Chemical Kinetics Tutorial
Creator of Tutorial: rvc

Question

Tutorials · Answer

To determine the rate of the reaction we have the rate law. A rate law is a mathematical equation that describes the progress of the reaction. Rate law is determined experimentally.There are 2 different forms of the law:  
A. Differential rate law 
B. Integrated rate law

$\huge\color{blue}{\bigstar}\color{red}{\rm Differential~Rate~Law}\color{blue}{\bigstar}$

The differential rate law relates the rate of reaction to the concentrations of the various species in the system.

Each rate law contains a constant, $\rm k$, called the rate constant. The units for the rate constant depend upon the rate law, because  the rate always has units of mole $\rm L^{-1}sec^{-1}$ and the concentration always has units of mole $\rm L^{-1}$.

$\begin{array}{|c|c|c|}
\hline
\rm{Order}&\rm{Explanation}&\rm{Differential~Rate~Law}\
\hline
\rm{Zero}~&~\rm{For~a~zero-order~reaction,~\ the~ rate~ of~ reaction~ is~ a~ constant. }~&~\rm{ r = k} \
\hline
\rm{First}~&~\rm{Rate~of~reaction~ proportional\~to~con~of~one~of~the~reactants.}~&~\rm{r = k [A]}\
\hline
\rm{Second}~&~\rm{Rate~of~reaction~is\~proportional~to~square~of\ concentration~of~one~\of~the~ reactants}~&~\rm{r=k[A]^2}~\
\hline
 \end{array}$
<hr class="bbcode_rule" />

$\begin{array}{|c|c|c|}
\hline
\Large\rm{\color{darkblue}{Order}}&\Large\rm{\color{darkblue}{Unit~of~k}}\
\hline
\rm{Zero}&\rm{mole \cdot L^{-1} \cdot   sec^{-1}. }\
\hline
\rm{First}&\rm{sec^{-1}. }\
\hline
\rm{Second}&\rm{ L \cdot mole^{-1} \cdot  sec^{-1}}\
\hline
 \end{array}$

Tutorials · Answer

$\huge\color{blue}{\bigstar}{\rm\color{red} {Integrated~ Rate~ Law}}\color{blue}{\bigstar}$

The differential rate law is directly proportional to $\rm conc^n$ of the reactants.That is, the rate is proportional to a derivative of a concentration.

Consider the reaction $\rm A \rightarrow B$

The rate of reaction, r, is given by: $\rm r=-\Large\frac{d[A]}{dt}$

Suppose this reaction obeys a first order rate law: $\rm r=k[A]$

Tutorials · Answer

This rate law can also be written as: $\rm r=-\large\frac{d[A]}{dt}=k[A]$

Well I will write the integrated rate law directly $\large \ddot\smile$

Tutorials · Answer

$\begin{array}{|c|c|c|}
\hline
\rm\Large{Reaction~order}&\rm\Large{Differential~law}&\Large\rm{Integrated~law}\
\hline
\rm\large{Zero}&\rm\large{-\large\frac{d[A]}{dt}=k}&\rm\large{[A] = [A]_0 - k t}\
\hline
\rm\large{First}&\rm\large{-\large\frac{d[A]}{dt}=k[A]}&\rm\large{[A] = [A]_0 e^{- k t}}\
\hline
\rm\large{Second}&\rm\large{-\large\frac{d[A]}{dt}=k[A]^2}&\rm\large{[A] =\large\frac{[A]_0}{1 + k t [A]_0}}\
\hline
\end{array}$

Ashely · Answer

thanks