Chemical Kinetics – NEET UG ChemistryPractice Questions & PYQs

The rate law for a general reaction can be expressed as $\text{rate} = k[A]^x[B]^y$, where $x$ and $y$ represent the orders with respect to reactants $A$ and $B$. Comparing the data from experiment 2 and experiment 3, where the concentration of $A$ is held constant at 0.024 and the concentration of $B$ is doubled from 0.035 to 0.070, the initial rate increases from 0.10 to 0.80, which is an eightfold increase. Setting up the ratio $\frac{0.80}{0.10} = \left(\frac{0.070}{0.035}\right)^y$ yields $2^y = 8$, demonstrating that the reaction is third order with respect to $B$, so $y = 3$. Next, comparing experiment 3 and experiment 1, where the concentration of $B$ remains constant at 0.035 while the concentration of $A$ is doubled from 0.012 to 0.024, the initial rate stays unchanged at 0.10. Evaluating the ratio $\frac{0.10}{0.10} = \left(\frac{0.024}{0.012}\right)^x$ results in $2^x = 1$, revealing that the reaction order with respect to $A$ is zero, meaning $x = 0$. Combining these findings yields the final rate law expression $\text{rate} = k[B]^3$.

The rate law for a zero-order reaction with a stoichiometric coefficient is given by $[A]_t = [A]_0 - 2kt$, where $k$ represents the rate constant and the factor of two reflects the stoichiometry of the reaction. Reaching 75% completion means that three-quarters of the initial concentration is consumed, leaving a remaining concentration of 0.5 M from an initial 2 M. Substituting these values into the integrated expression gives $0.5 = 2 - 2(1.0)t$, which simplifies to $2t = 1.5$. Dividing both sides yields a time of 0.75 min.

For a zero-order reaction, the integrated rate law is given by the equation $[R] = [R]_0 - kt$ where $[R]$ is the concentration, $[R]_0$ is the initial concentration, $k$ is the rate constant, and $t$ is time. This relationship directly mirrors the linear equation $y = mx + c$, meaning that plotting concentration $[R]$ against time produces a straight line with a constant negative slope of $-k$. Since other reaction orders require logarithmic or reciprocal plots to achieve linearity, a direct linear decrease of concentration over time is uniquely characteristic of zero-order kinetics.

The Arrhenius equation is expressed linearly as $\ln k = \ln A - \frac{E_a}{RT}$, where the vertical intercept corresponds to $\ln A$. Based on the provided graph, the intercept gives $\ln A = 6$. The rate constant is given as $e^2$, meaning its natural logarithm evaluates to 2. Converting the activation energy yields 6640 J mol$^{-1}$, and the gas constant is 8.3 J K$^{-1}$ mol$^{-1}$. Substituting these known parameters into the expression leads to the equation $2 = 6 - \frac{6640}{8.3 T}$. Rearranging this relation to isolate the temperature results \in $T = \frac{6640}{8.3 \times 4}$, which simplifies cleanly to 200 K.

The rate law for any reaction is expressed in the general form $\text{rate} = k[\text{A}]^x[\text{B}_2]^y$, where the exponents denote the reaction orders for each reactant. By comparing how individual concentrations impact the reaction velocity across the trials, these orders are easily calculated. Looking at the third and second trials, the concentration of $[\text{B}_2]$ is held constant at 1.0 while $[\text{A}]$ doubles from 0.50 to 1.0, but the rate remains completely unchanged at 3.2 x 10^-4. This reveals that the reaction rate is independent of the concentration of A, meaning its reaction order is zero. Next, evaluating the second and first trials, $[\text{A}]$ remains constant at 0.50 while $[\text{B}_2]$ increases from 0.50 to 1.0, leading the rate to double from 1.6 x 10^-4 to 3.2 x 10^-4. This shows a direct linear relationship, confirming that the reaction is first order with respect to $[\text{B}_2]$. Substituting these values back into the expression gives $\text{rate} = k[\text{A}]^0[\text{B}_2]^1$, which simplifies directly to $\text{rate} = k[\text{B}_2]$.

