//M0//QN1//CS//DL0//EQ

Rate of reaction relates to the concentration of reactants and products changing per unit time. “Rate of a reaction is the change in concentration of reactants or products per unit time,”

Rate =
Average Rate: Average rate is taken as the ratio of change in total concentration to total time taken.
Average Rate =
Instantaneous Rate: The instantaneous rate of a reaction is the rate at a specific time. The instantaneous rate of a reaction is the ratio of the change in concentration over a number of small time periods.
Instantaneous Rate =
(a) For the following reaction rate of appearance of I 2 is 1.14 × 10–2. Then find out rate of disappearance of MnO–4.
2MnO–4 + 10I– + 16H+ → 2Mn 2+ + 5I 2 + 8H 2 O
(b) In kinetic study of a chemical reaction, slopes are drawn at different times in the plot of concentration of reactants versus time. The magnitude of slopes with increase of time.(c) 2NO(g) + O 2(g) → 2NO 2(g); If = 0.052 Ms–1 then, = _________.(d) In the reaction 2A + B → A 2 reactant B will disappear _________.

//X

(a) 4.56 × 10–3 Ms–1
2MnO–4 + 10I– + 16H+ → 2Mn2+ + 5I2 + 8H2O
– = +
= × (1.14 × 10–2)
= 4.56 × 10–3 m/sec
(b) Decrease
As the reaction progresses, the concentration of reactants decrease. So, the rate of reaction slow down over time.
Therefore, the magnitude of slops decrease with the increase of time.
(c) 0.026 Ms–1
– = – = +
= × 0.052 ⇒ 0.026 m/sec
(d) At half-life the disappearance of rate of A
2A + B → A 2
– = –
Reactant B will disappear half as fast as reactant A.

//M0//QN2//CS//DL0//EQ

In Arrhenius equation K = A, E a is activation energy.
According to the collision theory, a reaction occurs only when reactant molecules come close and collide with each other at the same time. During the collisions rearrangement of atoms takes place leading to the formation of products. The rearrangement of an atom involves the breaking of a bond and the formation of a new bond. Molecules rearrangements can only occur when the colliding molecules have energy equal to or greater than the minimum energy required for rearrangement. If the atom/molecule do not have this minimum energy, no rearrangement of molecules will occur and no product will be formed. The difference between the minimum energy required to rearrange molecule and the average energy of the reaction is called the activation energy (E a). That is, the additional energy of a reactant molecule over and above the energy it already possesses to bring about a chemical change is called activation energy.
(a) Collision frequency is _________ .(b) For the process R → P the potential energy versus reaction axis is given. The enthalpy change of the reaction is ________ to energy corresponding.
(c) Activation energy required for a reaction can be reduced by what?(d) Which of the following statements is not true?
(A) For an endothermic reaction, the heat of reaction is less than the activation energy.
(B) For an exothermic reaction, the heat of reaction is greater than the activation energy.
(C) For an exothermic reaction, the activation energy of the forward reaction is lower than that of the backward reaction.
(D) For an endothermic process, the activation energy of the forward reaction is higher than that of the backward reaction.

//X

(a) Collision frequency (Z) is defined as the total number of collisions that occur per unit volume per unit time in a reaction mixture.
(b) b – a
Since the product energy (b) is lower than the reactant energy (a) in this specific graph, the reaction is exothermic, and Δ H would be negative.
The enthalpy change corresponds to the value (b−a).
(c) Adding of catalyst
The activation energy required for a reaction can be reduced by adding a catalyst.
(d) (B) For an exothermic reaction, the heat of reaction is greater than the activation energy.
For an exothermic reaction, the heat of reaction (ΔH) is the difference between reactants and products. It is not inherently greater than the activation energy.

