The positive constant k is a measure for the speed of the reaction. Assume that

Question

The positive constant k is a measure for the speed of the reaction. Assume that initially there are 5 moles of reactant A and 2 moles of reactant B.

a. Show that the difference A - B is constant in time.

b. Use (a) to eliminate the unkown B in the first equation of (1) and write down an initial value problem for A.

My answer: A' = -kA^2+3kA

c. It was measured that 4 moles of reactant A remained after the reaction had progressed for 1 second. What amounts of reactants A and B will be left after 4 seconds.                 

Only need answer for part C.

Explanation / Answer

A' = -kA^2+3kA

upon integrating u wil get

ln [(A/A-3] =3kt + C

at t=0 A =5 using this condition we get

C = 0.916

ln [(A/A-3] =3kt + 0.916

at t =1 A =4

ln 4 = 3k+ 0.916

k = 0.157

ln [(A/A-3] =0.47t + 0.916

at t =4sec

A/(A-3) = 16.38

A = 3.19 moles

A-B = 3

B =0.19 moles

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