Which of the following statements is correct?
Question: Which of the following statements is correct? (i) The rate of a reaction decreases over time as the concentration of reactants decreases. (ii) The rate of a reaction is the same at any time during the reaction. (iii) The rate of a reaction is independent of temperature change. (iv) The rate of a reaction decreases with increase in the concentration of the reactant(s) Solution: Option (i) is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x e^{2 x} d x$ Solution: Let $I=\int x e^{2 x} d x$ Using integration by parts, $I=x \int e^{2 x} d x-\int \frac{d}{d x} x \int e^{2 x} d x$ We know that, $\int e^{n x} d x=\frac{e^{x}}{n}$ and $\frac{d}{d x} x=1$ $=\frac{x e^{2 x}}{2}-\int \frac{e^{2 x}}{2} d x$ $=\frac{x e^{2 x}}{2}-\frac{e^{2 x}}{4}+c$ $I=\left(\frac{x}{2}-\frac{1}{4}\right) e^{2 x}+c$...
Read More →Consider the graph given in Fig. 4.2.
Question: Consider the graph given in Fig. 4.2. Which of the following options does not show the instantaneous rate of reaction at 40th second? (i) V5-V2/50-30 (ii) V4-V2/50-30 (iii) V3-V2/40-30 (iv) V3-V1/40-20 Solution: Option (ii) is the answer....
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $Z$ be the set of all integers and let $R$ be a relation on $Z$ defined by $a R b \Leftrightarrow a \geq b$. Then, $R$ is A. symmetric and transitive but not reflexive B. reflexive and symmetric but not transitive C. reflexive and transitive but not symmetric D. an equivalence relation Solution: According to the question , Given set $Z=\{1,2,3,4 \ldots . .\}$ And $R=\{(a, b): a, b \in Z$ and $a \geq b\}$ Formula For a relat...
Read More →Which of the following statements is not correct
Question: Which of the following statements is not correct about an order of a reaction. (i) The order of a reaction can be a fractional number. (ii) Order of a reaction is experimentally determined quantity. (iii) The order of a reaction is always equal to the sum of the stoichiometric coefficients of reactants in the balanced chemical equation for a reaction. (iv) The order of a reaction is the sum of the powers of the molar concentration of the reactants in the rate law expression. Solution: ...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x e^{x} d x$ Solution: Let $I=\int x e^{x} d x$ Using integration by parts, $I=x \int e^{x} d x-\int \frac{d}{d x} x \int e^{x} d x$ We know that, $\int e^{x} d x=e^{x}$ and $\frac{d}{d x} x=1$ $=x e^{x}-\int e^{x} d x$ $=x e^{x}-e^{x}+c$...
Read More →Consider the Arrhenius equation given below
Question: Consider the Arrhenius equation given below and mark the correct option. aE /RT k = A e (i) Rate constant increases exponentially with increasing activation energy and decreasing temperature. (ii) Rate constant decreases exponentially with increasing activation energy and decreasing temperature. (iii) Rate constant increases exponentially with decreasing activation energy and decreasing temperature. (iv) Rate constant increases exponentially with decreasing activation energy and increa...
Read More →Consider a first order gas phase decomposition
Question: Consider a first order gas phase decomposition reaction given below : A(g) B(g) + C(g) The initial pressure of the system before decomposition of A was pi. After lapse of time t, total pressure of the system increased by x units and became pt The rate constant k for the reaction is given as _________. (i) k = 2.303/t log Pi/Pi-x (ii) ) k = 2.303/t log Pi/2Pi-Pt (iii) ) k = 2.303/t log Pi/2Pi-2Pt (iv) ) k = 2.303/t log Pi/Pi+x Solution: Option (ii)k = 2.303/t log Pi/2Pi-Pt is the answer...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x^{3} \log x d x$ Solution: Let $I=\int x^{3} \log x d x$ Using integration by parts, $I=\log x \int x^{3} d x-\int \frac{d}{d x} \log x \int x^{3} d x$ We have, $\int x^{n} d x=\frac{x^{n+1}}{n+1}$ and $\int \log x=\frac{1}{x}$ $=\log x \times \frac{x^{4}}{4}-\int \frac{1}{x} \times \frac{x^{4}}{4}$ $=\log x \times \frac{x^{4}}{4}-\frac{1}{4} \int x^{3} d x$ $=\frac{x^{4}}{4} \log x-\frac{1}{4} \times \frac{x^{4}}{4}$ $=\frac{x^{4}}{4} \log x-\f...
Read More →Activation energy of a chemical reaction
Question: Activation energy of a chemical reaction can be determined by _____________. (i) determining the rate constant at standard temperature. (ii) determining the rate constants at two temperatures. (iii) determining the probability of collision. (iv) using catalyst. Solution: Option (ii)determining the rate constants at two temperatures is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \log (x+1) d x$ Solution: Let $I=\int \log (x+1) d x$ That is, $I=\int 1 \times \log (x+1) d x$ Using integration by parts, $I=\log (x+1) \int 1 d x-\int \frac{d}{d x} \log (x+1) \int 1 d x$ We know that, $\int 1 \mathrm{dx}=\mathrm{x}$ and $\int \log \mathrm{x}=\frac{1}{\mathrm{x}}$ $\frac{x}{x+1}=1-\frac{1}{x+1}$ $=x \log (x+1)-\int\left(1-\frac{1}{x+1}\right) d x$ $=x \log (x+1)-x+\log (x+1)+c$...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x \cos x d x$ Solution: Let $\mathrm{I}=\int \mathrm{x} \cos \mathrm{x} \mathrm{dx}$ We know that, $\int \mathrm{UV}=\mathrm{U} \int \mathrm{V} \mathrm{dv}-\int \frac{\mathrm{d}}{\mathrm{dx}} \mathrm{U} \int \mathrm{V} \mathrm{dv}$ Using integration by parts, $I=x \int \cos x d x-\int \frac{d}{d x} x \int \cos x d x I=\int x \cos x d x$ We have, $\int \sin x=-\cos x, \int \cos x=\sin x$ $=x \times \sin x-\int \sin x d x$ $=x \sin x+\cos x+c$...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $R$ be a relation on the set $N$ of all natural numbers, defined by $a R b \Leftrightarrow a$ is a factor of $b$. 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 $N=\{1,2,3,4 \ldots \ldots\}$ And $R=\{(a, b): a, b \in N$ and $a$ is a factor of $b\}$ ...
