Find the angle to intersection of the following curves:
Question: Find the angle to intersection of the following curves: $y=x^{2}$ and $x^{2}+y^{2}=20$ Solution: Given: Curves $y=x^{2} \ldots$ (1) $\ x^{2}+y^{2}=20 \ldots(2)$ First curve $y=x^{2}$ $\Rightarrow \mathrm{m}_{1}=\frac{\mathrm{dy}}{\mathrm{dx}}=2 \mathrm{x} \ldots$ (3) Second curve is $x^{2}+y^{2}=20$ Differentiating above w.r.t $x$, $\Rightarrow 2 x+2 y \cdot \frac{d y}{d x}=0$ $\Rightarrow y \cdot \frac{d y}{d x}=-x$ $\Rightarrow m_{2}=\frac{d y}{d x}=\frac{-x}{y} \ldots(4)$ Substituti...
Read More →In both water and dimethyl ether (CH3 —Ο — CH3 ),
Question: In both water and dimethyl ether (CH3 Ο CH3 ), the oxygen atom is the central atom and has the same hybridization, yet they have different bond angles. Which one has a greater bond angle? Give reason. Solution: Dimethyl ether will have a greater bond angle. There will be more repulsion between bond pairs of CH3 groups attached in ether than between bond pairs of hydrogen atoms attached to oxygen in the water....
Read More →Explain why PCl5 is trigonal bipyramidal
Question: Explain why PCl5 is trigonal bipyramidal whereas IF5 is square pyramidal. Solution: In PCl5, P has 5 valence electrons in orbitals and make 5 bonds with 5 Cl atoms, it will share one of its electrons from 3s to 3d orbital, therefore the hybridization will be sp3d and the geometry will be trigonal bipyramidal. IF5, the Iodine atom has 7 valence electrons in molecular orbitals it will form 5 bonds with 5 Cl atoms using 5 electrons from its molecular orbital, two electrons will form one l...
Read More →Explain the shape of BrF5.
Question: Explain the shape of BrF5. Solution: In BrF5 the central atom is bromine which has the hybridization sp3d2. Br atom has 7 valence electrons out of which 5 are used to make pair with the F atoms and two are used to make lone pair of electrons. The lone pair and bond pair repel each other. Thus, the shape is square pyramidal....
Read More →Draw the graphs of y = cos x and
Question: Draw the graphs of y = cos x and $y=\cos 2 x \operatorname{in}[0,2 \pi]$ on the same axes. Solution: For cosx For cos(2x) The graph is:- Blue line depicts curve cos(2x) Purple lines depict cos(x)....
Read More →Using molecular orbital theory,
Question: Using molecular orbital theory, compare the bond energy and magnetic character of O2+and O2-species. Solution: The Molecular Orbital configuration of O2+ and O-2 is given below: O2+(15): 1s2 *1s2 2s2 *2s2 2pz2 2px2 = 2py2 *2px1 O2-(17): 1s2 *1s2 2s2 *2s2 2pz2 2px2 = 2py2 *2px2= *2py1 Bond order for O2+ = 10-5/2 = 2.5 Bond order for O-2 = 10-7/2 = 1.5 According to Molecular Orbital Theory, the greater the bond order greater is the bond energy. Thus, O2+is more stable than O2-...
Read More →Explain the non-linear shape
Question: Explain the non-linear shape of H2 S and non-planar shape of PCl3 using valence shell electron pair repulsion theory. Solution: In H2S, the Sulphur atom is surrounded by the four electron pairs (two bond pairs and two lone pairs). These four electron pairs adopt tetrahedral geometry. The repulsion between the lone pair electrons brings distortion in the shape of the H2S. Thus, H2Sis not linear in shape....
Read More →Find the angle to intersection of the following curves:
Question: Find the angle to intersection of the following curves: $y^{2}=x$ and $x^{2}=y$ Solution: Given: Curves $y^{2}=x \ldots(1)$ $\ x^{2}=y \ldots(2)$ First curve is $y^{2}=x$ Differentiating above w.r.t $x$, $\Rightarrow 2 y \cdot \frac{d y}{d x}=1$ $\Rightarrow m_{1}=\frac{d y}{d x}=\frac{1}{2 x} \ldots(3)$ The second curve is $x^{2}=y$ $\Rightarrow 2 x=\frac{d y}{d x}$ $\Rightarrow m_{2}=\frac{d y}{d x}=2 x \ldots(4)$ Substituting (1) in (2), we get $\Rightarrow x^{2}=y$ $\Rightarrow\lef...
Read More →Which of the following statements
Question: Which of the following statements are not correct? (i) NaCl being an ionic compound is a good conductor of electricity in the solid-state. (ii) In canonical structures, there is a difference in the arrangement of atoms. (iii) Hybrid orbitals form stronger bonds than pure orbitals. (iv) VSEPR Theory can explain the square planar geometry of XeF4. Solution: Option (i) and (ii) are the answers. III. Short Answer Type...
