The decomposition of urea, (NH 2 ) 2 CO, in 0.10 M HCl follows the equation At 6

Question

The decomposition of urea, (NH2)2CO, in 0.10 M HCl follows the equation

At 65°C, k = 5.84 × 10-6 min-1 and at 75°C, k = 2.25 × 10-5 min-1. If this reaction is run at 85°C starting with a urea concentration of 0.0063 M, how many minutes will it take for the urea concentration to drop to 0.0012 M?

Using this example^ as background knowledge what is the difference between the rate of reaction and the reaction rate with respect to one component of the reaction?

Select all that apply.

Explanation / Answer

From the given data, activation energy (E) needs to be calculated which is obtained from Arhenius equation given by

K=Koe-Ea/RT , K= rate constant and T = temperature in K and E= activation energy , R = Gas Constant= 8.314 j/mol.k

At two different temperatures T1= 65+273.15=338.15 K and T2= 75+273.15= 348.15K, the rate constant K1 and   K1 are 5.84*10-6 min-1 and K K2 2.25*10-5 min-1

Ln (K2/K1)= (Ea/R)*(1/T1-1/T2)

Ln (2.25*10-5/ 5.84*10-6)= (Ea/8.314)*(1/338.15 -1/348.15)

1.348 = 8.494*10-5*(Ea/8.314)

Ea/8.314= 15878.8, Ea= 15878.8*8.314=132016.342 Joules

For calculating the rate at 85 deg.c, let it be T3= 85+273.15= 358.15K

Ln(K3/K2)= (Ea/R)*(1/T2-1/T3)= 15878.8*(1/348.15- 1/358.15) = 1.273

K3/K2= 3.57 , K3= 3.57*2.25*10-5 =8.0325*10-5 min-1      

For first order reaction, the relation between initial concentration (CAO) and concentration (CA)at any time are related as CA/CAO= e(-Kt), K is rate constant at 85 deg.c = 8.0325*10-5 min-1

Time = minutes

Given CAO= 0.0063M and CA= 0.0012, 0.0012/0.0063= e (-8.0325*10-5t)

Ln (0.0012/0.0063)= -8.0325*10-5t

-1.658 = -8.0325*10-5 t

Time t= 1.658*105/8.0325 =2*104 minutes

b) the rate of reaction is the rate with respect to the whole reaction (B). The rate of reaction is the reaction rate at that particular moment A. The rate wih respect to one component of reaction is the rate of overall reaction since although   Urea and H+ are participating, the rate is independent of H+.

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