Q.The length of core of an fcc unit cell is a and its atomic radius is r. The relationship between them is
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Types of Solutions: From Everyday Life to Chemistry
You already know what a solution is — sugar dissolved in water, salt in water, even the air you breathe. But not all solutions behave the same way. Some dissolve easily, some refuse to dissolve beyond a point, and some can hold more solute than they normally should. That difference is what we classify as types of solutions based on how much solute is dissolved.
The Intuition: A Cup of Tea
Imagine making a cup of tea. You add one spoon of sugar — it dissolves completely. You add a second spoon — still dissolves. A third spoon — maybe it dissolves, maybe it doesn't. At some point, no matter how much you stir, the sugar just sits at the bottom.
That moment — when no more sugar dissolves — is the saturation point. Before that, you have an unsaturated solution. At that exact point, you have a saturated solution. And if you carefully heat the tea, dissolve more sugar, then cool it down without disturbing it — you might get a supersaturated solution, where more sugar stays dissolved than should be possible at that temperature.
That's the entire idea. Three types, defined by how much solute is dissolved relative to the maximum possible.
The Precise Statement
A solution is a homogeneous mixture of a solute (the substance being dissolved) and a solvent (the substance doing the dissolving). Based on the amount of solute dissolved relative to its solubility at a given temperature, solutions are classified into three types:
Types of Solutions (by saturation)
- Unsaturated solution — contains less solute than the maximum that can be dissolved at that temperature.
- Saturated solution — contains exactly the maximum amount of solute that can be dissolved at that temperature.
- Supersaturated solution — contains more solute than the maximum normally possible at that temperature (a metastable state).
Breaking Down Each Type
Unsaturated solution — the most common type. You can still add more solute and it will dissolve. The concentration is below the solubility limit. If you have a glass of water at room temperature and add a pinch of salt, you get an unsaturated solution. Add more salt — still unsaturated, until you hit the limit.
Saturated solution — the solute and undissolved solute are in dynamic equilibrium. At the molecular level, the rate at which solute particles dissolve equals the rate at which they crystallize out. No net change. If you keep adding salt to water and it stops dissolving, the liquid above the undissolved salt is a saturated solution. The concentration is fixed at the solubility value for that temperature.
A common mistake: thinking a saturated solution is always "thick" or "concentrated." Not true. Saturation depends on the solute's solubility. Lead(II) chloride saturates at about 0.45 g per 100 mL water — that's a very dilute saturated solution. Saturation ≠ high concentration.
Supersaturated solution — this is a tricky one. You create it by heating the solvent, dissolving more solute than normally possible, then carefully cooling it. The excess solute stays dissolved because there's no nucleation site (no scratch, no dust particle) to trigger crystallization. It's unstable — the slightest disturbance (a dust speck, a scratch on the glass, even a sudden jolt) causes the excess solute to crystallize out instantly. …
Why this formula?
Types of Solutions: Why the Key Formulae Hold
Understanding why the formulae work is essential for Indian exams (JEE, NEET, CBSE). Let's break down the reasoning behind the most important relationships.
1. The Basic Classification: What Makes a Solution?
A solution is a homogeneous mixture of two or more substances. The key idea is intermolecular forces between solute and solvent particles.
- Ideal Solution: Solute-solvent interactions are identical to solute-solute and solvent-solvent interactions. Why? No net energy change on mixing — the molecules "fit" perfectly.
- Non-Ideal Solution: Interactions differ, leading to deviation from Raoult's law.
2. Raoult's Law: The Foundation
Formula:
Psolution=xsolvent⋅Psolvent0
Why does this hold?
Imagine a pure solvent surface. The vapour pressure P0 comes from molecules escaping the liquid. When you add a non-volatile solute, solute molecules occupy some surface area, blocking solvent molecules from escaping.
- The fraction of surface available to solvent = mole fraction of solvent (xsolvent).
- Therefore, the rate of escape (vapour pressure) is proportional to that fraction:
Psolution∝xsolvent
- At the limit xsolvent=1, Psolution=P0, so the constant is P0.
Key insight: Raoult's law is a surface-area argument, not a volume argument.
3. Relative Lowering of Vapour Pressure
Formula:
P0P0−P=xsolute
Derivation in one line:
From Raoult's law:
P=xsolvent⋅P0
Since xsolvent+xsolute=1,
P=(1−xsolute)P0
⇒P0−P=xsolute⋅P0
⇒P0P0−P=xsolute
Why is this useful?
It depends only on the mole fraction of solute, not on its identity — making it a colligative property.
4. Elevation of Boiling Point
Formula:
ΔTb=Kb⋅m
Why does boiling point rise?
