• $\rArr$ Rate of disappearance of reactants

or

• $\rArr$ Rate of appearance of products

• $=-\frac{\Delta[ClO^-]}{\Delta t}$ $=-\frac{\Delta[Br^-]}{\Delta t}$

• $\frac{\Delta[ClO^-]}{\Delta t}$ $=\frac{c_2 - c_1}{t_3 - t_1}=\frac{-ve}{+ve}=-ve$

• $=\frac{\Delta[BrO^-]}{[\Delta t]}$ $=\frac{\Delta[Cl^-]}{\Delta t}$ $=\frac{+ve}{+ve}=+ve$

• aA+bB+……$\rarr pP+qQ+….$

• A,B,C..$\quad$ $\rArr$ reactants

• a b c $\quad$ $\rArr$ stoichiometric coefficients

• P,Q,R $\quad$ $\rArr$ products

• p q r $\quad$ $\rArr$ stoichiometric coefficients

• For reactants - $\quad$ $\nu$ $\quad$is $\quad$-ve

• For products - $\quad$ $\nu$ $\quad$is $\quad$+ve

• $\nu_A$ $\quad$ = $\quad$ -a

• $\nu_B$ $\quad$ = $\quad$ -b

• $\nu_p$ $\quad$ = $\quad$ p

• $\nu_q$ $\quad$ = $\quad$ q

• $aA+bB \rarr pP+qQ$

• Degree of advancement of a reaction $\rightarrow$ $\xi$

• $n_i=n_i^0 + \nu_i \xi……(1)$

• $n_i$ number of moles of no chemical species i

• $n_i^0=$ the number of moles of the chemical species ‘i’ when $\xi= \leftarrow$ degree of advancement 0

• $\nu_i$ stoichiometric coefficients

• $n_i=n^0_i + \nu_i \xi……(1)$

• Differentiate (1) with respect to time

• $\frac{dn_i}{dt}$= $\frac{dn_i^0}{dt}+\frac{d(\nu_i \xi)}{dt}……(2)$

• Because $n_i^0$ is a constant , hence $\frac{dn_i^0}{dt}= 0$

• $\frac{d(\nu_i \xi)}{dt}=\nu_i \frac{d\xi}{dt}$

• $\frac{dn_i}{dt}=\nu_i \frac{d\xi}{dt}$

• $\frac{d\xi}{dt}=\frac{1}{\nu_i}\frac{dni}{dt}$…….(3)

• Rate of advancement of the reaction $\rightarrow$ rate of the reaction

• $aA+bB \rarr pP+qQ$

• $n_i=n^0_i + \nu_i \xi……(1)$

• $i \rarr A$

• $n_A=n_A^0+\nu_A \xi$

• $n_A=n^0_A - a \xi$

• $\frac{dn_A}{dt}=\frac{dn_A^0}{dt} + \frac{d(-a \xi)}{dt}$

• General reaction

• $\frac{dn_A}{dt}=-a\frac{d\xi}{dt}$

• $\frac{d\xi}{dt}=-\frac{1}{a}\frac{dn_A}{dt}$

• Rate of reaction in terms of the change in the number of moles of ‘A’

• $i\rarr B$

• $n_B=n^0_B + \nu_B \xi$

• $n_B=n^0_B - b \xi$

• $\frac{dn_B}{dt}=\frac{dn^0_B}{dt} + \frac{d(-b \xi)}{dt}$

• $\frac{dn_B}{dt}=-b\frac{d\xi}{dt}$

• $\frac{d\xi}{dt}=-\frac{1}{b} \frac{dn_B}{dt}$

• $aA+bB \rarr pP+qQ$

• $i\rarr P$

• $n_p=n^0_P+ \nu_P \xi$

• $n_p=n^0_P+ p \xi$

• $\frac{dn_P}{dt}$=$\frac{dn^0_P}{dt}+\frac{d(P\xi)}{dt}$

• $\frac{dn_P}{dt}=P\frac{d\xi}{dt}$ $∴ \frac{d\xi}{dt}=\frac{1}{P}\frac{dn_P}{dt}$

• $\frac{d\xi}{dt}$ $=-\frac{1}{a}\frac{dn_A}{dt}=-\frac{1}{b}\frac{dn_B}{dt}$*

• $=\frac{1}{p}\frac{Qn_p}{dt}=\frac{1}{q}\frac{dn_Q}{dt}$

• The stoichiometric coefficients is always positive

Reactant $\quad$ : $\quad$ Put a ‘-ve’ sign

$\qquad\qquad\quad$ before the coefficient

Product $\quad$ : $\quad$ Put a ‘+ve’ sign

• $2N_2O_5\rarr4NO_2 + O_2$

• $\frac{d\xi}{dt}$ $=-\frac{1}{2}\frac{dn_{N_2 O_5}}{dt}$ $=\frac{1}{4} \frac{dn_{NO_2}}{dt} =\frac{dn_{O_2}}{dt}$

• Since most of the reactions are done under constant volume conditions , then

• from-(1) $\rarr n_i=n^0_i + \nu_i \xi……(1)$

• $\frac{d\xi}{dt}=\frac{1}{\nu_i}\frac{dn_i}{dt}……(3)$

• $\frac{1}{V}\quad \frac{d\xi}{dt}$ $=\frac{1}{V}\quad \frac{1}{\nu_i}\frac{dn_i}{dt}$

• V(volume) is constant

• $\frac{d(\xi V)}{dt}$ $=\frac{1}{\nu_i}\frac{d(n_i/V)}{dt}$

• $\frac{d(\xi /V)}{dt}$ $=\frac{1}{\nu_i}\frac{d[i]}{dt}……(4)$

• [i] $\rArr$ concentration of species ‘i’

(rate of reaction)

• $CH_3CHO(g) \rarr CH_4(g)+CO(g)$

• The rate of this reaction can be followed by measuring the pressure in the system of constant volume and temperature

• Assume ideal gas behaviour of the gases

• $CH_3CHO(g) \rarr CH_4(g)+CO(g)$

Initial $\quad$ $n^0_{CH_3CHO} \quad\quad 0 \quad\quad\quad\quad 0$

$n^0_{CH_3CHO}-\xi \quad \quad \quad \quad\xi \quad \quad \quad\quad \xi$

• $n_{CH_3CHO}=n^0_{CH_3CHO}+\nu_i\xi$

• $n_{CH_3CHO}=n^0_{CH_3CHO}-\xi$

• $n_{CH_4}=n^0_{CH_4}+\nu_i \xi$

• $n_{CH_4}=n^0_{CH_4}+\xi$

• $n_{CH_4}=\xi \hspace{3 mm}[n^0_{CH_4=0}]$

• $n_{CO}=n^0_{CO}(=0) + \nu_i \xi (+1)$

• $n_{CO}=0+\xi$

• $n_{CO}=\xi$