Write redox couples involved in the reactions
Question: Write redox couples involved in the reactions (i) to (iv) given in question 34. Solution: Redox couple is a reducing element along with its oxidizing form. So for the given example, (i) Cu2+ /Cu and Zn2+/Zn (ii) Mg+/Mg and Fe2+/Fe (iii) Br-/Br and Cl-/Cl (iv) Fe2+ /Fe and Cd2+/Cd...
Read More →Why does fluorine not show
Question: Why does fluorine not show disproportionation reaction? Solution: Fluorine has the highest electronegativity in the entire periodic table with EN value of 3.98; this means that out of 4 bonded electrons 3.98 fractions of it is shared with fluorine. Thus the ability to attract an electron from other elements is more pronounced than the atom with which it is bonded. And as fluorine has the highest reduction potential (Ecell =2.87) in the spectrochemical series, it cannot undergo oxidatio...
Read More →The slope of the tangent to the curve
Question: The slope of the tangent to the curve $x=3 t^{2}+1, y=t^{3}-1$ at $x=1$ is A. $\frac{1}{2}$ B. 0 C. $-2$ D. $\infty$ Solution: Given that $x=3 t^{2}+1, y=t^{3}-1$ For $x=1$ $3 t^{2}+1=1$ $\Rightarrow 3 t^{2}=0$ $\Rightarrow t=0$ Now, differentiating both the equations w.r.t. t, we get $\frac{\mathrm{dx}}{\mathrm{dt}}=6 \mathrm{t}$ and $\frac{\mathrm{dy}}{\mathrm{dt}}=3 \mathrm{t}^{2}$ $\Rightarrow$ Slope of the curve: $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\frac{\mathrm{dy}}{\mathrm{dt...
Read More →If θ is the angle between the diagonals of a parallelogram ABCD
Question: If is the angle between the diagonals of a parallelogram ABCD whose vertices are A(0, 2), B(2,-1), C(4, Solution: Given points of the parallelogram are A(0, 2), B(2,-1), C(4, 0) and D(2, 3) slope $=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$ The slope of diagonal $A C=\left(\frac{0-2}{4-0}\right)=\frac{-2}{4}=\frac{-1}{2}=m_{1}$ The slope of diagonal $B D=\left(\frac{3+1}{2-2}\right)=\frac{4}{0}=\infty=m_{2}$ So diagonal BD is perpendicular to X-ax...
Read More →Based on standard electrode potential values,
Question: Based on standard electrode potential values, suggest which of the following reactions would take place? (Consult the book for E\degree value). (i) Cu + Zn2+ Cu2+ + Zn (ii) Mg + Fe2+ Mg2+ + Fe (iii) Br2 + 2Cl- Cl2 + 2Br- (iv) Fe + Cd2+ Cd + Fe2+ Solution: (i) Cu + Zn2+ Cu2+ + Zn Here Cu undergoes oxidation so it acts as anode and Zn acts as the cathode. So from the table For cathode Ecathode = -0.76 V For anode Eanode = 0.52 V Ecell = -0.24V As the EMF of the cell is negative the given...
Read More →Explain redox reactions based on electron transfer.
Question: Explain redox reactions based on electron transfer. Give suitable examples. Solution: In a redox reaction if one species loses electrons its considered to be undergoing oxidation reaction and acts as oxidizing agent or oxidant, and for species who accepts electrons is said to undergo reduction and behave as reductant. For example Zinc and HCl reaction Zn + 2HCl ZnCl2 + H2 zinc loses electrons to the electronegative atom Cl with the reaction for oxidation and reduction as follows: Oxida...
Read More →In the following questions,
Question: In the following questions, a statement of assertion (A) followed by a statement of the reason (R) is given. Choose the correct option out of the choices given below each question. Assertion (A): Redox couple is the combination of the oxidised and reduced form of a substance involved in an oxidation or reduction half cell. Reason (R) : In the representation E Fe3+/fe2+and Ecu2+/cu , Fe3+ / Fe2+ and Cu2+ are redox couples. (i) Both A and R are true and R is the correct explanation of A....
Read More →If the line y=x touches the curve
Question: If the line $y=x$ touches the curve $y=x^{2}+b x+c$ at a point $(1,1)$ then A. $b=1, c=2$ B. $b=-1, c=1$ C. $b=2, c=1$ D. $b=-2, c=1$ Solution: Given that line $y=x$ touches the curve $y=x^{2}+b x+c$ at a point $(1,1)$ Slope of line $=1$ Slope of tangent to the curve $=1$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=2 \mathrm{x}+\mathrm{b}$ $\Rightarrow 2 \mathrm{x}+\mathrm{b}=1$ $\Rightarrow 2+\mathrm{b}=1$ $\Rightarrow \mathrm{b}=-1$ Putting this and $x=1$ and $y=1$ in the equation o...
