Before I go to bed, I have this burning question I cant seem to comprehend.
Kinetics is such a wierd topic, sometimes it is doable, sometimes it is just impossible.
I have this question from past-year paper without answers,
NaN3 decompose to give N2 and Na.
Then they give us a table of Time/s and Vol. of N2 evolved/dm3.
After plotting the graph, I have a 2nd order reaction because there is no constant half-life and no constant gradient.
Then question asked ' HENCE, deduce rate constant, stating appropriate units'.
Now I am not sure if I can just take from the gradient at a point from the graph to get the rate and then substitute into the rate equation, rate = k [NaN3]^2 to find k.
But I realize if I were to do it this way, my units of k will not be mol-1dm3s-1, because the y-axis of the graph is a volume in dm3 only.
What assumptions do I have when calculating? I am missing something here I am sure, but just not sure what.
2) Another thing, if question gives table of values, and ask to plot graph to prove that reaction is first order. But the graph just dont have a constant value, what can I do to the graph? I am very sure my graph is correct. I would love to give the data here but I thought I should consult the idea of working out a question like this before giving the nitty-gritty details.
>>> NaN3 decompose to give N2 and Na.
Then they give us a table of Time/s and Vol. of N2 evolved/dm3.
After plotting the graph, I have a 2nd order reaction because there is no constant half-life and no constant gradient.
Then question asked ' HENCE, deduce rate constant, stating appropriate units'.
Now I am not sure if I can just take from the gradient at a point from the graph to get the rate and then substitute into the rate equation, rate = k [NaN3]^2 to find k.
But I realize if I were to do it this way, my units of k will not be mol-1dm3s-1, because the y-axis of the graph is a volume in dm3 only.
What assumptions do I have when calculating? I am missing something here I am sure, but just not sure what. <<<
Firstly, at constant temperature, volume is directly proportional to no. of moles.
Secondly, to check for a constant half-life in a "[product]" against "time" graph, you must use the y-axis intervals of 1/2a, 3/4a and 7/8a, in contrast to (if it were a usual [reactant] against time graph) 1/2a, 1/4a, 1/8a.
Thirdly, are you given the rate equation by the question? or does the quesiton provide you with the mechanism or elementary steps for the reaction? In other words, is "rate = k [NaN3]^2" a stated given, or your own assumption?
Fourthly, if you're indeed given the rate equation, then yes, you can substitute values of rate and molarity OF REACTANT into the rate equation to obtain the value of k. Note that if you're given the volume (hence molarity) of product, you can work out the molarity of reactant.
>>> 2) Another thing, if question gives table of values, and ask to plot graph to prove that reaction is first order. But the graph just dont have a constant value, what can I do to the graph? I am very sure my graph is correct. I would love to give the data here but I thought I should consult the idea of working out a question like this before giving the nitty-gritty details. <<<
See second point above.
For first order reaction, there are 3 possible axes, each with different graph shape :
"y-axis" against "x-asis"
1) rate against [reactant] - straight diagonal line
2) [reactant] against time - concave hill downwards
3) [product] against time - convex hill upwards
Qn 1:
I am not given rate equation. I derive the rate equation from the
graph I plot. I plotted the graph and I realized I have 2nd-order
reaction. I still am clueless how to find rate constant. Because at
different points on the graph, I have different rate constants. ( I
find gradient at a particular point of the graph to get the rate in
moldm-3 )
Should rate constant for a 2nd-order reaction be the same?.
Qn 2:
>>>"to check for a constant half-life in a "[product]"
against "time" graph, you must use the y-axis intervals of 1/2a,
3/4a and 7/8a, in contrast to (if it were a usual [reactant]
against time graph) 1/2a, 1/4a, 1/8a."
Do you mean that a refers to the initial concentration right from the start?
So I would need to find half-life from 1/2a to 1/4a,
another half-life from 3/4a to 3/8a
and so on... ??
>>> Qn 1:
I am not given rate equation. I derive the rate equation from the graph I plot. I plotted the graph and I realized I have 2nd-order reaction. I still am clueless how to find rate constant. Because at different points on the graph, I have different rate constants. ( I find gradient at a particular point of the graph to get the rate in moldm-3 )
Should rate constant for a 2nd-order reaction be the same?. <<<
Rate constant, by definition, is a constant (ie. fixed value) at any given temperature. In point of fact, Kc, Ksp, Kp, Ka, Kb, Kw, etc, are all constants because k is a rate constant at any given temperature. (Kinetics and Equilibria are actually intimately related, although most JC students don't appreciate this, because their JC teachers don't encourage them to truly understand and appreciate Chemistry, but to just follow dogmatic instructions for Chemistry.)
The decomposition of sodium azide to nitrogen gas involves the formation of a stable diatomic nitrogen molecule from a triatomic nitrogen azide ion, N3-. To do so would indeed require (stoichiometry) 2 sodium azide ions coming together in a redox reaction to form 3 nitrogen molecules and 2 sodium atoms. And since in order to reduce sodium ions to sodium metals we must involve lone electrons, we would expect photolytic cleavage to form nitrogen free radicals are involved.
And since the highly reactive free radical must be involved in the fast step, the formation of the free radical must be the slow step, the rate determining step.
Therefore, the rate determining elementary step is indeed the bimolecular reaction of 2 sodium azide formula units as the reactants, and thus it is indeed a 2nd order reaction, and the rate equation must be rate = k [NaN3]^2.
The above thought process, while not required at the JC level when attempting Kinetics questions, is encouraged because it helps you to see how all aspects of Chemistry are interconnected, and helps you to truly understand, appreciate and enjoy Chemistry.
Which provides support that your graph, and your interpretation of it, is indeed correct - it's a second order reaction.
For second order reactions, the half-life is not constant, but can still be calculated by the formula t(1/2) = 1 / (k [A]0), where the denominator is rate constant k multiplied by initial molarity of reactant.
For all reactions, including 2nd order, the rate constant for the reaction, k, can indeed be obtained by substituting any pairs of values (rate and molarity of reactant) from the table provided by the question, into the rate equation.
The perhaps-somewhat-annoying aspect of this question, is that you're given volume of product instead of reactant. Therefore, using stoichiometry of the overall equation, work out the volumes, proportional to moles, hence proportional to molarity, of the reactant. Hence, you can work out the rate of reaction based on how fast the reactant is being used up, and together with the molarity of reactant, substituted into the rate equation, gives you the value of rate constant k.
>>>Q2 "to check for a constant half-life in a "[product]" against "time" graph, you must use the y-axis intervals of 1/2a, 3/4a and 7/8a, in contrast to (if it were a usual [reactant] against time graph) 1/2a, 1/4a, 1/8a."
Do you mean that a refers to the initial concentration right from the start?
So I would need to find half-life from 1/2a to 1/4a,
another half-life from 3/4a to 3/8a
and so on... ?? <<<
Since your graph is based on product, a is the FINAL molarity of product. The initial molarity, is of course zero. (Doncha love these "product" instead of "reactant" sadistic kinetic qns? Woot!)
Half life t1 = t2 = t3
t1 = 0 to 1/2 a
t2 = 1/2 a to 3/4 a
t3 = 3/4 a to 7/8 a