Question on rate equations

[Firechicken18]

Hello, 

Whenever I face a problem of the following type, I am always baffled as to which answer is correct. This is because of conflicting answers given by my professor, and the answer given in the answer scheme, so even I do not know why or which answer is correct.

In the question in first picture, I chose B) as the answer since the stoichiometry matches . However according to the answer scheme, the correct answer is E). When I emailed my professor regarding this, he instead made me confused even more by stating that the answer is C) and not E) or B). 

Consequently, in the question in the second picture, I was utterly confused on which answer is correct. Based on the answer scheme, the answer is D), and I do not understand why (I am not even sure whether the answer scheme is reliable due to the conflicting answers given previously).

If anyone can explain to me which is the correct answer, and more importantly WHY, that would be greatly appreciated!

[studiot]

Goodmorning Firechicken18 and welcome to ScienceForums.

Yes chemical kinetics can be confusing, especially when deciding what power of the concentration to use in a rate calculation.

The method your questions use stem from classical thermodynamic considerations of free energy with the introduction of a variable called the extent of reaction or degree of advancement of the reaction.

I will use the symbol # for this variable because it is available on the keyboard and yet leaves Roman letter free for the Chemistry.

At any stage of the reaction the rate of the reaction is defined as the time rate of change of this variable.

So

[math]Rate = \frac{{d\left[ \#  \right]}}{{dt}}[/math]

The trick comes in relating this rate to the concentrations of the reactants and products.

To be asked these questions you should have covered some sort of derivation of the following for a general reaction with reagents A and B and products C and D

[math]aA + bB \to cC + dD[/math]

[math]Rate = \frac{{d\left[ \#  \right]}}{{dt}} = \frac{1}{c}\frac{{d\left[ C \right]}}{{dt}} = \frac{1}{d}\frac{{d\left[ D \right]}}{{dt}} =  - \frac{1}{a}\frac{{d\left[ A \right]}}{{dt}} =  - \frac{1}{b}\frac{{d\left[ B \right]}}{{dt}}[/math]

 

Note that the rate is the positive of the rates of change of the products but the negative of the rates of change of the reactants (can you see why?)

 

I suspect this will be sufficient for most of your requirements.

So substituting into your question A18

[math]A = \left[ {S{O_3}} \right]\;;\;a = 1[/math]

[math]B = \left[ / \right]\;;\;b = /[/math]

[math]C = \left[ {{O_2}} \right]\;;\;c = \frac{1}{2}[/math]

[math]D = \left[ {S{O_2}} \right]\;;\;d = 1[/math]

yields

 

[math]Rate = \frac{1}{{\frac{1}{2}}}\frac{{d\left[ {{O_2}} \right]}}{{dt}} = \frac{1}{1}\frac{{d\left[ {S{O_2}} \right]}}{{dt}} =  - \frac{1}{1}\frac{{d\left[ {S{O_3}} \right]}}{{dt}}[/math]

or

[math]Rate = \frac{{2d\left[ {{O_2}} \right]}}{{dt}} = \frac{{d\left[ {S{O_2}} \right]}}{{dt}} = \frac{{ - d\left[ {S{O_3}} \right]}}{{dt}}[/math]

Which means that answer C is the correct one.

 

Can you now tackle the second one again?

 

 

Edited January 30, 2018 by studiot

[Firechicken18]

1 hour ago, studiot said:

Goodmorning Firechicken18 and welcome to ScienceForums.

Yes chemical kinetics can be confusing, especially when deciding what power of the concentration to use in a rate calculation.

The method your questions use stem from classical thermodynamic considerations of free energy with the introduction of a variable called the extent of reaction or degree of advancement of the reaction.

I will use the symbol # for this variable because it is available on the keyboard and yet leaves Roman letter free for the Chemistry.

At any stage of the reaction the rate of the reaction is defined as the time rate of change of this variable.

So

Rate=d[#]dt

The trick comes in relating this rate to the concentrations of the reactants and products.

To be asked these questions you should have covered some sort of derivation of the following for a general reaction with reagents A and B and products C and D

aA+bB→cC+dD

Rate=d[#]dt=1cd[C]dt=1dd[D]dt=−1ad[A]dt=−1bd[B]dt

 

Note that the rate is the positive of the rates of change of the products but the negative of the rates of change of the reactants (can you see why?)

 

I suspect this will be sufficient for most of your requirements.

So substituting into your question A18

A=[SO3];a=1

B=[/];b=/

C=[O2];c=12

D=[SO2];d=1

yields

 

Rate=112d[O2]dt=11d[SO2]dt=−11d[SO3]dt

or

Rate=2d[O2]dt=d[SO2]dt=−d[SO3]dt

Which means that answer C is the correct one.

 

Can you now tackle the second one again?

 

 

Thank you very much!

[studiot]

1 hour ago, Firechicken18 said:

Thank you very much!

Your are welcome.

I was assuming you would come back with more questions if you wanted to discuss the subject (or any other) further.