Read More →If θ is the angle between the lines joining the points
Question: If is the angle between the lines joining the points (0, 0) and B(2, 3), and the points C(2, -2) and D(3, 5), show that $\tan \theta=\frac{11}{23}$ Solution: The given points are A(0,0),B(2,3) and C(2,-2),D(3,5). slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ The slope of line $\mathrm{AB}$ is $\left(\frac{3-0}{2-0}\right)=\frac{3}{2}=\mathrm{m}_{1}$ And the slope of line $C D$ is $\left(\frac{5+2}{3-2}\right)=7=\mathrm{m}_{2}$ We know that angle between two lines with their slo...
Read More →Assertion (A): The decomposition of hydrogen
Question: Assertion (A): The decomposition of hydrogen peroxide to form water and oxygen is an example of a disproportionation reaction. Reason (R): The oxygen of peroxide is in 1 oxidation state and it is converted to zero oxidation state in O2 and 2 oxidation state in H2O. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (i) Both A ...
Read More →Assertion (A): In the reaction between potassium permanganate
Question: Assertion (A): In the reaction between potassium permanganate and potassium iodide, permanganate ions act as an oxidising agent. Reason (R): Oxidation state of manganese changes from +2 to +7 during the reaction. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (iii) A is true but R is falseis correct....
Read More →Assertion (A): Among halogens,
Question: Assertion (A): Among halogens, fluorine is the best oxidant. Reason (R): Fluorine is the most electronegative atom. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (ii)Both A and R are true but R is not the correct explanation of Ais correct....
Read More →If the curve
Question: If the curve ay $+x^{2}=7$ and $x^{3}=y$ cut orthogonally at $(1,1)$, then a is equal to A. 1 B. $-6$ C. 6 D. 0 Solution: Given that the curves $a y+x^{2}=7$ and $x^{3}=y$ Differentiating both of them w.r.t. $x$, $a \frac{d y}{d x}+2 x=0$ and $3 x^{2}=\frac{d y}{d x}$ $\Rightarrow \frac{d y}{d x}=\frac{-2 x}{a}$ and $\frac{d y}{d x}=3 x^{2}$ For $(1,1)$ $\frac{d y}{d x}=\frac{-2}{a}$ and $\frac{d y}{d x}=3$ Let $\mathrm{m}_{1}=\frac{-2}{a}$ and $\mathrm{m}_{2}=3$ $m_{1} \times m_{2}=-1...
Read More →If A(1, 2), B(-3, 2) and C(3, 2) be the vertices of a ΔABC, show that
Question: If $A(1,2), B(-3,2)$ and $C(3,2)$ be the vertices of a $\triangle A B C$, show that (i) $\tan \mathrm{A}=2$ (ii) $\tan \mathrm{B}=\frac{2}{3}$ (iii) $\tan \mathrm{C}=\frac{4}{7}$ Solution: Points A,B,C lie on a same line, therefore the slope of each line is same and hence it does not form a triangle....
Read More →Match the items in Column I with
Question: Match the items in Column I with relevant items in Column II. Solution: (i) is e (ii) is d (iii) is c (iv) is b (v) is f...
Read More →Find the angle between the lines whose slopes are
Question: Find the angle between the lines whose slopes are $(2-\sqrt{3})$ and $(2+\sqrt{3})$ Solution: We know that if slope of two lines are m1 and m2 respectively, then the angle between them is given by $\tan \theta=\frac{\mathrm{m}_{2}-\mathrm{m}_{1}}{1+\mathrm{m}_{1} \mathrm{~m}_{2}}$ Here $\mathrm{m}_{2}=2+\sqrt{3}$ and $\mathrm{m}_{1}=2-\sqrt{3}$ $\tan \theta=\frac{(2+\sqrt{3})-(2-\sqrt{3})}{1+(2+\sqrt{3})(2-\sqrt{3})}$ $=\frac{2 \sqrt{3}}{1+\left(2^{2}-(\sqrt{3})^{2}\right)}$ $=\frac{2 ...
Read More →Match Column I with Column II
Question: Match Column I with Column II for the oxidation states of the central atoms. Solution: (i) is d (ii) is e (iii) is c (iv) a...
Read More →The angle of intersection of the curves
Question: The angle of intersection of the curves $x y=a^{2}$ and $x^{2}-y^{2}=2 a^{2}$ is: A. $0^{\circ}$ B. $45^{\circ}$ C. $90^{\circ}$ D. $30^{\circ}$ Solution: Given that the curves $x y=a^{2}$ and $x^{2}-y^{2}=2 a^{2}$ Differentiating both of them w.r.t. $x$, $x \frac{d y}{d x}+y=0$ and $2 x-2 y \frac{d y}{d x}=0$ $\Rightarrow \frac{d y}{d x}=\frac{-y}{x}$ and $\frac{d y}{d x}=\frac{x}{y}$ Let $\mathrm{m}_{1}=\frac{-\mathrm{y}}{\mathrm{x}}$ and $\mathrm{m}_{2}=\frac{\mathrm{x}}{\mathrm{y}}...