//M0//QN3//CS//DL0//EQ

A pharmaceutical company is studying how the rate of drug decomposition changes with temperature. The drug breaks down following first order kinetics. At different temperatures, the following rate constants were measured:

Temperature (0°C) | Rate Constant k(s–1)
25°C | 3.0 × 10–4
35°C | 8.1 × 10–4

The drug must remain stable during storage, so scientist want to predict:
The activation energy (Ea) using the Arrhenius equation.
The half-life of the drug at 25°C.
Whether the drug decomposes significantly in 6 hours.
How increasing temperature affects shelf life.
(R = 8.314 J mol–1 K–1).
(a) Using the Arrhenius equation, calculate the activation energy (E a).(b) Calculate the half-life (t 1/2) of the drug at 25°C.(c) What fractions of the drug will remain after 6 hours at 25°C?(d) Explain how an increase from 25°C to 35°C affects the drug's shelf life.

//X

(a) Arrhenius equation
l n = =
k 1 = 3.0 × 10–4 T 1 = 298 K
k 2 = 8.1 × 10–4 T 2 = 308 K
∴ ln (2.7) =
∴ 0.993 = (0.000109)
∴ E a =
= 75.8 kJ / mol
(b) t 1/2 = =
= 2310 second
= 38.5 minutes
(c) Fraction remaining after 6 hours
First - order: N = Noe–kt (t = 21600 sec)
N = e–(3 × 10–4) (21600)
N = e–6.48
= 0.015
= 0.15%
(d) Rate increases from 3 × 10–4 to 8.1 × 10–4 (Almost 2.7 times).

//M0//QN4//CS//DL0//EQ

Higher temperature accelerates decomposition, reducing shelf life drastically. A chemical industry studies the decomposition of N 2 O 5, which follows first order kinetics: 2N 2 O 5 → 4 NO 2 + O 2 At 25°C, the rate constant is 6.5 × 10–3 s–1. Samples show the following data:

Initial concentration: 0.50 M
After t seconds, conc. reduces to 0.10 M
The industry aims to determine: 1. Time required to reach 0.10 M. 2. Total gas evolved. 3. Whether the reaction is feasible at low temperatures. 4. Importance of first order kinetics in industrial reactors.(a) Calculate the time required for concentration to fall from 0.50 M to 0.10 M.(b) How many moles of O 2 are formed from 0.50 mol of N 2 O 5?(c) If temperature decrease, what happens to the rate constant?(d) State one industrial advantage of first order reactions.

//X

(a) t = ln
= ln
= 153.8 (1.609)
t = 247.5 seconds.
(b) 2 mole N 2 O 5 → 1 mol O 2
∴ 0.50 mole N 2 O 5 → 0.25 mole O 2
(c) Temp ↓ → Rate constant decreases exponentially (Arrhenius eq.)
Reaction slow down drastically.
(d) The half-life of f irst order reaction is independent of the initial reactant concentration. So, it is easy to control and predictable.
Reaction Rate: Change in concentration of reactants or products per unit time.
Average Rate: Rate calculated over a long-time interval from overall concentration change.
Instantaneous Rate: Rate at a specific moment, obtained from the slope of tangent on a concentration–time curve.
Rate Law: Experimentally derived expression relating rate to reactant concentrations.
Rate Constant (k): Proportionality constant in the rate law; depends on temperature and catalyst.
Order of Reaction: Sum of powers of concentration terms appearing in the rate law.
Molecularity: Number of species colliding in a single elementary step to form products.
Zero-Order Reaction: Reaction whose rate is independent of reactant concentration.
First-Order Reaction: Reaction whose rate is proportional to the first power of one reactant.
Half-Life (t½): Time required for the concentration of a reactant to become half of its initial value.
Pseudo First-Order Reaction: Higher-order reaction that behaves like first order because one reactant is in excess.
Activation Energy (E a): Minimum energy required for reactants to form the activated complex.
Activated Complex / Transition State: High-energy, unstable intermediate formed during reaction progression.
Arrhenius Equation: Equation relating rate constant (k) with temperature and activation energy.
Collision Theory: Reaction occurs only when molecules collide with sufficient energy and correct orientation.
Steric Factor (P): Fraction of collisions with the proper orientation to form products.
Reaction Coordinate: Path showing energy changes as reactants convert into products.
Rate-Determining Step: Slowest step in a multi-step mechanism controlling total reaction rate.
Exothermic Reaction: Reaction releasing heat where products have lower energy than reactants (ΔH < 0).
Endothermic Reaction: Reaction absorbing heat where products have higher energy than reactants (ΔH > 0).