a reaction is first order and it takes 324 minutes for the reaction to be 50% complete. How long will it take for the reaction to be 85% complete at the same temperature?
ln(No/N) = kt
ln(100/50) = k*324.
Solve for k, then substitute back into
ln(100/15) = k*t and solve for t.
it says the answer is 887 minutes. am i doing something wrong . when i use that formula i don't get 887
To determine the time it takes for the reaction to be 85% complete, we can use the concept of first-order reaction kinetics.
In a first-order reaction, the rate of reaction is proportional to the concentration of the reactant. The mathematical expression for a first-order reaction is given by the equation:
ln(A₀/A) = kt
Where:
A₀ is the initial concentration of reactant
A is the concentration of reactant at time t
k is the rate constant of the reaction
t is the time
In this case, we know that the reaction is 50% complete at 324 minutes, which means that the concentration of reactant has decreased by 50%. Let's assume the initial concentration of reactant A₀ is 1 (you can use any value as long as you are consistent). So, at 50% completion, the concentration A would be 0.5.
ln(1/0.5) = k * 324
Now, we can solve for k:
ln(2) = k * 324
k = ln(2) / 324
Given that we have determined the rate constant (k), we can use this value to find the time required for the reaction to be 85% complete.
ln(1/0.85) = (ln(2) / 324) * t
Now, we can solve for t:
t = [ln(1/0.85)] / [(ln(2) / 324)]
Simply calculate this expression to find the time it takes for the reaction to be 85% complete.