GTU BE01000031 Chemistry Summer 2025 Solved Paper & Solutions

A biodegradable polymer is a polymer that can be broken down by the action of microorganisms (bacteria, fungi and algae) into simple harmless products: carbon dioxide, water and biomass. It does not stay in the environment for hundreds of years, as plastics like polythene do.

Examples: PHBV (poly-hydroxybutyrate-co-hydroxyvalerate), polylactic acid (PLA), polycaprolactone and starch-based plastics.

Uses: carry bags, packaging films, surgical stitches, and drug delivery.

The zeolite (permutit) process is a method of softening hard water by passing it through a bed of sodium zeolite.

Zeolite: hydrated sodium aluminium silicate, $\text{Na}_2\text{O}\cdot\text{Al}_2\text{O}_3\cdot x\text{SiO}_2\cdot y\text{H}_2\text{O}$, written as $\text{Na}_2\text{Z}$. It has a porous structure, and its sodium ions can be exchanged with the calcium and magnesium ions of hard water.

Process: hard water is passed slowly through the bed from the top. The $\text{Ca}^{2+}$ and $\text{Mg}^{2+}$ ions are taken by the zeolite, and $\text{Na}^+$ goes into the water:

Regeneration: when the bed has exchanged all its sodium (it becomes $\text{CaZ}$ and $\text{MgZ}$), it is washed with a 10% solution of NaCl (brine):

The washings of $\text{CaCl}_2$ and $\text{MgCl}_2$ are drained, and the bed is used again.

Advantages:

1. The water has a very low hardness, about 10 ppm.
2. The equipment is small and easy to run, and the process is quick.
3. No sludge is formed, so there is no problem of disposal.
4. The cost of regeneration is low, as the salt is cheap.

Disadvantages:

1. The soft water has sodium salts, so the dissolved solids are not removed. It is not suitable for high pressure boilers.
2. Turbid water, and ions such as Fe$^{2+}$ and Mn$^{2+}$, clog or foul the zeolite.
3. Acidic water damages the zeolite, and the water must be neutral.
4. It does not remove anions such as bicarbonate.

Caustic embrittlement is a type of boiler corrosion in which the boiler metal becomes brittle and cracks at the stressed places (rivets, bends and joints), due to high concentration of sodium hydroxide in the boiler water.

Cause: in a high pressure boiler, $\text{Na}_2\text{CO}_3$ used for softening hydrolyses to give NaOH: $\text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \to 2\text{NaOH} + \text{CO}_2$. The NaOH enters the small cracks by capillary action, and its concentration increases as water evaporates. It attacks the stressed iron, which is the anode, and cracks form.

Prevention: use sodium phosphate in place of sodium carbonate for softening, add tannin or lignin to coat the cracks, and add sodium sulphate to block the cracks.

There are two approaches to make nanomaterials.

1. Top-down approach: a bulk material is made smaller, by cutting, grinding or etching, until it reaches the nanoscale. Material is removed from the large piece.

• Methods: ball milling, lithography, etching and sputtering.
• Example: making nanoparticles of a metal by ball milling.
• Limits: it may bring defects and impurities, and the particle size is not easy to control.

2. Bottom-up approach: the nanomaterial is built up from atoms or molecules, which assemble into the larger nano structure. It is the method of nature.

• Methods: sol-gel, chemical vapour deposition (CVD), precipitation, and self-assembly.
• Example: growing carbon nanotubes by CVD, or gold nanoparticles from gold salt by chemical reduction.
• Advantage: better control of the size and shape, with fewer defects.

Pitting corrosion is a localised form of corrosion in which small pits (holes) form on the metal surface, while the rest of the surface is not affected. It can cause a hole through the metal and sudden failure with little loss of metal.

Causes: a break in the protective oxide film at a point, because of scratches, dirt, a non-uniform surface, or chloride ions (Cl$^-$) in the water. It is common for stainless steel and aluminium in sea water.

Mechanism: the small bare area becomes the anode, and the large area of the unbroken film around it becomes the cathode.

• Anode (inside the pit): $\text{Fe} \to \text{Fe}^{2+} + 2e^-$
• Cathode (outside the pit, the large surface): $\text{O}_2 + 2\text{H}_2\text{O} + 4e^- \to 4\text{OH}^-$

The area of the anode is small and the cathode is large, so the rate of attack at the anode is very high, and the pit goes deeper.

