For the simple decomposition reactionAB(g)→ A(g) + B(g)Rate =k[AB]2 and k=0.2 L/mol*s . How long will it takefor [AB] to reach 1/3 of its initial concentration 1.50 mol/L?

Respuesta :

Answer:

6.66 s will it take for [AB] to reach 1/3 of its initial concentration 1.50 mol/L.

Explanation:

[tex]Rate = k[AB]^2[/tex]

The order of the reaction is 2.

Integrated rate law for second order kinetic is:

[tex]\frac{1}{[A_t]} = \frac{1}{[A]_0}+kt[/tex]

Where, [tex][A_0][/tex] is the initial concentration  = 1.50 mol/L

[tex][A_t][/tex] is the final concentration  = 1/3 of initial concentration = [tex]\frac{1}{3}\times 1.50\ mol/L[/tex] = 0.5 mol/L

Rate constant, k = 0.2 L/mol*s

Applying in the above equation as:-

[tex]\frac{1}{0.5} = \frac{1}{1.50}+0.2t[/tex]

[tex]\frac{1}{1.5}+0.2x=\frac{1}{0.5}[/tex]

[tex]t = 6.66\ s[/tex]

6.66 s will it take for [AB] to reach 1/3 of its initial concentration 1.50 mol/L.