Read More →Balance the following ionic equations
Question: Balance the following ionic equations (i) Cr2O72- + H+ + I- Cr3+ + I2 + H2O (ii) Cr2O2-7 + Fe2+ + H+ Cr3+ + Fe3+ + H2O (iii) MnO-4 + SO2-3 + H+ Mn2+ + SO42- + H2O (iv) MnO4- + H+ + Br- Mn2+ + Br2 + H2O Solution: (i) 6I + Cr2O72- + 14H+ 2Cr3+ + 3I2 + 7H2O (ii) Cr2O2-7 + 6Fe2+ + 14H+ 2Cr3+ + 6Fe3+ + 7H2O (iii) 2MnO-4 + 5SO2-3 + 6H+ 2Mn2+ + 5SO42- + 3H2O (iv) 2MnO4- + 16H+ + 10Br- 2Mn2+ + 5Br2 + 8H2O...
Read More →Find the angle between the lines whose slopes are
Question: Find the angle between the lines whose slopes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$. Solution: To find out the angle between two lines, the angle is equal to the difference in . The slope of a line $=\tan \theta=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$ So slope of the first line $=\sqrt{3}=\tan \theta_{1} \Rightarrow \tan \theta_{1}=\sqrt{3}$ $\Rightarrow \theta_{1}=\tan ^{-1}(\sqrt{3})$ $\Rightarrow \theta_{1}=60^{\circ}$ The slope of the sec...
Read More →Identify the redox reactions out of the following
Question: Identify the redox reactions out of the following reactions and identify the oxidising and reducing agents in them. (i) 3HCI(aq) + HNO3 (aq) CI2(g) + NOCI (g) + 2H2O(l) (ii) HgCI2 (aq) + 2KI (aq) HgI2 (s) + 2KCI (aq) (iii) Fe2O3 (s) + 3CO(g) 2Fe (s) + 3CO2(g) (iv) PCI3 (I) + 3H2O (I) 3HCI (aq) + H3 Po3 (aq) (v) 4NH3 + 3O2 (g) 2N2 (g) + 6H2 O (g) Solution: (i) (iii) and (iv) are redox reactions In (i) Reducing agent: HCl Oxidizing agent: HNO3 In (iii) Oxidising agent: Fe2O3 Reducing age...
Read More →At what points the slope of the tangent to the curve
Question: At what points the slope of the tangent to the curve $x^{2}+y^{2}-2 x-3=0$ is zero. A. $(3,0),(-1,0)$ B. $(3,0),(1,2)$ C. $(-1,0),(1,2)$ D. $(1,2),(1,-2)$ Solution: Given that the curve $x^{2}+y^{2}-2 x-3=0$ Differentiation on both the sides, $2 x+2 y \frac{d y}{d x}-2=0$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1-\mathrm{x}}{\mathrm{y}}$ According to the question, Slope of the tangent $=0$ $\Rightarrow \frac{1-x}{y}=0$ $\Rightarrow x=1$ Putting this in equation of curve, $1+...
Read More →Balance the following equations by
Question: Balance the following equations by the oxidation number method. (i) Fe2+ + H+ + Cr2 O2-7 Cr3+ + Fe3+ + H2O (ii) I2+ N O3 NO2+ I O3 (iii) I2 + S22 O3 I + S42 O (iv) MnO2 + C2 O2-4 Mn2+ + CO2 Solution: (i) 6Fe2+ + Cr2O72- + 14H+ 6Fe3+ + 2Cr3+ + 7H2O (ii) I2 + 10NO3- + 8H+ 2IO3- + 10NO2 +4H2O (iii) 2S2O3 2- + I2 S4O62- + 2l- (iv) C2O402- +MnO2 + 4H+ 2CO2 +MN2+ +2H2O...
Read More →Calculate the oxidation number of phosphorus
Question: Calculate the oxidation number of phosphorus in the following species. (a) Na2S2O3 (b) Na2S4O6 (c) Na2SO3 (d) Na2SO4 Solution: Na2S2O3 x= +2 Na2S4O6 x= +5 Na2SO3 x= +4 Na2SO4 x= +6...
Read More →Calculate the oxidation number
Question: Calculate the oxidation number of phosphorus in the following species. (a) HPO2-3 and PO42- Solution: HPO2-3 x= +3 PO42- x=+5...
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