The following reaction was monitored as a function of time: AB--->A+B
A plot of 1/[AB] versus time yields a straight line with slope 5.2×10−2 .
If the initial concentration of is 0.240M , and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s?
To determine the concentrations of A and B after 75 seconds, we need to use the data obtained from the given plot. Let's break down the process step-by-step:
1. The given reaction is AB → A + B, where AB is the reactant and A and B are the products.
2. We are given a plot of 1/[AB] vs. time, which yields a straight line with a slope of 5.2×10−2. The plot shows the inverse of the concentration of AB.
3. From the plot, we can see that the rate of the reaction is proportional to the concentration of AB. The rate equation for a first-order reaction is defined as: rate = k[AB], where k is the rate constant.
4. The slope of the plot is equal to -k, the negative value of the rate constant. In this case, the slope is -5.2×10−2.
5. We can calculate the rate constant (k) by taking the negative of the slope: k = -(-5.2×10−2) = 5.2×10−2.
6. Now, let's use the rate constant (k) to determine the reaction rate at any given time. The rate equation, as mentioned earlier, is rate = k[AB].
7. We know the initial concentration of AB is 0.240 M. Let's substitute the values in the rate equation:
rate = (5.2×10−2)(0.240) = 1.248×10−2 M/s.
8. From the given information, we need to find the concentrations of A and B after 75 seconds. Since the initial concentration of AB is 0.240 M and it is decreasing with time, we can assume that the reaction is going to completion.
9. To find the amount of AB remaining after 75 seconds, we can multiply the initial concentration by the fraction remaining after that time period:
[AB] remaining = (1 - Fraction reacted) × Initial concentration.
10. The fraction reacted can be found by integrating the rate equation:
Fraction reacted = ∫(0 to t) (k dt) = ∫(0 to 75 s) (5.2×10−2 dt) = (5.2×10−2)(75) = 3.9.
11. Using the fraction reacted, we can find the concentration of AB remaining:
[AB] remaining = (1 - Fraction reacted) × Initial concentration = (1 - 3.9) × 0.240 M = -2.16 M.
12. Since the concentration cannot be negative, we can conclude that the reaction is complete, and there is no AB remaining after 75 seconds.
13. Finally, since AB completely reacts to form A and B, the concentrations of A and B after 75 seconds will be equal to the initial concentration of AB, which is 0 M and 0 M, respectively.
Therefore, after 75 seconds, the concentrations of A and B are 0 M and 0 M, respectively.