Consider the reaction of water with F2 and suggest,

Question: Consider the reaction of water with F2and suggest, in terms of oxidation andreduction, which species are oxidized/reduced. Solution: The reaction between fluorine and water can be represented as: $2 \mathrm{~F}_{2(g)}+2 \mathrm{H}_{2} \mathrm{O}_{(t)} \longrightarrow 4 \mathrm{H}_{(a q)}^{+}+4 \mathrm{~F}_{(a q)}^{-}+\mathrm{O}_{2(g)}$ This is an example of a redox reaction as water is getting oxidized to oxygen, while fluorine is being reduced to fluoride ion. The oxidation numbers of...

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction.

Question: A short bar magnet placed in a horizontal plane has its axis alignedalong the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earths magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the nullpoint (i.e., 14 cm) from the centre of the magnet? (Atnull points, field due to a magnet is equal and opposite ...

show that

Question: If $F(x)=\left[\begin{array}{ccc}\cos x -\sin x 0 \\ \sin x \cos x 0 \\ 0 0 1\end{array}\right]$, show that $F(x) F(y)=F(x+y)$. Solution: $F(x)=\left[\begin{array}{ccc}\cos x -\sin x 0 \\ \sin x \cos x 0 \\ 0 0 1\end{array}\right], F(y)=\left[\begin{array}{ccc}\cos y -\sin y 0 \\ \sin y \cos y 0 \\ 0 0 1\end{array}\right]$ $F(x+y)=\left[\begin{array}{lcl}\cos (x+y) -\sin (x+y) 0 \\ \sin (x+y) \cos (x+y) 0 \\ 0 0 1\end{array}\right]$ $F(x) F(y)$ $=\left[\begin{array}{ccc}\cos x -\sin x ...

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction.

Question: A short bar magnet placed in a horizontal plane has its axis alignedalong the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earths magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the nullpoint (i.e., 14 cm) from the centre of the magnet? (Atnull points, field due to a magnet is equal and opposite ...

What do you understand by the term ’auto-protolysis’ of water?

Question: What do you understand by the term auto-protolysis of water? What is itssignificance? Solution: Auto-protolysis (self-ionization) of water is a chemical reaction in which two water molecules react to produce a hydroxide ion ( $\mathrm{OH}^{-}$) and a hydronium ion $\left(\mathrm{H}_{3} \mathrm{O}^{+}\right)$. The reaction involved can be represented as: Auto-protolysis of water indicates its amphoteric nature i.e., its ability to act as an acid as well as a base. The acid-base reaction...

Question: Given $3\left[\begin{array}{ll}x y \\ z w\end{array}\right]=\left[\begin{array}{cc}x 6 \\ -1 2 w\end{array}\right]+\left[\begin{array}{cc}4 x+y \\ z+w 3\end{array}\right]$, find the values of $x, y, z$ andw. Solution: $3\left[\begin{array}{ll}x y \\ z w\end{array}\right]=\left[\begin{array}{rc}x 6 \\ -1 2 w\end{array}\right]+\left[\begin{array}{cc}4 x+y \\ z+w 3\end{array}\right]$ $\Rightarrow\left[\begin{array}{cc}3 x 3 y \\ 3 z 3 w\end{array}\right]=\left[\begin{array}{lc}x+4 6+x+y \...

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Question: An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Solution: We are given that an army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. We need to find the maximum number of columns in which they can march. Members in army = 616 Me...

A short bar magnet has a magnetic moment of

Question: A short bar magnet has a magnetic moment of $0.48 \mathrm{~J} \mathrm{~T}^{-1}$. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of $10 \mathrm{~cm}$ from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet. Solution: Magnetic moment of the bar magnet, $M=0.48 \mathrm{~J} \mathrm{~T}^{-1}$ (a)Distance,d= 10 cm = 0.1 m The magnetic field at distanced, from the centre of the magnet on the axis is g...

Compare the structures of H2O and H2O2.

Question: Compare the structures of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{H}_{2} \mathrm{O}_{2}$. Solution: In gaseous phase, water molecule has a bent form with a bond angle of $104.5^{\circ}$. The O-H bond length is $95.7$ pm. The structure can be shown as: Hydrogen peroxide has a non-planar structure both in gas and solid phase. The dihedral angle in gas and solid phase is $111.5^{\circ}$ and $90.2^{\circ}$ respectively....

