The decomposition reaction, X → products, has rate constant k = 0.00437 mol−1 L s−1. How long will it take for the decomposition to be 75% complete, if the initial concentration of X is 1.85 mol L−1 ?
got 423s by doing ln(.25)(1.85)/0.00437, but thats wrong
I couldn't pull up the second link. From what you have written here I think you must have used a first order equation. From a scare glimpse I think this is a second order equation so put the date into the integrated form of a second order and try that.
how do you know that this is a second order equation?
From the units. The units are different for zero, first, second, third order etc. Pull up Google, look at Wikipedia. They tell you the units for which order.
For second order that is 1/A + 1/Ao = kt
hmm still not getting the right ans. i did (1/.25 - 1/1.85)1/.00437. what am i doing wrong?
I think we goofed. I wrote the equation wrong. It should be
1/[A] - 1/([A]o = kt.
Second, from the problem [A]o = 1.85. But [A] = 1.85*0.25 = 0.4625
Try that.
To determine how long it will take for the decomposition to be 75% complete, we can use the concept of first-order reaction kinetics and the equation for the reaction rate.
The equation for a first-order reaction is given by:
Rate = -k[A]
Where:
- Rate is the rate of change of concentration of the reactant (in this case, X)
- k is the rate constant of the reaction
- [A] is the concentration of X at any given time
The negative sign indicates that the concentration of X decreases over time.
Now, we can rearrange the equation to solve for time (t):
Rate = -k[A]
Rate = d[A]/dt
Therefore,
d[A]/dt = -k[A]
To integrate this equation, we can separate the variables:
1/[A] d[A] = -k dt
Now, we can integrate from the initial concentration of X ([A]₀ = 1.85 mol L⁻¹) to the final concentration of X ([A]):
∫ [A]₀ to [A] 1/[A] d[A] = -k ∫ 0 to t dt
ln([A]) - ln([A]₀) = -k t
Now, we can rearrange the equation to solve for t:
ln([A]/[A]₀) = -k t
From the given problem, we know that the decomposition is 75% complete, which means that the concentration of X is reduced to 25% of the initial concentration. Therefore, [A]/[A]₀ = 0.25.
ln(0.25) = -k t
Now, we can plug in the given rate constant (k = 0.00437 mol⁻¹ L s⁻¹) and solve for t:
t = ln(0.25) / (-k)
t = ln(0.25) / (-0.00437 mol⁻¹ L s⁻¹)
Using a calculator, we can evaluate the natural logarithm (ln) of 0.25 to find:
t ≈ 158.33 s
Therefore, it will take approximately 158.33 seconds (s) for the decomposition to be 75% complete.