The $\text{Fe}^{2+}$ ions in the pit are hydrolysed to give $\text{H}^+$, so the inside of the pit becomes acidic. The chloride ions move into the pit to balance the charge. This makes the attack self-increasing (autocatalytic). The pit grows downward, because the solution in it is heavier. The corrosion product $\text{Fe(OH)}_2$ forms a cap over the pit.

Prevention: use a smooth, polished surface, keep it clean, avoid stagnant water, use alloys with molybdenum (like stainless steel 316), and add inhibitors.

Applications of IR spectroscopy:

1. Identification of functional groups: each group absorbs at a typical wavenumber, such as O-H at about 3300 cm$^{-1}$, C=O at about 1700 cm$^{-1}$ and C$\equiv$N at about 2250 cm$^{-1}$.
2. Identification of a compound from its fingerprint region (1500 to 400 cm$^{-1}$), by comparing it with a known spectrum.
3. Checking the purity of a sample, as extra peaks show an impurity.
4. Following a reaction: the loss of a reactant peak and the growth of a product peak.
5. Study of hydrogen bonding and quantitative analysis of a mixture.

Copper alloys:

• Brass (Cu 60 to 70% and Zn 30 to 40%): harder and stronger than copper, resists corrosion, and is easy to cast. Used for utensils, taps, pipe fittings and electrical parts.
• Bronze (Cu and Sn): hard, tough and resistant to corrosion by sea water. Used for statues, coins, bearings and ship parts.

Aluminium alloys:

• Duralumin (Al, 4% Cu, 0.5% Mg, 0.5% Mn): light, with high strength, and is hardened by ageing. Used in aircraft, automobile bodies and utensils.
• Magnalium (Al and 5 to 10% Mg): very light and strong. Used in aircraft and scientific instruments.

Nickel alloys:

• Monel (Ni 67% and Cu 30%): resistant to corrosion and acids. Used in chemical plants, and in marine engineering.
• Nichrome (Ni, Cr and Fe): high resistance and withstands high temperature. Used in heating elements.
• Invar (Fe and 36% Ni): very small thermal expansion, used in clocks and measuring tapes.

Hybridization is the mixing of atomic orbitals of nearly the same energy of an atom, to form the same number of new equivalent orbitals called hybrid orbitals. They have the same energy and shape, and they explain the shapes of molecules and the bond angles. The type depends on the number of orbitals mixed.

Explanation with the examples:

1. sp (BeCl$_2$): beryllium (2s$^2$) promotes one electron to 2p, and one 2s and one 2p orbital mix to give two sp orbitals, which are on a straight line. They overlap with two chlorine atoms. In C$_2$H$_2$, each carbon is sp hybridised with a triple bond.
2. sp$^2$ (BF$_3$): one 2s and two 2p orbitals of boron give three sp$^2$ orbitals in a plane at $120^\circ$. In ethene, each carbon is sp$^2$ with a double bond.
3. sp$^3$ (CH$_4$): one 2s and three 2p orbitals of carbon give four sp$^3$ orbitals directed to the corners of a tetrahedron, at $109.5^\circ$. In NH$_3$ and H$_2$O, the lone pairs take some of the orbitals, so the angles are less (107$^\circ$ and 104.5$^\circ$).
4. sp$^3$d (PCl$_5$): one s, three p and one d orbital of phosphorus make five orbitals. Three are in a plane at $120^\circ$, and two are above and below at $90^\circ$.
5. sp$^3$d$^2$ (SF$_6$): one s, three p and two d orbitals of sulphur make six orbitals along the axes of an octahedron.

A corrosion inhibitor is a substance that is added in a small amount to the environment to reduce the corrosion rate. Types:

1. Anodic inhibitors: they form a protective film on the anode. Examples: chromates, nitrites and phosphates.
2. Cathodic inhibitors: they slow the cathodic reaction, either by removing dissolved oxygen (sodium sulphite, hydrazine) or by forming insoluble hydroxides on the cathode (salts of Mg, Ca and Zn).
3. Vapour phase inhibitors: volatile compounds that form a protective layer on the metal in closed spaces. Example: dicyclohexylamine nitrite, used to pack machine parts.
4. Organic inhibitors: they stick to the metal surface. Examples: amines, thiourea.