If the HCF of 657 and 963 is expressible in the form $657 x+963 x-15$, find $x$.

Question: If the HCF of 657 and 963 is expressible in the form $657 x+963 x-15$, find $x$. Solution: We need to find $x$ if the H.C.F of 657 and 963 is expressible in the form $657 x+963 y(-15)$. Given integers are 657 and 963. By applying Euclid's division lemma, we get $963=657 \times 1+306$. Since the remainder $\neq 0$, so apply division lemma on divisor 657 and remainder 306 $657=306 \times 2+45$ Since the remainder $\neq 0$, so apply division lemma on divisor 306 and remainder 45 $306=45 \...

Arrange the following

Question: Arrange the following (i) $\mathrm{CaH}_{2}, \mathrm{BeH}_{2}$ and $\mathrm{TiH}_{2}$ in order of increasing electrical conductance. (ii) $\mathrm{LiH}, \mathrm{NaH}$ and $\mathrm{CsH}$ in order of increasing ionic character. (iii) $\mathrm{H}-\mathrm{H}, \mathrm{D}-\mathrm{D}$ and $\mathrm{F}-\mathrm{F}$ in order of increasing bond dissociation enthalpy. (iv) $\mathrm{NaH}, \mathrm{MgH}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ in order of increasing reducing property. Solution: (i)The ele...

At a certain location in Africa, a compass points 12º west of the geographic north.

Question: At a certain location in Africa, a compass points 12 west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60 above the horizontal. The horizontal component of the earths field is measured to be 0.16 G. Specify the direction and magnitude of the earths field at the location. Solution: Angle of declination,= 12 Angle of dip, $\delta=60^{\circ}$ Horizontal component of earths magnetic field,BH= 0.16 G Earths mag...

IQ of a person is given by the formula

Question: IQ of a person is given by the formula $\mathrm{IQ}=\frac{\mathrm{MA}}{\mathrm{CA}} \times 100$ Where $M A$ is mental age and $C A$ is chronological age. If $80 \leq I Q \leq 140$ for a group of 12 years old children, find the range of their mental age. Solution: It is given that for a group of 12 years old children, $80 \leq I Q \leq 140 \ldots$ (i) For a group of 12 years old children, $\mathrm{CA}=12$ years $\mathrm{IQ}=\frac{\mathrm{MA}}{12} \times 100$ Putting this value of IQ in ...

Saline hydrides are known to react with water violently producing fire.

Question: Saline hydrides are known to react with water violently producing fire. Can $\mathrm{CO}_{2}$, a well known fire extinguisher, be used in this case? Explain. Solution: Saline hydrides (i.e., NaH, LiH, etc.) react with water to form a base and hydrogen gas. The chemical equation used to represent the reaction can be written as: $\mathrm{MH}_{(s)}+\mathrm{H}_{2} \mathrm{O}_{(\text {av })} \longrightarrow \mathrm{MOH}_{(\text {aq })}+\mathrm{H}_{2(g)}$ The reaction is violent and produces...

find values of x and y.

Question: If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$, find values of $x$ and $y$. Solution: $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{l}10 \\ 5\end{array}\right]$ $\Rightarrow\left[\begin{array}{l}2 x \\ 3 x\end{array}\right]+\left[\begin{array}{c}-y \\ y\end{array}\right]=\left[\begin{array}{l}10 \\ 5\end{array}\ri...

A magnetic needle free to rotate in a vertical plane

Question: A magnetic needle free to rotate in a vertical plane parallel to themagnetic meridian has its north tip pointing down at 22 with the horizontal. The horizontal component of the earths magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earths magnetic field at the place. Solution: Horizontal component of earths magnetic field,BH= 0.35 G Angle made by the needle with the horizontal plane $=$ Angle of dip $=\delta=22^{\circ}$ Earthsmagnetic field strength =B...

How many litres of water will have to be added to 1125 litres of the 45%

Question: How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content? Solution: Letxlitres of water is required to be added. Then,total mixture = (x+ 1125) litres It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres. This resulting mixture will contain more than 25% but less than 30% acid content. $\therefore 30 \%$ of $(1125+x)45 \%$ of...

