State a condition under
Question: State a condition under which a bimolecular reaction is a kinetically first-order reaction. Solution: A condition under which the order of a chemical reaction can be altered is by taking the solvent or the reactant in the excess amount due to which its concentration does not change much. Consider a bimolecular reaction A + B Product Rate = k[A][B] When concentration B is large rate becomes k[A] Where k=k[B] The order of the reaction will be equal to one....
Read More →Mark the incorrect statements.
Question: Mark the incorrect statements. (i) Catalyst provides an alternative pathway to a reaction mechanism. (ii) Catalyst raises the activation energy. (iii) A catalyst lowers the activation energy. (iv) Catalyst alters enthalpy change of the reaction. Solution: Option (ii) and (iv) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{2} \cos x d x$ Solution: Let $I=\int x^{2} \cos x d x$ Using integration by parts, $=x^{2} \int \cos x d x-\int \frac{d}{d x} x^{2} \int \cos x d x$ We know that, $\int \cos n x=\frac{\sin n x}{n}$ $=x^{2} \sin x-\int 2 x \sin x d x$ $=x^{2} \sin x-2 \int x \sin x d x$ Using integration by parts in second integral, $=x^{2} \sin x-2\left(x \int \sin x d x-\int \frac{d}{d x} x \int \sin x d x\right)$ $=x^{2} \sin x-2\left(-x \cos x+\int \cos x d...
Read More →Which of the following statements are in accordance
Question: Which of the following statements are in accordance with the Arrhenius equation? (i) Rate of a reaction increases with increase in temperature. (ii) Rate of a reaction increases with a decrease in activation energy. (iii) Rate constant decreases exponentially with an increase in temperature. (iv) Rate of reaction decreases with a decrease in activation energy. Solution: Option (i) and (ii) are the answers....
Read More →In the graph showing Maxwell Boltzman
Question: In the graph showing Maxwell Boltzman distribution of energy, ___________. (i) the area under the curve must not change with an increase in temperature. (ii) the area under the curve increases with increase in temperature. (iii) the area under the curve decreases with increase in temperature. (iv) with the increase in the temperature, curve broadens and shifts to the right-hand side. Solution: Option (i) and (iv) are the answers....
Read More →According to Maxwell Boltzmann distribution of energy,
Question: According to Maxwell Boltzmann distribution of energy, __________. (i) the fraction of molecules with most probable kinetic energy decreases at higher temperatures. (ii) the fraction of molecules with most probable kinetic energy increases at higher temperatures. (iii) most probable kinetic energy increases at higher temperatures. (iv) most probable kinetic energy decreases at higher temperatures. Solution: Option (i) and (iii) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\log (\log x)}{x} d x$ Solution: Let $I=\int \frac{\log (\log x)}{x} d x$ It can be written as, $=\int\left(\frac{1}{x}\right)(\log (\log x)) d x$ Using integration by parts, $I=\log (\log x) \int \frac{1}{x} d x-\int\left(\frac{1}{x \log x} \int \frac{1}{x} d x\right) d x$ We know that, $\int \log x=\frac{1}{x}$ and $\frac{d}{d x} \frac{1}{x}=\log x$ $=\log x(\log x) \times \log x-\int \frac{1}{x \log x} \times \log x d x$ $=\log x(\log x)...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $S$ be the set of all real numbers and let $R$ be a relation on $S$, defined by $a R b \Leftrightarrow|a-b| \leq 1$. Then, $R$ is A. reflexive and symmetric but not transitive B. reflexive and transitive but not symmetric C. symmetric and transitive but not reflexive D. an equivalence relation Solution: According to the question, Given set $S=\{\ldots \ldots,-2,-1,0,1,2 \ldots . .\}$ And $R=\{(a, b): a, b \in S$ and $|a-b| ...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $S$ be the set of all real numbers and let $R$ be a relation on $S$, defined by $a R b \Leftrightarrow|a-b| \leq 1$. Then, $R$ is A. reflexive and symmetric but not transitive B. reflexive and transitive but not symmetric C. symmetric and transitive but not reflexive D. an equivalence relation Solution: According to the question, Given set $S=\{\ldots \ldots,-2,-1,0,1,2 \ldots . .\}$ And $R=\{(a, b): a, b \in S$ and $|a-b| ...