Schrodinger's wave equation is the basic equation of quantum mechanics. It describes the wave nature of a microscopic particle (such as an electron). It gives the wave function $\psi$, and $|\psi|^2$ gives the probability of finding the electron at a point.

Equation for a particle of mass $m$, total energy $E$ and potential energy $V$ (time independent, in three dimensions):

It is also written as $\hat H\psi = E\psi$, where $\hat H$ is the Hamiltonian operator (the energy operator).

How it is obtained: the classical wave equation is $\nabla^2\psi + \dfrac{4\pi^2}{\lambda^2}\psi = 0$. Put the de Broglie wavelength $\lambda = \dfrac{h}{mv}$, and use $\tfrac{1}{2}mv^2 = E - V$, so that $m^2v^2 = 2m(E - V)$. This gives the equation above.

Significance: solving it gives the allowed energy levels and the orbitals of an atom, and the quantum numbers appear from the solution.

Crude petroleum is a dark, viscous mixture of hydrocarbons (paraffins, naphthenes and aromatics) with a small amount of sulphur, nitrogen and oxygen compounds. It is separated into useful fractions by fractional distillation in a refinery. The fractions boil in different temperature ranges.

Process:

1. The crude oil is heated to about 400$^\circ$C in a furnace. It becomes a hot mixture of vapour and liquid.
2. It enters the fractionating column near the bottom. The column is a tall steel tower with horizontal trays with bubble caps, and it is hotter at the bottom and cooler at the top.
3. The vapours rise, cool and condense on the trays at the level where the temperature is below their boiling point. The heavier fractions condense lower, and the lighter ones go higher.
4. Each liquid fraction is drawn off from its tray. The gas goes out from the top, and the residue at the bottom.

Statement: it is impossible to measure both the exact position and the exact momentum of a microscopic particle (such as an electron) at the same time. The product of the uncertainty in position $\Delta x$ and that in momentum $\Delta p$ is never less than $\dfrac{h}{4\pi}$:

Here $h = 6.626\times 10^{-34}$ J s. If the position is known more precisely, the momentum is less certain. It does not apply to large objects, as the uncertainty is then too small to notice. It shows that the electron has no fixed orbit, and it led to the idea of orbitals (regions of probability).

A bomb calorimeter is used to find the calorific value of a solid or non-volatile liquid fuel.

Construction:

1. A strong stainless steel bomb with a gas-tight lid, an oxygen inlet and two electrodes. A small crucible hangs from one electrode, and a fine fuse wire joins the electrodes, touching the fuel.
2. The bomb is placed in a copper calorimeter with a known mass of water, a stirrer and a Beckmann thermometer.
3. The calorimeter is in an air jacket (and water jacket) to reduce the loss of heat.

Working:

1. A known mass $x$ (about 1 g) of fuel is put in the crucible. The bomb is closed and filled with pure oxygen at 25 to 30 atm.
2. The bomb is put in the calorimeter, which has a known mass $W$ of water. The initial temperature $t_1$ is noted.
3. The fuel is ignited by an electric current through the fuse wire. It burns completely in oxygen, and the heat raises the temperature of the water. It is stirred, and the highest temperature $t_2$ is noted.

Calculation: let $w$ be the water equivalent of the calorimeter (the mass of water that takes the same heat). Heat given by the fuel = heat taken by the water and the calorimeter:

For accuracy, corrections are made for the heat of the fuse wire and for the acids (HNO$_3$ and H$_2$SO$_4$) formed. Then $\text{GCV} = \dfrac{(W + w)(t_2 - t_1) - (\text{corrections})}{x}$.

Example: $x = 1.0$ g, $W = 2000$ g, $w = 500$ g and a rise of $2.4^\circ$C give $\text{GCV} = \dfrac{2500\times 2.4}{1.0} = 6000$ cal/g.

The net calorific value is found from the GCV by subtracting the latent heat of the water vapour formed: $\text{NCV} = \text{GCV} - 0.09\,H \times 587$ (cal/g), where $H$ is the percentage of hydrogen.