The rate of any chemical reaction is defined by the rate of disappearance of reactants or appearance of products divided by their respective stoichiometric coefficients. For a general gas-phase reaction, reactants consume over time and are therefore preceded by a negative sign, whereas products form and take a positive sign. Applying this principle to the synthesis of hydrogen iodide where both reactants have a coefficient of one and the product has a coefficient of two results in the balanced expression $-\frac{\Delta[\mathrm{H}_2]}{\Delta t} = -\frac{\Delta[\mathrm{I}_2]}{\Delta t} = \frac{1}{2}\frac{\Delta[\mathrm{HI}]}{\Delta t}$.

Enzymes function as specialized biological catalysts that accelerate metabolic processes by significantly lowering the activation energy barrier required for reactants to transform into products. By offering an alternative reaction pathway with a reduced energy threshold, a much larger fraction of molecules possess the necessary energy to react per unit time. Consequently, the overall velocity of biochemical transformations increases dramatically in the presence of these catalytic proteins.

The Arrhenius equation in logarithmic form is expressed as $\ln k = \ln A - \frac{E_a}{RT}$, which relates the temperature dependence of the rate constant to the activation energy. By comparing this standard form directly with the given expression, the coefficient of the inverse temperature term corresponds to $\frac{E_a}{R} = 1.25 \times 10^4$. Multiplying this value by the universal gas constant of 1.987 yields the activation energy in calories per mole. Converting this result into kilocalories per mole by dividing by 1000 gives 24.84.

The overall order of a reaction is determined by the sum of the concentration term exponents in the rate law, such that for an elementary process expressed as $\text{Rate} = k[\text{A}]^x[\text{B}]^y$, the order is $x + y$. In the given redox transformation, two moles of iron(III) chloride and one mole of tin(II) chloride directly participate as reactants whose concentration changes dictate the kinetics. Because three total molecules undergo concentration changes during the process, the overall kinetic order sums to three.

The unit of a rate constant is determined by substituting the overall reaction order $n$ into the standard rate law dimensional expression. For a zero order process where $n$ equals 0, the resulting unit evaluates to mol L$^{-1}$ s$^{-1}$, which corresponds to list item IV. When the reaction is of the first order with $n$ equal to 1, the concentration components cancel out completely leaving just s$^{-1}$, matching list item III. Progressing to a second order reaction where $n$ is 2 produces mol$^{-1}$ L s$^{-1}$, connecting with list item I. Lastly, a third order pathway characterized by $n$ equal to 3 yields mol$^{-2}$ L$^2$ s$^{-1}$, which lines up with list item II.

The integrated rate law for a first-order process is expressed as $k_1 = \frac{1}{t} \ln\left(\frac{a}{a-x}\right)$, where $a$ represents the initial reactant concentration and $(a-x)$ represents the concentration remaining at time $t$. By substituting the half-life condition where $t = t_{1/2}$ and $x = a/2$, the concentration term simplifies inside the logarithmic function to yield $k_1 = \frac{\ln 2}{t_{1/2}}$. Rearranging this expression reveals that the half-life depends exclusively on the rate constant, demonstrating that it remains completely unaffected by changes in the starting concentration of the reactants.

The temperature dependence of reaction rates is quantitatively governed by the Arrhenius equation, which relates the rate constants at different temperatures through the activation energy. Expressed logarithmically as $\log\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303 R}\left(\frac{T_2 - T_1}{T_1 T_2}\right)$, the formula demonstrates that measuring the rate constants $k_1$ and $k_2$ at distinct temperatures $T_1$ and $T_2$ provides all necessary variables to calculate the activation energy. Therefore, experimental determination relies entirely on observing how the velocity of the reaction shifts when subjected to thermal variations.

The time required for a first-order reaction to reach a specific completion percentage is determined by the integrated rate equation $t = \frac{2.303}{k} \log \left(\frac{[A]_0}{[A]_t}\right)$, combined with the half-life relationship $k = \frac{0.693}{t_{1/2}}$. When a reaction reaches 99.9% completion, only one-thousandth of the original reactant remains, making the concentration ratio equal to 1000. Evaluating the logarithmic term shows that this specific milestone requires approximately ten times the half-life duration. Multiplying the given half-life of 1 minute by ten yields a total time of 10.

