Question

The time and amount of decomposition of 0.056 M glucose at 140 degrees Celsius in an aqueous solution containing 0.35 N HCl were found to be

Time (Hr)	Glucose, remaining (Mole/Liter*10^2
0.5	5.52
2	5.31
3	5.18
4	5.02
6	4.78
8	4.52
10	4.31
12	4.11

What are the reaction order, the half-life, and the specific reaction rate of this decomposition? Can one unquestionably determine the order from the data given?

Answer 1

Decomposition of glucose

C6H12O6 + conc HCl=furfural +3H2O

Rate law gives,

Initial rate=-dCo/dt=K[glucose]^m [HCl]^n

Co=initial concentration of reactant

M,n=order of reaction with respect to glucose and hydrochloric acid respectively.

m=1,n=1

Order of reaction can also be determined graphically by plotting graphs between 1) C Vs t (straight line=zero order)

2)log C and t (straight line=first order)

3)1/C vs t ( if straight linesecond order)

Where C is concentration of glucose after time t.

By plotting graph between log C vs t

Time (Hr)        Glucose, remaining (Mole/Liter*10^-2 (C)   log C

0.5       5.52                                                                            -1.26                                                           

2          5.31                                                                             -1.27

3          5.18                                                                              -1.28

4          5.02                                                                             -1.30

6          4.78                                                                             -1.32

8          4.52                                                                               -1.34

10        4.31                                                                           -1.36

12        4.11                                                                             -1.39

Plot graph and find logC vs T is a straight line(refer image)

For first order rxn,

K=rate constant=1/t ln Co/Ct   where Co=initial concentration of glucose=0.056 M

Ct=concentration of glucose after time t

K=0.0266 hr-1

Specific reaction rate=rate of a reaction when molar concentration of each reactant is unity

For first order reaction, for A→Product

Rate=-dCA/dt=kCA

CA=concentration of A

So if CA=1, rate=K=rate constant=0.0266M/hr