Read More →During decomposition of an activated complex
Question: During decomposition of an activated complex (i) energy is always released (ii) energy is always absorbed (iii) energy does not change (iv) reactants may be formed Solution: Option (i) and (iv) are the answers....
Read More →At high pressure, the following reaction is zero order.
Question: At high pressure, the following reaction is zero order. 2NH3(g) 1130 K Platinum catalyst N2(g) + 3H2(g) Which of the following options are correct for this reaction? (i) Rate of reaction = Rate constant (ii) Rate of the reaction depends on the concentration of ammonia. (iii) Rate of decomposition of ammonia will remain constant until ammonia disappears completely. (iv) Further increase in pressure will change the rate of reaction. Solution: Option (i), (iii) and (iv) are the answers....
Read More →For a complex reaction ______________.
Question: For a complex reaction ______________. (i) order of an overall reaction is the same as molecularity of the slowest step. (ii) order of an overall reaction is less than the molecularity of the slowest step. (iii) order of an overall reaction is greater than molecularity of the slowest step. (iv) the molecularity of the slowest step is never zero or non-integer. Solution: Option (i) and (iv) are the answers....
Read More →In any unimolecular reaction ______________.
Question: In any unimolecular reaction ______________. (i) only one reacting species is involved in the rate-determining step. (ii) the order and the molecularity of the slowest step are equal to one. (iii) the molecularity of the reaction is one and order is zero. (iv) both molecularity and order of the reaction are one. Solution: Option (i) and (ii) is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x \sin 2 x d x$ Solution: Let $I=\int x \sin 2 x d x$ Using integration by parts, $=x \int \sin 2 x d x-\int \frac{d}{d x} x \int \sin 2 x d x$ We know that, $\int \sin n x=\frac{-\cos n x}{n}$ and $\int \cos n x=\frac{\sin n x}{n}$ $=\frac{x}{2}-\cos 2 x+\int \frac{\cos 2 x d x}{2}$ $=-\frac{x}{2} \cos 2 x+\frac{1}{2} \frac{\sin 2 x}{2}+c$ $=-\frac{x}{2} \cos 2 x+\frac{1}{4} \sin 2 x+c$...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{2} \cos 2 x d x$ Solution: Let $I=\int x^{2} \cos 2 x d x$ Using integration by parts, $=x^{2} \int \cos 2 x d x-\int \frac{d}{d x} x^{2} \int \cos 2 x d x$ We know that, $\int \cos 2 x d x=\sin 2 x$ and $\frac{d}{d x} x^{2}=2 x$ Then, $=\frac{x^{2}}{2} \sin 2 x-\int 2 x \frac{\sin 2 x d x}{2}$ $=\frac{x^{2}}{2} \sin 2 x-\int x \sin 2 x d x$ Using integration by parts in $\int x \sin 2 x d x$ $=\frac{x^{2}}{2} \sin 2 x-\left(x \int \sin 2 x d ...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $S$ be the set of all real numbers and let $R$ be a relation on $S$ defined by $a R b \Leftrightarrow|a| \leq b$. Then, $R$ is A. reflexive but neither symmetric nor transitive B. symmetric but neither reflexive nor transitive C. transitive but neither reflexive nor symmetric D. none of these Solution: According to the question, Given set $S=\{\ldots \ldots,-2,-1,0,1,2 \ldots \ldots\}$ And $R=\{(a, b): a, b \in S$ and $|a| ...
Read More →Rate law cannot be determined from
Question: Rate law cannot be determined from the balanced chemical equation if _______. (i) the reverse reaction is involved. (ii) it is an elementary reaction. (iii) it is a sequence of elementary reactions. (iv) any of the reactants is in excess Solution: Option (i), (iii) and (iv) are the answers....
