The reaction X + Y --> Z the reaction rate is for to depend only upon the concentration of X. A plot of 1/X versus time gives a straight line. What is the rate law for this reation?
To determine the rate law for the given reaction, we can use the data provided that a plot of 1/X versus time gives a straight line.
First, let's understand what the plot of 1/X versus time means. In a chemical reaction, the rate of reaction is often expressed as the change in concentration over time. In this case, it appears that the rate of reaction is directly proportional to the inverse of the concentration of X.
Now, let's define the reaction rate in terms of the concentrations of the reactants. Based on the given information, the reaction rate is only dependent on the concentration of X. Therefore, we can write the rate of reaction as:
Rate = k[X]^a
Where:
- Rate is the reaction rate,
- k is the rate constant,
- [X] is the concentration of X, and
- a is the order of the reaction with respect to X.
Since the rate of reaction is proportional to 1/X, we can rewrite the rate equation as:
Rate = k / [X]
Comparing this with the general rate equation, we can see that the order of the reaction with respect to X is 1.
Therefore, the rate law for this reaction is first-order with respect to X:
Rate = k[X]