A second-order reaction has a rate constant of 1.65 M–1 s–1. If the initial reactant concentration is 1.0 M, calculate the time (in seconds) required for the reaction to become 90% complete.
i got 0.06734 seconds but that's incorrect i have no idea what i am doing wrong! HELP!!!!
The equation is
[1/(A)] - [1/(Ao)] = kt
Ao = 1
A = 0.1 if it is to be 90% complete.
k is given.
Solve for t.
I plugged in your number for t and apparently you substituted 0.9 for (A) but if it's 90% complete, that means A is 0.1. Try that, see if it doesn't work.
The way DrBob222 did is correct.
To solve this problem, we can use the second-order integrated rate equation:
1/[A]t - 1/[A]0 = kt
Where:
[A]t is the reactant concentration at time t
[A]0 is the initial reactant concentration
k is the rate constant
t is the time
In this case, the reaction is considered 90% complete when the reactant concentration is reduced to 10% of its initial concentration ([A]t = 0.10[A]0).
Using this information, let's substitute the known values into the integrated rate equation and solve for t:
1/0.10[A]0 - 1/[A]0 = k * t
Simplifying further:
10/[A]0 - 1/[A]0 = k * t
Now we can substitute the given values:
k = 1.65 M^(-1) s^(-1)
[A]0 = 1.0 M
Plugging these values into the equation:
10/1.0 - 1/1.0 = 1.65 * t
Simplifying further:
10 - 1 = 1.65 * t
9 = 1.65 * t
Dividing both sides by 1.65:
t = 9 / 1.65
t ≈ 5.45 seconds (rounded to two decimal places)
Therefore, the time required for the reaction to become 90% complete is approximately 5.45 seconds.
To solve this problem, we can use the integrated rate equation for a second-order reaction:
1/[A]t - 1/[A]0 = kt
where [A]t represents the concentration of reactant A at time t, [A]0 represents the initial concentration of reactant A, k is the rate constant, and t is the reaction time.
In this case, we know that [A]t = 0.10 M (90% of the initial concentration [A]0 = 1.0 M). We also know the rate constant k = 1.65 M^(-1) s^(-1). Plugging in these values into the integrated rate equation, we can solve for t:
1/0.10 - 1/1.0 = (1.65) t
Simplifying this equation gives:
10 - 1 = 1.65t
9 = 1.65t
Now, to find t, we can divide both sides of the equation by 1.65:
t = 9 / 1.65
t ≈ 5.4545 s (rounded to 4 decimal places)
Therefore, the time required for the reaction to become 90% complete is approximately 5.4545 seconds.