Question

Urea decomposes as a first order in respect to urea and as a first order overall reaction. The decomposition of urea in a 0.16M HCl occurs according to:

    NH₂CONH₂ (aq)   +   H⁺ (aq)   +   2 H₂O (l)                             2 NH₄⁺ (aq) + HCO₃^- (aq)

When [NH₂CONH₂] = 0.250 M, the rate at 60.5°C is 8.45 × 10^-5 M/s.

What is the rate constant? What is the concentration of urea in this solution after 5.00 × 10³ sec?

What is the half life for this reaction at 60.5°C ?

Answer 1

The overall rate law is then
Rate = k[A]^1.

Here rate = 8.45 × 10^-5 M/s. and [A]= [NH₂CONH₂] = 0.250 M

Rate = k [NH₂CONH₂]

8.45 × 10^-5 M/s.=k* 0.250 M

k= 3.38*10^-4 s

What is the concentration of urea in this solution after 5.00 × 10³ sec?

For first order reaction:
or [NH₂CONH₂] = [NH₂CONH₂]₀ ∙e^(-k∙t)

Here [NH₂CONH₂]0= 0.250 M and t= 5.00 × 10³ sec

[NH₂CONH₂] = 0.250 M ∙e^(- 3.38*10^- 4s *5.00 × 10³ sec)

[NH₂CONH₂] = 0.250 M ∙e^(-1.69)

[NH₂CONH₂] = 0.046 M

What is the half life for this reaction at 60.5°C ?

t ½ = 0.693 /k

t1/2 = 0.693 / 3.38*10^-4 s

t1/2= 2050.3 s or 34.17 min