The time required for a first-order reaction to proceed from an initial concentration to a final concentration is governed by the integrated rate expression $t = \frac{2.303}{k} \log \left(\frac{[A]_0}{[A]_t}\right)$. Substituting the rate constant of 0.03 along with the initial concentration of 7.2 and final concentration of 0.9 into the formula gives $t = \frac{2.303}{0.03} \log \left(\frac{7.2}{0.9}\right)$. Simplifying the logarithmic term yields $\log 8$, which can be rewritten as $3 \log 2$. Using the given logarithmic value of 0.301 and completing the arithmetic steps results in a time of 69.3.

The differential rate law for a reaction involving two reactants is written in the general form $\text{Rate} = k[A]^x[B]^y$, where $x$ and $y$ represent the respective reaction orders. Comparing the first two experimental trials shows that doubling the concentration of reactant $A$ while holding reactant $B$ constant causes the rate to double, proving that the reaction is first-order with respect to $A$. Comparing the second and third trials reveals that doubling the concentration of reactant $B$ while keeping $A$ constant causes the rate to quadruple, indicating a second-order dependence on $B$. Thus, the respective orders for $A$ and $B$ are 1 and 2.

The variation of reaction rates with temperature is quantitatively linked to activation energy through the Arrhenius temperature coefficient formula. Substituting the absolute temperatures of $300 \text{ K}$ and $330 \text{ K}$ and the rate ratio of $4$ into the logarithmic Arrhenius expression gives $\log 4 = \frac{E_a}{2.303 \times 8.314} \left(\frac{330 - 300}{300 \times 330}\right)$. Inserting the given value of $\log 4$ as $0.6021$ and isolating the activation energy yields $E_a = \frac{0.6021 \times 2.303 \times 8.314 \times 300 \times 330}{30}$. Multiplying these terms results in $38040 \text{ J/mol}$, which converts cleanly to $38.04 \text{ kJ/mol}$.

The activation energy of a chemical process can be determined quantitatively using the Arrhenius equation when the specific reaction rates are measured at two distinct temperature values. This relationship mathematically connects the ratio of the two rate constants with the temperature difference, making them the only necessary kinetic variables alongside the universal gas constant. Knowing how the rate responds to a change in thermal conditions directly exposes the energy barrier the reacting species must overcome to proceed.

The temperature dependence of reaction rates is quantified by the Arrhenius equation, written as $k = A e^{-\frac{E_a}{RT}}$. Taking the natural logarithm of both sides transforms this exponential expression into the linear form $\ln k = \ln A - \frac{E_a}{R} \left(\frac{1}{T}\right)$, which reveals that plotting $\ln k$ versus $\frac{1}{T}$ produces a straight line graph with a negative slope of $-\frac{E_a}{R}$ and a y-intercept equal to $\ln A$.

The temperature dependence of a reaction rate constant is described by the Arrhenius equation, $k = A e^{-\frac{E_a}{R T}}$, which transforms into a linear relationship when taking the natural logarithm on both sides. Expressing this as $\ln k = -\frac{E_a}{R} \left(\frac{1}{T}\right) + \ln A$ maps directly onto the slope-intercept equation $y = mx + c$, where $\ln k$ acts as the dependent variable on the vertical axis and $\frac{1}{T}$ acts as the independent variable on the horizontal axis. This yields a straight line with a negative slope of $-\frac{E_a}{R}$ and a positive y-intercept of $\ln A$, which corresponds to the graphical trend depicted in option C.

The temperature dependence of a reaction rate constant is governed by the Arrhenius relation, which expressed logarithmically allows the determination of activation energy from rate constants measured at two different temperatures. Substituting the given values into this integrated form yields $\log \left(\frac{0.14}{0.04}\right) = \frac{E_a}{2.303 \times 8.31} \left(\frac{700 - 500}{500 \times 700}\right)$. Simplifying the logarithmic term to $\log 3.5$ and substituting its given value of $0.5441$ transforms the expression into $0.5441 = \frac{E_a}{2.303 \times 8.31} \times \frac{200}{350000}$. Rearranging this equation to solve for $E_a$ gives a product of $0.5441 \times 2.303 \times 8.31 \times 250 \times 7$, which evaluates directly to $18219 \text{ J}$.