiment 4 where
[Y] is constant:
‌‌| ‌ Rate ‌4 |
| ‌ Rate ‌1 |
=(‌)m‌‌=(‌)m‌4=(4)m⟶m=1To find
n (the order with respect to
Y ):
Comparing Experiment 2 and Experiment 3 where
[X] is constant:
‌‌| ‌ Rate ‌3 |
| ‌ Rate ‌2 |
=(‌)n‌‌| 576.0×10−3 |
| 144.0×10−3 |
=(‌)n‌4=(2)n⟶n=2The overall order of the reaction is
m+n=1+2=3. Therefore, the correct option is: