Top 50 Most Important
Subjective Questions
Chemical Kinetics. Master Reaction Rates, Rate Laws, Half-Life Equations, and the Collision Theory.
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Rate of Reaction & Factors
The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit of time.
Unit: $\text{mol L}^{-1} \text{s}^{-1}$ (for solutions) or $\text{atm s}^{-1}$ (for gaseous reactions).
As the reaction proceeds, the concentration of reactants decreases, making the change in concentration ($\Delta[R]$) a negative value. Since the rate of a reaction must always be a positive quantity, a negative sign is placed in the formula ($-\frac{\Delta[R]}{\Delta t}$) to mathematically convert the negative change into a positive rate.
Average Rate: The change in concentration of a reactant or product over a macroscopic (large) time interval ($\Delta t$). It is calculated as $\pm\frac{\Delta[C]}{\Delta t}$.
Instantaneous Rate: The true rate of the reaction at a specific, particular instant of time. It is obtained when $\Delta t \to 0$, calculated using calculus as $\pm\frac{d[C]}{dt}$ (the slope of the tangent on the concentration-time curve).
According to the rate law, the rate of a reaction is directly proportional to the concentration of the reactants. As time passes, reactants are continuously consumed, meaning their concentration drops. With fewer reactant molecules available to collide, the rate of reaction steadily decreases.
The unique overall rate of reaction requires dividing the individual rate of change of each species by its stoichiometric coefficient:
$\text{Rate} = -\frac{d[N_2]}{dt} = -\frac{1}{3} \frac{d[H_2]}{dt} = +\frac{1}{2} \frac{d[NH_3]}{dt}$
- Concentration of reactants: Higher concentration usually increases the rate.
- Temperature: Rate generally increases rapidly with temperature.
- Presence of a Catalyst: A positive catalyst increases the rate.
- Surface Area: For solid reactants, powdered forms react faster than large blocks due to increased exposed surface area.
The rate constant ($k$) is defined as the rate of the reaction when the molar concentration of every reactant in the rate law expression is exactly unity ($1 \text{ mol L}^{-1}$). It is characteristic of a specific reaction and depends only on temperature, not on concentration.
Powdering a solid drastically increases its total exposed surface area. A larger surface area allows more reactant molecules (e.g., a gas or liquid) to come into contact and collide simultaneously with the solid, significantly increasing the frequency of collisions and thus the rate of reaction.
No. The rate constant $k$ is an inherent property of the reaction at a given temperature. It is entirely independent of the initial concentrations of the reactants. It only changes if the temperature is altered or a catalyst is added.
Photochemical reactions are reactions that are triggered by the absorption of light (photons) of specific energy (e.g., Photosynthesis, or $H_2 + Cl_2 \rightarrow 2HCl$). Their rate is directly proportional to the intensity of the incident light, not just the concentration of reactants.
Rate Law, Order & Molecularity
The rate law is a mathematical equation that relates the rate of a reaction directly to the molar concentrations of the reactants, each raised to some power.
No. The rate law cannot be deduced theoretically from the balanced chemical equation; it must be determined strictly through experiments.
The order of a reaction is the sum of the powers (exponents) to which the concentration terms are raised in the experimentally determined rate law expression.
If Rate = $k[A]^x [B]^y$, then Overall Order = $x + y$.
Molecularity is the exact number of reacting species (atoms, ions, or molecules) taking part in an elementary reaction, which must collide simultaneously to bring about a chemical reaction.
- Nature: Order is an experimental value; Molecularity is a theoretical concept.
- Values: Order can be zero, fractional, or an integer. Molecularity must always be a positive whole number (1, 2, or 3) and can never be zero or fractional.
Molecularity represents the physical number of particles that must collide to react. A molecularity of zero would absurdly imply that a chemical reaction is taking place without any reactant molecules colliding, which is physically impossible.
For a reaction to occur, particles must collide simultaneously and with proper orientation. The statistical probability of four or more particles colliding at the exact same point in space, at the exact same instant, with the required energy and orientation, is extremely low. Thus, such reactions happen in a series of simpler steps.
For zero order, Rate = $k[A]^0 = k$.
Therefore, the unit of $k$ is the exact same as the unit of Rate: $\text{mol L}^{-1} \text{s}^{-1}$.
For first order, Rate = $k[A]^1$.
$k = \frac{\text{Rate}}{[A]} = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol L}^{-1}}$.
Therefore, the unit of $k$ is time inverse: $\text{s}^{-1}$ (or $\text{min}^{-1}, \text{hr}^{-1}$).
The general unit for an $n^{th}$ order reaction is derived from $k = \frac{\text{Rate}}{[\text{Conc}]^n}$:
$(\text{mol L}^{-1})^{1-n} \text{ s}^{-1} \quad \text{or} \quad \text{mol}^{1-n} \text{ L}^{n-1} \text{ s}^{-1}$
The overall order is simply the sum of the exponents in the rate law.
Order = $\frac{1}{2} + 2 = \mathbf{2.5}$ (or $5/2$).
This proves that the order of a reaction can indeed be a fractional value.
Integrated Rate Eqs & Half-Life
A zero order reaction is one whose rate is absolutely independent of the concentration of the reactants (Rate = $k$). The reaction proceeds at a constant speed until the reactant is exhausted.
Example: The thermal decomposition of $HI$ on a gold surface, or the decomposition of ammonia on a hot platinum surface at high pressure.
The integrated equation is: $[R] = [R]_0 - kt$
Where $[R]_0$ is initial concentration, $[R]$ is concentration at time $t$.
Graph: A plot of $[R]$ versus time $t$ gives a straight line with a negative slope equal to $-k$, and an y-intercept of $[R]_0$.
For a first order reaction, integrating the rate law gives:
$k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$
Alternatively, in exponential form: $[R] = [R]_0 e^{-kt}$.
Rearranging the first-order equation yields: $\log[R] = -\frac{k}{2.303}t + \log[R]_0$.
If we plot $\log[R]$ on the y-axis against time $t$ on the x-axis, we get a straight line with a negative slope equal to $-\frac{k}{2.303}$ and a y-intercept of $\log[R]_0$.
The half-life of a reaction is the time required for the concentration of a reactant to be reduced to exactly one-half of its initial value (i.e., when $[R] = \frac{[R]_0}{2}$).
For zero order: $t_{1/2} = \frac{[R]_0}{2k}$.
This formula shows that the half-life of a zero order reaction is directly proportional to the initial concentration of the reactant ($[R]_0$).
For first order: $t_{1/2} = \frac{0.693}{k}$.
Unique property: The half-life equation contains no concentration term. Therefore, the half-life of a first order reaction is completely independent of the initial concentration of the reactant.
Because the rate of a first-order reaction is directly proportional to the concentration of the reactant, as the concentration dwindles, the rate becomes infinitely slow. Mathematically, in the equation $[R] = [R]_0 e^{-kt}$, the concentration $[R]$ becomes zero only when time $t = \infty$.
All natural and artificial radioactive decays of unstable nuclei are strictly First Order reactions. Their half-life is constant regardless of how much radioactive sample is initially present.
30 minutes represents exactly 3 half-lives ($n = 30/10 = 3$).
Fraction remaining = $(1/2)^n = (1/2)^3 = 1/8$.
Therefore, $1/8$th (or 12.5%) of the original reactant remains.
Pseudo First Order & Mechanisms
A pseudo first order reaction is a reaction that has higher order molecularity (typically bimolecular, molecularity = 2), but behaves as a first order reaction kinetically. This happens when one of the reactants is present in such a massive excess (like solvent water) that its concentration practically remains constant throughout the reaction.
The acid-catalyzed hydrolysis of ethyl acetate.
$CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$.
Because water is the solvent and present in huge excess, Rate = $k'[Ester][H_2O]$ becomes Rate = $k[Ester]$. The reaction appears first order.
The acid-catalyzed inversion of cane sugar (sucrose) into glucose and fructose.
$C_{12}H_{22}O_{11} + H_2O \xrightarrow{H^+} C_6H_{12}O_6 + C_6H_{12}O_6$.
Again, water is in immense excess, so the rate depends only on the concentration of sucrose, making it pseudo first order.
Elementary Reaction: A reaction that occurs in a single, simple step. For these, molecularity equals order.
Complex Reaction: A reaction that occurs in a sequence of multiple elementary steps (a mechanism). Molecularity has no meaning for the overall complex reaction.
In a complex, multi-step reaction mechanism, the slowest elementary step acts as a bottleneck. It completely controls the overall rate of the reaction. This slowest step is known as the Rate Determining Step, and the overall rate law is derived directly from it.
Because it is specified as an elementary reaction (single step), the stoichiometric coefficients exactly match the exponents in the rate law.
Rate = $k[A]^2 [B]^1$.
Order = $2 + 1 = \mathbf{3}$. Molecularity is also 3.
The Initial Rate Method is used experimentally to find the order of a reaction. The reaction is run multiple times. In each run, the initial concentration of only one reactant is changed (e.g., doubled), while others are kept constant. By observing how the initial rate changes (e.g., if it quadruples, order is 2 w.r.t that reactant), the exponents of the rate law are deduced.
The thermal decomposition of Acetaldehyde ($CH_3CHO$) to form methane and carbon monoxide has a fractional order.
Reaction: $CH_3CHO \rightarrow CH_4 + CO$.
Experimental Rate Law: Rate = $k[CH_3CHO]^{3/2}$.
The overall order is exactly 1.5.
For reactions involving gases in a closed vessel, it is difficult to measure concentration directly. Instead, kinetics are monitored by measuring the change in total pressure of the system over time at constant volume and temperature, relating partial pressures to concentration via the ideal gas law ($P = CRT$).
The general relationship is $t_{1/2} \propto [R]_0^{1-n}$.
If doubling $[R]_0$ leads to doubling $t_{1/2}$, they are directly proportional. This occurs when $1-n = 1$, meaning $n = 0$.
Therefore, it is a Zero Order reaction.
Temp Dependence & Collision Theory
The temperature coefficient is the ratio of the rate constant of a reaction at two temperatures differing by $10^\circ\text{C}$ (usually 308 K and 298 K). For most chemical reactions, this value lies between 2 and 3, meaning a $10^\circ$ rise roughly doubles the rate.
$k = A \cdot e^{-E_a / RT}$
- $k$ = Rate constant
- $A$ = Arrhenius factor (Frequency factor)
- $E_a$ = Activation energy
- $R$ = Gas constant
- $T$ = Temperature in Kelvin
According to Boltzmann distribution, the exponential term $e^{-E_a/RT}$ represents the fraction of reactant molecules that possess kinetic energy equal to or greater than the activation energy ($E_a$). Only these molecules are capable of making effective collisions.
Threshold Energy: The absolute minimum total energy that reacting molecules must possess to yield a product upon collision.
Activation Energy ($E_a$): The extra amount of energy the reactant molecules must absorb to reach the threshold energy.
$E_{\text{Threshold}} = E_{\text{Reactants (average)}} + E_a$.
A $10^\circ$ rise in temperature barely increases the total number of collisions. However, it shifts the Maxwell-Boltzmann energy distribution curve significantly, completely doubling the fraction of molecules that possess energy greater than the activation energy ($E_a$). More molecules with sufficient energy leads to a doubled reaction rate.
A catalyst provides an entirely alternative reaction pathway or mechanism that requires a lower Activation Energy ($E_a$). By lowering the energy barrier, a much larger fraction of molecules can easily cross it at the same temperature, massively increasing the rate.
No. A catalyst does not change the thermodynamics of the reaction. It does not alter $\Delta H$ (enthalpy), $\Delta G$ (Gibbs free energy, spontaneity), or $K_c$. It simply accelerates both the forward and backward reactions equally, helping the system reach equilibrium faster.
- Energy Barrier: The colliding molecules must possess kinetic energy greater than or equal to the threshold energy.
- Orientation Barrier: The molecules must be properly oriented in space at the exact moment of impact to allow old bonds to break and new bonds to form.
The Arrhenius equation was modified to: $\text{Rate} = P \cdot Z_{AB} \cdot e^{-E_a/RT}$.
The factor '$P$' strictly accounts for the orientation barrier. It represents the fraction of molecules that possess the correct spatial orientation during collision, explaining why complex molecules react slower than predicted by energy alone.
Practically, no for most stable molecules. If $E_a$ were zero, every single collision would be effective (ignoring orientation). The reaction would occur instantaneously at an explosive rate the moment reactants were mixed, making it impossible to control or measure. All stable chemical reactions possess some kinetic barrier ($E_a > 0$).
Chapter 3 Mastered!
You have just conquered the 50 most critical subjective questions for Class 12 Chemistry, Chapter 3: Chemical Kinetics. Your speed to success just increased!
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