Read More →Species having same bond
Question: Species having same bond order are : (i) N2 (ii) N2- (iii) F2+ (iv) O2 Solution: Option (iii)F2+ and (iv)O2 are the answers....
Read More →Draw the graphs of y = sin x and
Question: Draw the graphs of y = sin x and $y=\cos x$ in $[0,2 \pi]$ on the same axes. Solution: For sinx For cosx The green line represents curve for $\sin (x)$ and blue for $\cos (x)$ for $[0,2 \pi]$....
Read More →Diamagnetic species are those
Question: Diamagnetic species are those which contain no unpaired electrons. Which among the following are diamagnetic? (i) N2 (ii) N22- (iii) O2 (iv) O22- Solution: Option (i)N2 and (iv)O22- are the answers...
Read More →Draw the graph of each of the following functions:
Question: Draw the graph of each of the following functions: $\sin \frac{x}{2}$ Solution: To draw the graph of the curve sin(x/2) assume some standard angle measures which will help in locating the points and drawing the curve. Therefore, the graph of curve 2cos(3x) can be drawn as Here, the frequency of the function sin(x) is decreased by 0.5 times....
Read More →Which of the following statements are
Question: Which of the following statements are correct about CO32-? (i) The hybridisation of the central atom is sp3. (ii) Its resonance structure has one CO single bond and two C=O double bonds. (iii) The average formal charge on each oxygen atom is 0.67 units. (iv) All CO bond lengths are equal. Solution: Option (iii) and (iv) are the answers....
Read More →Which of the following species
Question: Which of the following species have the same shape? (i) CO2 (ii) CCl4 (iii) O3 (iv) NO2 Solution: Option (iii) and (iv) are the answers....
Read More →Draw the graph of each of the following functions:
Question: Draw the graph of each of the following functions: 2cos 3x Solution: To draw the graph of the curve 2cos(3x) assume some standard angle measures which will help in locating the points and drawing the curve. Therefore, the graph of curve 2cos(3x) can be drawn as Here, the amplitude and frequency of the function cos(x) is increased by 2 and 3 times respectively....
Read More →CO is isoelectronic with
Question: CO is isoelectronic with (i) NO+ (ii) N2 (iii) SnCl2 (iv) NO2 Solution: Option (i) and (ii) are the answers....
Read More →Which of the following attain
Question: Which of the following attain the linear structure: (i) BeCl2 (ii) NCO+ (iii) NO2 (iv) CS2 Solution: Option (i) and (iv) are the answers....
Read More →Draw the graph of each of the following functions:
Question: Draw the graph of each of the following functions: 2sin 3x Solution: To draw the graph of the curve 2sin(3x) assume some standard angle measures which will help in locating the points and drawing the curve The graph looks like:...
Read More →Which of the following have
Question: Which of the following have identical bond order? (i) CN (ii) NO+ (iii) O2 (iv) O2 Solution: Option (i) and (ii) are the answers....
Read More →Draw the graph of each of the following functions:
Question: Draw the graph of each of the following functions: 3sin x Solution: To draw the graph of the curve 3sin(x) assume some standard angle measures which will help in locating the points and drawing the curve. Therefore, the graph of curve 3sin(x) can be drawn as Here, the amplitude of the function sin(x) is increased by 3 times....
Read More →Find the equation of the tangents
Question: Find the equation of the tangents to the curve $3 x^{2}-y^{2}=8$, which passes through the point $(4 / 3,0)$. Solution: assume point $(a, b)$ which lies on the given curve finding the slope of the tangent by differentiating the curve $6 x-2 y \frac{d y}{d x}=0$ $\frac{d y}{d x}=\frac{3 x}{y}$ m(tangent) at $(a, b)$ is $\frac{3 a}{b}$ Since this tangent passes through $\left(\frac{4}{3}, 0\right)$, its slope can also be written as $\frac{b-0}{a-\frac{4}{3}}$ Equating both the slopes as ...
Read More →Draw the graph of each of the following functions:
Question: Draw the graph of each of the following functions: Sin 3x Solution: To draw the graph of the curve sin(3x) assume some standard angle measures which will help in locating the points and drawing the curve. Therefore, the graph of curve sin(3x) can be drawn as Here, the frequency of the function sin(x) is increased by 3 times....
Read More →Amongst the following elements
Question: Amongst the following elements whose electronic configurations are given below, the one having the highest ionisation enthalpy is (i) [Ne]3s23p1 (ii) [Ne]3s23p3 (iii) [Ne]3s23p2 (iv) [Ar]3d104s24p3 Solution: Option (ii) is the answer....
Read More →The electronic configuration
Question: The electronic configuration of the outer most shell of the most electronegative element is (i) 2s22p5 (ii) 3s23p5 (iii) 4s24p5 (iv) 5s25p Solution: Option (i) is the answer....
Read More →