Order of reaction numerical part 5

Order of reaction-

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Order of reaction-

Q 1)

i) If concentrations  of  A and B are expressed in terms of mole dm^-3 and time in min. Calculate the units of  rate constant for the following reaction-

A + B ———>AB

ii) What are the units for a zero order reaction? (concentrations are expressed in mole / litre and time in seconds)

Solution)

Reaction,

A + B ———>AB

Rate       [A][B]

Rate = K[A][B]

mole dm ^-3/min = K [mole dm^-3]²

unit of K = mole dm^-3 /min (mole dm^-3)²

 unit of K = dm³ mole^-1 min^-1 Ans.

ii) For zero order reaction,

Rate = K

dx/dt = K

unit of K =( mole / litre)/sec

Unit of K = mole  litre^-1sec^-1 Ans.

Q2) Write the units of the rate constant for a n^th order reaction . Deduce from this the units of rate constant for ,

i) half order reaction

ii) 3/2 ^th order reaction

iii) third order reaction = K[A]ⁿ

Solution)

Rate = K[A]ⁿ

mole litre^-1/sec. = K [mole litre^-1]ⁿ

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]ⁿ

unit of K =  [mole litre^-1]^{(1-n )}sec^-1

i) If n=1/2, then

unit of K =  [mole litre^-1]^(1-n)sec^-1

unit of K =  [mole litre^-1]^(1-1/2) sec^-1

unit of K =  [mole litre-^-1]^1/2 sec^-1 Ans.

ii) If n=3/2, then

unit of K =  [mole litre^-1]^{(1 -n)}sec^-1

unit of K =  [mole litre^-1]^{(1- 3/2)} sec^-1

unit of K =  [mole litre^-1]^-1/2sec^-1 Ans.

iii) If n=3 , then

unit of K =  [mole litre^-1]^{(1 -n)}sec^-1

unit of K =  [mole litre^-1]^{(1 -3)} sec^-1 =  [mole litre^-1]^-2 sec^-1

Unit of  K = litre²mole^-2sec^-1 Ans.

Q3 ) State the order  with respect to each reactant and overall order for the following reactions-

i) 2 H₂ + 2 NO ——-> 2H₂O + N₂

Rate = K [H₂][NO]²

ii) H₂O₂ + 3I^– + 2H⁺ ——-> 2H₂O + I₃^–

Rate = K [H₂O₂][I^–]

iii) CH₃CHO ——–> CH₄ + CO

Rate = K [CH₃CHO]^3/2

iv) 2NOBr ———> 2 NO + Br₂

Rate = K[NOBr]²

v) 3NO ——-> N₂O + NO₂

Rate = K [NO]²

What are the dimensions of rate constant in each case ?

Solution )

i)  Rate = K [H₂][NO]²

order with respect to H₂ =1 Ans.

order with respect to NO =2 Ans.

Overall order = 1 +2= 3 Ans.

Rate = K [H₂][NO]²

unit of K = rate / [H₂][NO]²

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]³

   unit of K = [mole litre^-1]² sec^-1 = mole ² litre ^-2 sec^-1 Ans.

ii)  Rate = K [H₂O₂][I^–]

order with respect to H₂O₂ =1 Ans.

order with respect to I^– = 1Ans.

Overall order = 1 +1= 2 Ans.

Rate = K [H₂O₂][I^–]

unit of K = rate / [H₂O₂][I^–]

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]²

   unit of K = [mole litre^-1 ]sec^-1 = mole ^-1 litre  sec^-1 Ans.

iii)

Rate = K [CH₃CHO]^3/2

order with respect to CH₃CHO =3/2 Ans.

Overall order = 3/ 2 Ans.

Rate = K [CH₃CHO]^3/2

unit of K = rate / [CH₃CHO]^3/2

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]^3/2

   unit of K = mole^-1/2 litre^1/2 sec^-1 Ans.

iv)

Rate = K [NOBr]²

order with respect to NOBr =2 Ans.

Overall order =  2 Ans.

Rate = K [NOBr]²

unit of K = rate /[NOBr]²

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]²

   unit of K = [mole litre^-1 ]sec^-1 = mole ^-1 litre  sec^-1 Ans.

v)

Rate = K [NO]²

order with respect to NO =2 Ans.

Overall order =  2 Ans.

Rate = K [NO]²

unit of K = rate /[NO]²

unit of K = [mole litre^-1sec^-1] / [mole litre^-1]²

   unit of K = [mole litre^-1 ]sec^-1= mole ^-1 litre  sec^-1 Ans.