Q.A beaker of ice and water is left standing at $1\ \text{atm}$ pressure while heat is very slowly supplied. Explain why the thermometer reading stays fixed at $0\,^\circ\text{C}$ throughout the melting, only rising once every last piece of ice has melted.

Equilibrium is a dynamic balance — forward and reverse processes keep occurring at equal rates, they never stop.

Checking each option against the real characteristics of physical equilibria:

• (a) True — equilibrium can only be established in a closed system at a given temperature (no matter exchange with surroundings).

• (b) True — once equilibrium is reached, all measurable properties (pressure, concentration, colour, etc.) stay constant with time.

• (c) False — equilibrium is dynamic, meaning the opposing physical processes (e.g. evaporation and condensation) continue to occur even at equilibrium; they do not stop, they merely proceed at equal and opposite rates so there's no net change.

• (d) True — this is exactly the definition of dynamic equilibrium: opposing processes occurring at the same rate.

Applying pressure to a solid <=> liquid equilibrium shifts it toward the denser (smaller-volume) phase; whether that phase is the solid or the liquid depends on the specific substance, so the melting point may go up or down depending on the substance's nature.

According to Le Chatelier's principle, if pressure is increased on a system at equilibrium, the equilibrium shifts in the direction that reduces the total volume, i.e. toward the side (solid or liquid) that is more compact/denser.

• For most substances, the solid phase is denser than the liquid phase. Increasing pressure then favours the solid, so a higher temperature is needed to melt it under the higher pressure — the melting point increases.
• For a few substances (most famously water/ice, also substances like bismuth, gallium, and silicon), the solid is actually LESS dense than the liquid. For these, increasing pressure favours the liquid phase instead, so less thermal energy (a lower temperature) is enough to keep it liquid — the melting point decreases with increasing pressure.

Because the direction of the shift depends on which phase (solid or liquid) is denser for that particular substance, the general statement must allow for either outcome.

Increasing pressure on the ice-water equilibrium melts more ice, because water (the denser phase) is favoured.

Unusually, ice is less dense than liquid water (water expands on freezing). By Le Chatelier's principle, increasing pressure on a system at equilibrium shifts the equilibrium in the direction that reduces volume, i.e. towards the denser phase. Since liquid water occupies less volume than the same mass of ice, increased pressure shifts the ice ⇌ water equilibrium towards water, so more ice melts (this is also why the melting point of ice decreases with increasing pressure).

The statement is False: this reaction is a homogeneous, not heterogeneous, equilibrium, because every species is a gas.

An equilibrium is called homogeneous when all the reactants and products are present in the same phase, and heterogeneous when they are present in more than one phase (e.g. a solid and a gas). In N2(g) + 3H2(g) <=> 2NH3(g), nitrogen, hydrogen, and ammonia are all gases -- a single phase -- so this is a homogeneous gaseous equilibrium (the basis of the industrial Haber process).

Henry's law states that the partial pressure of a gas over a solution is directly proportional to its mole fraction in the solution: p = KH . x.

Henry's law is used to describe gas-liquid equilibrium (solubility of a gas in a liquid). It states that at constant temperature, the partial pressure (p) of a gas in the vapour phase, in equilibrium with its dissolved form in a solution, is directly proportional to the mole fraction (x) of that gas in the solution: p = KH . x, where KH is the Henry's law constant, which depends on the nature of the gas and the temperature.

The dissolution equilibrium of a gas in a liquid (like CO2 gas dissolving in solution) is described by Henry's Law, which relates the partial pressure of the gas above the liquid to the mole fraction of gas dissolved in it.

The equilibrium CO2(gas) rightleftharpoons CO2(in solution) is a physical (gas-liquid) equilibrium — it's how CO2 stays dissolved in a sealed soft-drink bottle, or how oxygen dissolves in water for aquatic life.

Henry's Law states: at a given temperature, the partial pressure (p) of a gas in equilibrium with its solution is directly proportional to the mole fraction (x) of the gas in the solution:

$p = K_H \cdot x$

where $K_H$ (Henry's law constant) is different for every gas-solvent pair and increases with temperature (which is why a soda bottle fizzes more, i.e. releases more dissolved CO2, when warm than when cold).

The other named laws don't fit: Kohlrausch's Law relates to the independent migration of ions in electrolytic conductance; Hooke's Law relates force to extension in elasticity (a physics law, not chemistry); the general Law of Chemical Equilibrium (law of mass action) is broader and doesn't specifically capture the gas-solubility relationship being tested here.