Explanation:
The integrated rate law for the zeroth order reaction is:
[tex][A]=-kt+[A]_0[/tex]
The integrated rate law for the first order reaction is:
[tex][A]=[A]_0e^{-kt}[/tex]
The integrated rate law for the second order reaction is:
[tex]\frac{1}{[A]}=kt+\frac{1}{[A]_0}[/tex]
Where,
[tex][A][/tex] is the active concentration of A at time t
[tex][A]_0[/tex] is the active initial concentration of A
t is the time
k is the rate constant
Answer:
- 0th: [tex]C_A=C_{A0}-kt[/tex]
- 1st: [tex]C_A=C_{A0}exp(-kt)[/tex]
- 2nd: [tex]\frac{1}{C_A}=kt+\frac{1}{C_{A0}}[/tex]
Explanation:
Hello,
For the ideal reaction A→B:
- Zeroth order rate law: in this case, we assume that the concentration of the reactants is not included in the rate law, therefore the integrated rate law is:
[tex]\frac{dC_A}{dt}=-k\\ \int\limits^{C_A}_{C_{A0}} {} \ dC_A= \int\limits^{t}_{0} {-k} \ dt\\C_A-C_{A0}=-kt\\C_A=C_{A0}-kt[/tex]
- First order rate law: in this case, we assume that the concentration of the reactant is included lineally in the rate law, therefore the integrated rate law is:
[tex]\frac{dC_A}{dt}=-kC_A\\ \int\limits^{C_A}_{C_{A0}} {\frac{1}{C_A} } \ dC_A= \int\limits^{t}_{0} {-k} \ dt\\ln(\frac{C_{A}}{C_{A0}} )=-kt\\C_A=C_{A0}exp(-kt)[/tex]
- Second order rate law: in this case, we assume that the concentration of the reactant is squared in the rate law, therefore the integrated rate law is
[tex]\frac{dC_A}{dt}=-kC_A^{2} \\ \int\limits^{C_A}_{C_{A0}} {\frac{1}{C_A^{2} } } \ dC_A= \int\limits^{t}_{0} {-k} \ dt\\-\frac{1}{C_A}+\frac{1}{C_{A0}}=-kt\\\frac{1}{C_A}=kt+\frac{1}{C_{A0}}[/tex]
Best regards.
