Rate of Reaction - Practice Questions & MCQ

There are majorly three parameters regarding a chemical reaction: 

(1) Feasibility of a reaction

(2) Extent to which a reaction will proceed

(3) Speed of the reaction

We learnt about the feasibility of a reaction in Thermodynamics and about the extent of reaction in Equilibrium. Along with the feasiblity and the extent, it is also important to know the rate and the factors affecting the rate of reaction. Here in Chemical Kinetics, we are going to learn how to answer the above specified questions. 

Type of Reaction in terms of their rate:

(1) Very fast reactions: 

Some reactions such as ionic reactions occur very fast and it is difficult to calculate the rate of these reactions

e.g. Precipitation of AgCl upon mixing aqeuous solutions of $\mathrm{AgNO}_3$ and NaCl.

(2) Moderate reactions: 

These reactions occur at moderate rates and it becomes easier to calculate the rate due to the moderate pace.

e.g. Hydrolysis of esters, inversion of cane sugar etc.

(3) Very slow reactions : 

These reactions occur at very slow rates and it becomes very difficult to percieve these changes.

e.g. Rusting of iron, conversion of diamond to graphite. 

Rate of reaction

Rate of reaction can be defined in terms of change in concentration of reactant or product in unit time.

To be more specific it can be expressed in terms of 

(i) the rate of decrease in concentration of any one of the reactants, or 

(ii) the rate of increase in concentration of any one of the products.

There are two types of rates which are generally measured for a chemical reaction

(1) Average Rate

(2) Instantaneous Rate

You will learn about these rates in the subsequent concepts in this chapter.

Average Rate of Reaction:

It is defined as "The rate of change of concentration of a reactant or a product per unit time" 

Rate of reaction $(r)=\frac{\mathrm{C}_2-\mathrm{C}_1}{\mathrm{t}_2-\mathrm{t}_1}$

As rate of reaction varies greatly with time, so generally, average reaction rate and instantaneous reaction rates are used. 

For a reaction $\mathrm{A} \rightarrow \mathrm{P}$
Rate of disappearance of $\mathrm{A}=-\frac{\Delta[\mathrm{A}]}{\Delta \mathrm{T}}$
Rate of appearance of $\mathrm{P}=\frac{\Delta[\mathrm{P}]}{\Delta \mathrm{T}}$

It is to be noted that rate of reaction is always a positive quantity and hence, there is a negative sign that has to be included in the expression for rate.

Unit of average velocity $=\frac{\text { Unit of concentration }}{\text { Unit of time }}=\frac{\text { mole }}{\text { litre second }}=$ mole litre $^{-1}$ second $^{-1}$

However, depending upon the data given in the question, different units may be used.

Instantaneous Rate of Reaction

As the average reaction rate fails to predict the rate at a particular moment of time so we use instantaneous rate which is equal to a small change in concentration (dx) during a small interval of time (dt). It is given as dx/dt.

$\lim _{\Delta t \rightarrow 0} \frac{\Delta \mathrm{c}}{\Delta \mathrm{t}}=\frac{\mathrm{dc}}{\mathrm{dt}}$

Rate of reaction $=$ slope of curve $=\frac{\mathrm{dx}}{\mathrm{dt}}$

It can be written for any of the reactant or the product in terms of stoichiometric coefficients V_j which is negative for reactants and positive for products as follows:$\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{1}{\mathrm{~V}_{\mathrm{j}}} \frac{\mathrm{d}(\mathrm{J})}{\mathrm{dt}}$

For example, if we have the reaction

$
\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{cC}+\mathrm{dD}
$
Rate w.r.t. $[\mathrm{A}]=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}} \times \frac{1}{\mathrm{a}}$
Rate w.r.t. $[B]=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}} \times \frac{1}{\mathrm{~b}}$
Rate w.r.t. $[\mathrm{C}]=-\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}} \times \frac{1}{\mathrm{c}}$
Rate w.r.t. $[\mathrm{D}]=-\frac{\mathrm{d}[\mathrm{D}]}{\mathrm{dt}} \times \frac{1}{\mathrm{~d}}$

• For the reactants, the negative sign indicates the decrease of concentration and for products positive sign indicates an increase in concentration.
• For a reversible reaction at dynamic equilibrium, the net reaction rate is always zero as:$\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)_{\text {forward }}=\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)_{\text {backward }}$

There are various factors on which the rate of reaction depends:

• Nature of reactant and product: 
  • For ionic reactants reaction rate is fast as activation energy is zero for them. For example:$\mathrm{BaCl}_2+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{BaSO}_4+2 \mathrm{HCl}$
  • Molecules have slow reaction rate due to need of more activation energy. For example:$2 \mathrm{CO}+\mathrm{O}_2 \rightarrow 2 \mathrm{CO}_2$
• Physical state of reactants: Rate also changes with physical state.
  Gaseous states > Liquid states > Solid states
• Pressure: For gaseous reactants rate varies with pressure just like concentration.

$\frac{\mathrm{dx}}{\mathrm{dt}} \propto$ Pressure $($ as $\mathrm{P} \propto \mathrm{C})$

• Surface Area: Greater the surface area, faster is the rate of reaction due to more number of active sites.

Rate $(\mathrm{dx} / \mathrm{dt}) \propto$ Surface area

• Temperature: Rate of reaction increases with the increase of temperature as it increases the number of effective collisions. It is observed that for every 10^oC rise in temperature -dx/dt or rates become nearly double.
  Temp. Coefficient $(\mu)=\frac{\mathrm{K} \text { at } \mathrm{t}^{\circ} \mathrm{C}+10^{\circ} \mathrm{C}}{\mathrm{K} \text { at } \mathrm{t}^{\circ} \mathrm{C}}$
  The value of the temperature coefficient lies in between 2-3. In case we increase the temperature by more than 10^oC the above relation can be given as:
  $\frac{\mathrm{K}_{\mathrm{T}_2}}{\mathrm{~K}_{\mathrm{T}_1}}=(\mu)^{\Delta \mathrm{T} / 10}$
  $\left[\right.$ Here $\left.\Delta \mathrm{T}=\mathrm{T}_2-\mathrm{T}_1\right]$
  
  $\log _{10} \frac{\mathrm{~K}_{\mathrm{T}_2}}{\mathrm{~K}_{\mathrm{T}_1}}=\frac{\Delta \mathrm{T}}{10} \log _{10} \mu$
  
  $\frac{\mathrm{K}_{\mathrm{T}_2}}{\mathrm{~K}_{\mathrm{T}_1}}=$ Antilog $\left[\frac{\Delta \mathrm{T}}{10} \log _{10} \mu\right]$
• Catalyst: It increases the rate of a reaction by decreasing the activation energy by accepting a new alternative smaller path for the reaction. It is reverse in case of negative catalyst to that of positive catalyst. Catalysts are more effective in 'Solid powdered form' due to larger surface area, that is, more active sites.
  
• Intensity of light: Rate of photochemical reactions depends upon intensity of light radiations.$\frac{\mathrm{dx}}{\mathrm{dt}} \propto$ Intensity of radiation
• Concentration of reactants: Rate increases with the increase of concentration as due to more number of reactants there are more collisions.

Rate of reaction $(\mathrm{dx} / \mathrm{dt}) \propto$ Concentration