Reaction rate and stoichiometric

Reaction rate and stoichiometric

The reaction rate or speed of reaction or rate of reaction in terms of reactant and product is formally defined as how fast or slow reaction occurs. For example the rusting of iron by oxidative under earth’s atmosphere is slow reaction that can cover many years but the reaction like combustion of fire with cellulose that take place in certain fraction of second. The concept of rate of reactions in chemical kinetics are applied in many sectors like chemical engineering, environmental engineering, geological engineering, genetic engineering, enzymology etc.

Formal definition of reaction rate can be expressed by fallowing:-

Let us consider a general reaction

aA + bB → pP + qQ

The lowercase letters (a,b,c,p and q) represents the stoichiometric coefficients while the capital letter (A and B) represents reactant and p and q represents product.

$$MgCl_2+NaCl_2\longrightarrow 2NaCl+ Mg(OH)_2$$

Here 2 is stoichiometric coefficient for product NaCl and other 1, 1

Order of reaction (n)= 2+1-(1+1)= 3-2=1

Adding the complete definition of IUPAC’s Gold Book the rate of reaction for a chemical reaction occurring in a closed system under isochoric condition without a builds up of reaction intermediates is defined as:-

r= $$\frac{1×d[A]}{a×dt}$$=$$\frac{1×d[B]}{b×dt}$$ =$$\frac{1×d[P]}{p×dt}$$ =$$\frac{1×d[Q]}{q×dt}$$

The negative sign shows that rate of reaction is decreasing and IUPAC tell us that unit of time always be in second. In this cases rate of reaction differ from the rate of concentration of product by constant factors or stoichiometric coefficient and for reactant A by minus the reciprocal of stoichiometric number. Reaction rate are usually unit of mol/L/s. It should be noticed that previous definition for a signal reaction in a closed system of constant volume. When we added water a glass containing salt the concentration or quantity of salt decreases, although there is no chemical reaction.

For an open system,

Full mass balance is expressed as accumulation = in – out +generation – consumption.

F_Ao - F_{A +}∫_o^vUdv =$$\frac{dNA}{dt}$$

Where fae is inflow of rate of A in moleculels within one second, fa is out flow and V is the instanneous reaction rate of A (in number concentration than in moles) in differential volume, integrated over the entire system volume V at given moment., where we applied it in a closed system at constant volume. Above reactin can be reduced as;

r= $$\frac{dNA}{dt}$$ where concentration [A] is related to number of molecules N_A by [A]= $$\frac{V}{NoV}$$.here No is taken as Avogadro constant.

Rate of conversion can be used for single reaction in a closed system varying with volume derivative of extent of reaction within is;

r= $$\frac{dε}{dt}$$=$$\frac{dni}{Vi.dt}$$ =$$\frac{dC(iv)}{ Vi.dt}$$=[ $$\frac{VdCi}{dt}$$+ $$\frac{Cidv}{dt}$$]

Here vi is the stoichiometric coefficient for substances, I equal to a,b, p and q in above typical reaction also Vis the volume of reaction and Ci is the concentration of substrate ‘I’.

Where side product or intermediate is formed or change in concentration takes place IUPAC recommends as rate of appearance and rate of disappearance for products and reactants. Use of catalyst on reaction can be expressed as catalyst weight ( mol/g/s) or surface area(mol/m2/s) basis. If specific catalyst is in site bases which may be counted by specific method the rate is taken as in units of /s and is called a turnover frequency.

Chemical reaction is different is speed in which they occur. Some reaction are can reach equilibrium with certain time and some reation takes several year to reach an equilibrium. Rate of reaction is dependent upn difference concentration is dependent upon difference concentration reacant or product per unit time. The speed of reaction with time can be expressed concentration change devide by time

Rate= $$\frac{Δconcentration}{Δ time}$$

For the reation

X+Y→ Z

The rae can be expressed as change in concentration by its component.

rate=$$-\frac{Δ[X]}{Δt}$$

rate =$$-\frac{Δ[Y]}{Δt}$$

rate=$$-\frac{Δ[Z]}{Δt}$$

In which ΔX.is difference between concentration of X over time interval t₂- t₁

ΔX = X₂- X₁

Again where we consider the following reation

P + 3Q→ 2R

It is clear that [Q] so to obtain constant rate of each component we should devided by these number which is written front side of concentration of each component

Rate=$$-\frac{Δ[P]}{Δt}$$=$$-\frac{Δ[Q]}{3Δt}$$=$$-\frac{Δ[D]}{2Δt}$$

Here ‘3’ in above equation shows stoichiometric coefficient of Q and ‘2’ is stoichiometric coefficient of R.

Let us consider a typical reaction

$$NH₃+ 3No₂→ 2N₂+ 6H₂O

Stoichiometric coefficient of ammonia is 4. Similarly stoichiometric coefficient of oxygen is 2 and stoichiometric coefficient of water is 6.

Which clears that stoichiometric coefficient gives the ratio of rate of reaction equal with respect to another.

When we observe chemical reaction or reaction rate with different temperature i.e. higher and lower temperature obviously we will find the high rate of reaction with low temperature. This is due to collision frequency of molecule increase and move rapidly at higher temperature rather than lower temperature .also the kinetic energy also increases with increase in temperature. Experimentally it was found theat rate of reaction becomes doubles with increase in every 10 degree celsc….. temperature. It will happens when concentration of reactant remain and then start to decreased.

Catalyst used in reaction will be faster. In biological process enzyme catalyzes particular compound only. Negative catalyst decreases rate of reaction and positive catalyst increase rate of reaction.

Reference

Bahl, B.S. Essential of Physical Chemistry. New Delhi: S. Chand & Company Pvt. Ltd, 2005.

Bahl, B.S., Arun Bahl and G.D. Tuli. Essential of Physical chemistry . New Delhi: S. Chand & Company Pvt. Ltd., 2005.