## Order of reaction-

source : www.gardencity.k12.ny.us

## 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 = dm*^{3} mole^{-1} min^{-1} Ans.

^{3}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*^{-1}sec^{-1} Ans.

^{-1}sec

^{-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}

^{n}

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

*unit of K = [mole litre ^{-1}sec^{-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.

^{-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}]^{-1/2}sec^{-1} Ans.

^{-1}]

^{-1/2}sec

^{-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 = litre*^{2}mole^{-2}sec^{-1} Ans.

^{2}mole

^{-2}sec

^{-1}Ans.

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

### i) 2 H_{2} + 2 NO ——-> 2H_{2}O + N_{2}

### Rate = K [H_{2}][NO]^{2}

### ii) H_{2}O_{2} + 3I^{–} + 2H^{+} ——-> 2H_{2}O + I_{3}^{–}

### Rate = K [H_{2}O_{2}][I^{–}]

### iii) CH_{3}CHO ——–> CH_{4} + CO

### Rate = K [CH_{3}CHO]^{3/2}

### iv) 2NOBr ———> 2 NO + Br_{2}

### Rate = K[NOBr]^{2}

### v) 3NO ——-> N_{2}O + NO_{2}

### Rate = K [NO]^{2}

### What are the dimensions of rate constant in each case ?

### Solution )

*i) Rate = K [H*_{2}][NO]^{2}

_{2}][NO]

^{2}

*order with respect to H*_{2} =1 Ans.

_{2}=1 Ans.

*order with respect to NO =2 Ans.*

*Overall order = 1 +2= 3 Ans.*

*Rate = K [H _{2}][NO]^{2}*

*unit of K = rate / [H _{2}][NO]^{2}*

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

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

^{-1}]

^{2}sec

^{-1}= mole

^{2}litre

^{-2}sec

^{-1}Ans.

*ii) Rate = K [H _{2}O_{2}][I^{–}]*

*order with respect to H*_{2}O_{2} =1 Ans.

_{2}O

_{2}=1 Ans.

*order with respect to I*^{–} = 1Ans.

^{–}= 1Ans.

*Overall order = 1 +1= 2 Ans.*

*Rate = K [H _{2}O_{2}][I^{–}]*

*unit of K = rate / [H _{2}O_{2}][I^{–}]*

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

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

^{-1}]sec

^{-1}= mole

^{-1}litre sec

^{-1}Ans.

*iii)*

*Rate = K [CH _{3}CHO]^{3/2}*

*order with respect to CH*_{3}CHO =3/2 Ans.

_{3}CHO =3/2 Ans.

*Overall order = 3/ 2 Ans.*

*Rate = K [CH _{3}CHO]^{3/2}*

*unit of K = rate / [CH _{3}CHO]^{3/2}*

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

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

^{-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 ^{-1}sec^{-1}] / [mole litre^{-1}]^{2}*

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

^{-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 ^{-1}sec^{-1}] / [mole litre^{-1}]^{2}*

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

^{-1}]sec

^{-1}= mole

^{-1}litre sec

^{-1}Ans.