Kinetics ( Rate of reaction)

Question

Sulfur concentration of desulphurised liquid pig iron using a basic slag at 1500 ºC is given below.

 

1. Calculate the rate of reaction

2. Prove that the desulphurisation reaction is a 1st order reaction. Calculate the rate constant of the reaction.

3. Calculate the reaction rate at the 30th minute.

 

Time (minute)                    0        10        20       30          40

Sulfur concentration (%)    0.8      0.67     0.56    0.47        0.4

Answer 1

To obtain an average rate of reaction, one can look at initial concentration of 0.8% and the final concentration of 0.4% and the overall time of 40 minutes.  The ∆concentration/∆time = rate = 0.4%/40min = 0.01%/min = rate

It is first order because as the concentration changes from 0.8 to 0.67 to 0.56 etc. ,the rate stays the same, so it is directly related to the concentration.  For example from 0 to 10 min rate is 0.13/10 min when conc. is 0.8 so 0.13/0.8 = 0.16.  In the next time epoch, the conc. is 0.67 and goes to 0.56 so you have a rate of 0.11/10 min and 0.11/0.67 = 0.16, the same as previously.  This shows it is first order with respect to the reactant.

rate = k[ ]
0.01 = k [0.8%]
k = 0.0125

 

Reaction rate at 30 minutes = (0.8 - 0.47)/30 min = 0.33%/30 min = 0.011%/min (virtually same as average rate of 0.01%/min).