Calculating rate constant from a set of data?

[SeaNanners]

Homework Statement

For a reaction, A + H₂O --> B + C

We're given that d[A]/dt = k[A]ⁿ[H₃O⁺]^m

And also a table of [A] vs time at T₁ and pH 1, pH 2; as well as [A] vs time at T₂ and the same pH 1 and 2. From this data, we're to find pseudo-n-order rate constants, and then n itself. Next, the activation energy at each pH, and then the value of k at each temperature. Finally, we need the activation energy for the overall reaction.

The Attempt at a Solution

I'm not really familiar with this kind of problem, unfortunately. I started by plotting ln[A] vs. time, and got a straight line, from which I concluded that it was 1st order relative to [A]. I found the slopes of each of these 4 lines (T₁, pH 1; T₁, pH 2; etc), and I determined that the negative of each of these was the pseudo-n-order constants.

That was the first two parts. I was also able to find the activation energy for each pH, by using the formula ln(k₂/k₁) = E_a(1/T₂ - 1/T₁). I used the two pseudo equation k values at each temperature to calculate these, and got 2 activation energy values, which were about 1000 J off from each other.

Here's where I'm stuck. I can't think of any way to go about calculating k for each temperature. I thought about using k = Ae^-E_a/RT, but I don't know A, for one, and the activation energies I just calculated are separate for each pH, not temperature, so that doesn't help me much either.

Thanks for any help.

 

[Chestermiller]

Homework Statement

For a reaction, A + H₂O --> B + C

We're given that d[A]/dt = k[A]ⁿ[H₃O⁺]^m

And also a table of [A] vs time at T₁ and pH 1, pH 2; as well as [A] vs time at T₂ and the same pH 1 and 2. From this data, we're to find pseudo-n-order rate constants, and then n itself. Next, the activation energy at each pH, and then the value of k at each temperature. Finally, we need the activation energy for the overall reaction.

The Attempt at a Solution

I'm not really familiar with this kind of problem, unfortunately. I started by plotting ln[A] vs. time, and got a straight line, from which I concluded that it was 1st order relative to [A]. I found the slopes of each of these 4 lines (T₁, pH 1; T₁, pH 2; etc), and I determined that the negative of each of these was the pseudo-n-order constants.

That was the first two parts. I was also able to find the activation energy for each pH, by using the formula ln(k₂/k₁) = E_a(1/T₂ - 1/T₁). I used the two pseudo equation k values at each temperature to calculate these, and got 2 activation energy values, which were about 1000 J off from each other.

Here's where I'm stuck. I can't think of any way to go about calculating k for each temperature. I thought about using k = Ae^-E_a/RT, but I don't know A, for one, and the activation energies I just calculated are separate for each pH, not temperature, so that doesn't help me much either.

Thanks for any help.

Once you had that n = 1 from the plots of ln(A) vs time, you could have determined the slopes of these four plots. These would have been k[H30]^m. From the pH's you could have calculated the [H30]'s. If, at each temperature, you plotted on a log-log plot the values of k[H30]^m versus [H30], the slopes of these two plots (at T1 and T2) should have been m, and you should have gotten the same values for m. You could then go back and determine k at each temperature by dividing of k[H30]^m by [H30]^m. This would give you what you need to determine the pre-exponential factor and the activation energy, both of which should be independent of temperature and concentration.