Read More →In the presence of a catalyst,
Question: In the presence of a catalyst, the heat evolved or absorbed during the reaction ___________. (i) increases. (ii) decreases. (iii) remains unchanged. (iv) may increase or decrease. Solution: Option (iii)remains unchanged is the answer....
Read More →Evaluate the integral
Question: Evaluate the integral $\int \frac{4 \sin x+5 \cos x}{5 \sin x+4 \cos x} d x$ Solution: Ideas required to solve the problems: * Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integration. If derivative of a function is present in an integration or if chances of its presence after few modification is possible then we apply integration by substitution method. * Knowledge of integration of fundamental functions like ...
Read More →The role of a catalyst is to change ______________.
Question: The role of a catalyst is to change ______________. (i) gibbs energy of reaction. (ii) enthalpy of reaction. (iii) activation energy of reaction. (iv) equilibrium constant. Solution: Option (iii)activation energy of reaction is the answer....
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: Let $Z$ be the set of all integers and let $R$ be a relation on $Z$ defined by a $R b \Leftrightarrow(a-b)$ is divisible by $3 .$ 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 $Z=\{1,2,3,4 \ldots . .\}$ And $R=\{(a, b): a, b \in Z$ and $(a-b)$ is divis...
Read More →Why on dilution the ˄m of CH3COOH increases
Question: Why on dilution the ˄mof CH3COOH increases drastically, while that of CH3COONa increases gradually? Solution: CH3COOH is a weak electrolyte and CH3COONa is a strong electrolyte. A weak electrolyte has a lower degree of dissociation at higher concentration but upon dilution, the degree of dissociation increases, the number of ions per unit volume increases and this lead to an increase in....
Read More →Write the cell reaction of a lead storage
Question: Write the cell reaction of a lead storage battery when it is discharged. How does the density of the electrolyte change when the battery is discharged? Solution: Pb(s)+PbO2(s)+2H2SO4(aq) 2PbSO4(s) + 2H2O(l) Density decreases as the product water form dilute the H2SO4 concentration during the discharge of the battery....
Read More →What advantage do the fuel cells
Question: What advantage do the fuel cells have over primary and secondary batteries? Solution: Fuel cells are cells that convert the energy of combustion of fuels like hydrogen, methanol into electrical energy. Fuel cells run continuously as long as reactants are supplied. Primary batteries discharge and are one-time use only, and secondary batteries can be recharged, but recharging takes a lot of time....
Read More →Write the Nernst equation for the cell reaction
Question: Write the Nernst equation for the cell reaction in the Daniel cell. How will the ECell be affected when the concentration of Zn2+ ions is increased? Solution: Ecell = Ecell RT[Zn2+]/ nF[Cu2+] Galvanic cell reaction: Zn(s)|Zn2+(aq)||Cu2+(aq)|Cu(s) Anode- oxidation half-cell: Zn(s) Zn2+ (aq)+ 2e Cathode- reduction half-cell: Cu2+ (aq)+ 2e- Cu(s) Overall reaction: Zn(s) + Cu2+ (aq) Zn2+(aq) +Cu(s) [Zn2+] and [Cu2+] are the concentration of the Zn2+ and Cu2+ ion in the solution. Ecell = Ec...
Read More →Consider a cell given below
Question: Consider a cell given below Cu|Cu2+|| Cl|Cl2, Pt Write the reactions that occur at anode and cathode. Solution: Galvanic cell: Cu|Cu2+|| Cl|Cl2, Pt Anode- Oxidation half-cell: Cu(s) Cu2+ + 2e- Cathode- Reduction half-cell: Cl2(g)+ 2e- 2Cl- Thus, Cu is anode as it is getting oxidised....
Read More →Which reference electrode is used to measure
Question: Which reference electrode is used to measure the electrode potential of other electrodes? Solution: Standard hydrogen electrode (SHE) is used as a reference electrode. The potential of SHE is assigned the value zero. The electrode potential of other electrodes is measured with respect to this....
Read More →In an aqueous solution,
Question: In an aqueous solution, how does specific conductivity of electrolytes change with the addition of water? Solution: The addition of water dilutes the electrolyte. The number of ions in a given volume decreases and conductivity also reduces....
Read More →Evaluate the integral
Question: Evaluate the integral $\int \frac{8 \cot x+1}{3 \cot x+2} d x$ Solution: Ideas required to solve the problems: * Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integration. If derivative of a function is present in an integration or if chances of its presence after few modification is possible then we apply integration by substitution method. * Knowledge of integration of fundamental functions like sin, cos, poly...
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