A magnetic needle free to rotate in a vertical plane

Question: A magnetic needle free to rotate in a vertical plane parallel to themagnetic meridian has its north tip pointing down at 22 with the horizontal. The horizontal component of the earths magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earths magnetic field at the place. Solution: Horizontal component of earths magnetic field,BH= 0.35 G Angle made by the needle with the horizontal plane $=$ Angle of dip $=\delta=22^{\circ}$ Earthsmagnetic field strength =B...

Among NH3, H2O and HF, which would you expect to have highest magnitude

Question: Among $\mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{O}$ and $\mathrm{HF}$, which would you expect to have highest magnitude of hydrogen bonding and why? Solution: The extent of hydrogen bonding depends upon electronegativity andthe number of hydrogen atoms available for bonding. Among nitrogen, fluorine, and oxygen, the increasing order of their electronegativities are N O F. Hence, the expected order of the extent of hydrogen bonding is HF H2O NH3. But, the actual order is H2O HF NH3. Alth...

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it.

Question: A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added? Solution: Letxlitres of 2% boric acid solution is required to be added. Then,total mixture = (x+ 640) litres This resulting mixture is to be more than 4% but less than 6% boric acid. $\therefore 2 \% x+8 \%$ of $6404 \%$ of $(x+64...

A circular coil of 16 turns and radius 10 cm carrying a current

Question: A circular coil of 16 turns and radius 10 cm carrying a current of0.75 A rests with its plane normal to an external field of magnitude 5.0102T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s1. What is the moment of inertia of the coil about its axis of rotation? Solution: Number of turns inthe circular coil,N= 16 Radius of the co...

Solve the equation for x, y, z and t if

Question: Solve the equation for $x, y, z$ and $t$ if $2\left[\begin{array}{ll}x z \\ y t\end{array}\right]+3\left[\begin{array}{rr}1 -1 \\ 0 2\end{array}\right]=3\left[\begin{array}{ll}3 5 \\ 4 6\end{array}\right]$ Solution: $2\left[\begin{array}{ll}x z \\ y t\end{array}\right]+3\left[\begin{array}{rr}1 -1 \\ 0 2\end{array}\right]=3\left[\begin{array}{ll}3 5 \\ 4 6\end{array}\right]$ $\Rightarrow\left[\begin{array}{ll}2 x 2 z \\ 2 y 2 t\end{array}\right]+\left[\begin{array}{lr}3 -3 \\ 0 6\end{a...

How does the atomic hydrogen or oxy-hydrogen torch function for cutting and welding purposes

Question: How does the atomic hydrogen or oxy-hydrogen torch function for cutting andwelding purposes? Explain. Solution: Atomic hydrogen atoms are produced by the dissociation of dihydrogen with the help of an electric arc. This releases a huge amount of energy (435.88 kJ mol1). This energy can be used to generate a temperature of 4000 K, which is ideal for welding and cutting metals. Hence, atomic hydrogen or oxy-hydrogen torches are used for these purposes. For this reason, atomic hydrogen is...

If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.

Question: If the HCF of 408 and 1032 is expressible in the form 1032m 408 5, findm. Solution: We need to find $m$ if the H.C.F of 408 and 1032 is expressible in the form $1032 m-408 \times 5$. Given integers are 408 and 1032 where $4081032$. By applying Euclid's division lemma, we get $1032=408 \times 2+216$. Since the remainder $\neq 0$, so apply division lemma on divisor 408 and remainder 216 $408=216 \times 1+192$ Since the remainder $\neq 0$, so apply division lemma on divisor 216 and remain...

A solution is to be kept between 68°F and 77°F.

Question: A solution is to be kept between 68F and 77F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by $\mathrm{F}=\frac{9}{8} \mathrm{C}+32 ?$ Solution: Since the solution is to be kept between $68^{\circ} \mathrm{F}$ and $77^{\circ} \mathrm{F}$, $68F77$ Putting $\mathrm{F}=\frac{9}{5} \mathrm{C}+32$, we obtain $68\frac{9}{5} \mathrm{C}+3277$ $\Rightarrow 68-32\frac{9}{5} \mathrm{C}77-32$ $\Rightarrow 36\frac{9}{5} \mathrm{C}4...