Read More →The value of rate constant of a pseudo
Question: The value of rate constant of a pseudo first order reaction ____________. (i) depends on the concentration of reactants present in a small amount. (ii) depends on the concentration of reactants present in excess. (iii) is independent of the concentration of reactants. (iv) depends only on temperature. Solution: Option (ii)depends on the concentration of reactants present in excessis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{2} \cos x d x$ Solution: Let I $=\int x^{2} \cos x d x$ Using integration by parts, $=x^{2} \int \cos x d x-\int \frac{d}{d x} x^{2} \int \cos x d x$ We know that, $\int \cos x d x=\sin x$ and $\frac{d}{d x} x^{n}=n x^{n-1}$ $=x^{2} \sin x-\int 2 x \sin x d x$ $=x^{2} \sin x-2 \int x \sin x d x$ We know that, $\int \sin x d x=-\cos x$ $=x^{2} \sin x-2\left(x \int \sin x d x-\int \frac{d}{d x} x \int \sin x d x\right)$ $=x^{2} \sin x-2\left(-x ...
Read More →Which of the following statement is not correct
Question: Which of the following statement is not correct for the catalyst? (i) It catalyses the forward and backward reaction to the same extent. (ii) It alters ∆G of the reaction. (iii) It is a substance that does not change the equilibrium constant of a reaction. (iv) It provides an alternate mechanism by reducing activation energy between reactants and products. Solution: Option (ii)It alters ∆G of the reactionis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{2} e^{-x} d x$ Solution: Let $I=\int x^{2} e^{-x} d x$ Using integration by parts, $=x^{2} \int e^{-x} d x-\int \frac{d}{d x} x^{2} \int e^{-x} d x$ We know that, $\int e^{n x} d x=\frac{e^{x}}{n}$ and $\frac{d}{d x} x^{n}=n x^{n-1}$ $=x^{2} \times-e^{-x}-\int 2 x \times-e^{-x} d x$ Using integration by parts in second integral, $=-\mathrm{x}^{2} \mathrm{e}^{-\mathrm{x}}+2\left(\mathrm{x} \int \mathrm{e}^{-\mathrm{x}} \mathrm{dx}-\int \frac{\m...
Read More →Compounds ‘A’ and ‘B’ react according to
Question: Compounds A and B react according to the following chemical equation. A (g) + 2 B (g) 2C (g) The concentration of either A or B was changed keeping the concentrations of one of the reactants constant and rates were measured as a function of initial concentration. Following results were obtained. Choose the correct option for the rate equations for this reaction. (i) Rate = k [A]2[B] (ii) Rate = k [A] [B]2 (iii) Rate = k [A] [B] (iv) Rate = k [A]2[B]0 Solution: Option (ii)Rate = k [A]...
Read More →A first-order reaction is 50% completed
Question: A first-order reaction is 50% completed in 1.26 1014 s. How much time would it take for 100% completion? (i) 1.26 1015s (ii) 2.52 1014s (iii) 2.52 1028s (iv) infinite Solution: Option (iv)infinite is the answer....
Read More →Which of the following statements is incorrect
Question: Which of the following statements is incorrect about the collision theory of chemical reaction? (i) It considers reacting molecules or atoms to be hard spheres and ignores their structural features. (ii) A number of effective collisions determine the rate of reaction. (iii) The collision of atoms or molecules possessing sufficient threshold energy results into the product formation. (iv) Molecules should collide with sufficient threshold energy and proper orientation for the collision ...
Read More →The rate law for the reaction A + 2B → C is found to be
Question: The rate law for the reaction A + 2B C is found to be Rate = k [A][B] The concentration of reactant B is doubled, keeping the concentration of A constant, the value of rate constant will be______. (i) the same (ii) doubled (iii) quadrupled (iv) halved Solution: Option (i)the same is the answer....
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