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chem question- rates

Hi, please could I have help on 2aiii?
Paper: https://physicsandmathstutor.co.uk/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.co.uk%2Fdownload%2FChemistry%2FA-level%2FPast-Papers%2FCAIE%2FPaper-4%2FQP%2FJune%202013%20(v1)%20QP.pdf
Mark scheme: https://physicsandmathstutor.co.uk/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.co.uk%2Fdownload%2FChemistry%2FA-level%2FPast-Papers%2FCAIE%2FPaper-4%2FMS%2FJune%202013%20(v1)%20MS.pdf
I was confused on how we could use initial rate to work out the order of reaction with respect to HCl? The y-axis has ethyl ethanoate plotted so how can I work it out?
Thank you.

(edited 3 months ago)

Reply 1

TypicalNerd

Original post by anonymous56754

I’d use the half-life method. After one half life, [reactant] = 1/2 initial [reactant] = 0.10 M and after the second half life, [reactant] = 1/2 x 0.10 M = 0.05 M

Start by drawing a horizontal line from the y-axis at the point (0.00, 0.10) to the curve. Draw a vertical line at the point at which this line meets the curve and use it to read off the time, which is the first half life.

Next, repeat the above, but instead draw the horizontal line from (0.00, 0.05). The time read off the vertical line you should get will be the sum of the first half-life and the second half-life. Calculate the second half-life by subtracting the first off the time you have just read off it.

If the half-lives are the same, the reaction is first order. If not, it’s second. The graph is curved as opposed to linear and thus it can’t be zero-order.

Reply 2

TypicalNerd

Original post by TypicalNerd

I’d use the half-life method. After one half life, [reactant] = 1/2 initial [reactant] = 0.10 M and after the second half life, [reactant] = 1/2 x 0.10 M = 0.05 M
Start by drawing a horizontal line from the y-axis at the point (0.00, 0.10) to the curve. Draw a vertical line at the point at which this line meets the curve and use it to read off the time, which is the first half life.
Next, repeat the above, but instead draw the horizontal line from (0.00, 0.05). The time read off the vertical line you should get will be the sum of the first half-life and the second half-life. Calculate the second half-life by subtracting the first off the time you have just read off it.
If the half-lives are the same, the reaction is first order. If not, it’s second. The graph is curved as opposed to linear and thus it can’t be zero-order.

However, since you asked about initial rates, first of all, you plot a tangent to the curve at the time of interest and calculate its gradient. For the initial rate, you do this at t = 0, which is pretty difficult to do accurately. You then repeat this at the time when the initial concentration is halved.

If the initial rate is twice the rate at half the concentration, then it’s first order reaction wrt the reactant (since [reactant]initial = 2 x [reactant]later and rate α [reactant])

If the initial rate is four times the rate at half the concentration, it is second order wrt the reactant (similar reasoning, but the rate law becomes rate α [reactant]^2)