- Boiling occurs when vapour pressure = atmospheric pressure.
- Adding a non-volatile solute lowers vapour pressure (Raoult's law).
- To reach atmospheric pressure again, you must raise the temperature.
- The shift ΔTb is proportional to the molality m (moles of solute per kg of solvent), because:
- More solute → greater vapour pressure lowering → more temperature needed.
- Kb (ebullioscopic constant) is a property of the solvent only.
5. Depression of Freezing Point
Formula:
ΔTf=Kf⋅m
Why does freezing point drop?
- At the freezing point, solid and liquid solvent are in equilibrium.
- Adding solute disrupts this equilibrium — solute molecules interfere with the orderly crystal formation of the solvent.
- To re-establish equilibrium, you must lower the temperature.
- Again, ΔTf∝m, and Kf depends only on the solvent.
Common exam trap: Both ΔTb and ΔTf are colligative — they depend on number of solute particles, not their nature.
6. Osmotic Pressure
Formula:
Π=i⋅C⋅R⋅T
Why does this hold?
- Osmosis is the net movement of solvent from low solute concentration to high solute concentration across a semipermeable membrane.
- The solvent moves to dilute the higher concentration — this is a entropy-driven process (mixing increases disorder). …
In a face-centred cubic (fcc) cell the atoms touch along the face diagonal, which links the edge length a to the atomic radius r. …
In fcc, atoms touch along the face diagonal: 4r = (sqrt2)a, so r = (sqrt2/4)a, i.e. option (b).
In a face-centred cubic unit cell, the corner atom and the face-centre atom touch each other along the diagonal of a face. The length of a face diagonal is (sqrt2) times the edge, i.e. (sqrt2)a.
…
Showing the 12 most recent of 24 on this concept.
- CBSE 2026Set 56/3/11 markMCQQ.The boiling point of an azeotropic mixture of water and ethanol is less than that of pure water and ethanol. The mixture shows : (A) positive deviation from Raoult's Law. (B) negative deviation from Raoult's Law. (C) no deviation from Raoult's Law. (D) that the solution is an ideal solution.
›Reveal solutionSolution
A mixture with a boiling point lower than its pure components is a minimum boiling azeotrope, which occurs when the solution exhibits positive deviation from Raoult's Law due to higher vapor pressure.
When we talk about solutions, especially liquid-liquid mixtures, their behavior is often described relative to Raoult's Law. This law provides a baseline for ideal solutions, and deviations from it tell us about the intermolecular interactions within the mixture.
Understanding Raoult's Law and Deviations
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Raoult's Law: For an ideal solution, the partial vapor pressure of each volatile component in the solution is directly proportional to its mole fraction in the solution and the vapor pressure of the pure component.
PA=xAPA∘
PB=xBPB∘
Where PA and PB are the partial vapor pressures of components A and B in the solution, xA and xB are their respective mole fractions, and PA∘ and PB∘ are the vapor pressures of the pure components.
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Ideal Solutions: These solutions perfectly obey Raoult's Law over the entire range of concentrations. In an ideal solution, the intermolecular forces between A-A, B-B, and A-B molecules are all very similar.
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Non-Ideal Solutions: Most real solutions do not behave ideally and show deviations from Raoult's Law. These deviations arise from differences in intermolecular forces.
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Positive Deviation: This occurs when the intermolecular forces between A-B molecules are weaker than the average of A-A and B-B forces. This makes it easier for molecules to escape into the vapor phase, leading to a higher vapor pressure than predicted by Raoult's Law.
PA>xAPA∘ and PB>xBPB∘.
Examples: Ethanol-water, acetone-carbon disulfide.
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Negative Deviation: This occurs when the intermolecular forces between A-B molecules are stronger than the average of A-A and B-B forces. This makes it harder for molecules to escape into the vapor phase, leading to a lower vapor pressure than predicted by Raoult's Law.
PA<xAPA∘ and PB<xBPB∘.
Examples: Acetone-chloroform, nitric acid-water.
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Connecting Vapor Pressure to Boiling Point
The boiling point of a liquid is the temperature at which its vapor pressure equals the external atmospheric pressure.
- If a solution has a higher vapor pressure at a given temperature, it will reach the atmospheric pressure at a lower temperature. Thus, a higher vapor pressure corresponds to a lower boiling point.
- Conversely, if a solution has a lower vapor pressure, it will require a higher temperature to reach atmospheric pressure. Thus, a lower vapor pressure corresponds to a higher boiling point.
Azeotropes
Azeotropes are constant boiling mixtures that distill without change in composition. They are a specific type of non-ideal solution.
- Minimum Boiling Azeotropes: These are formed by solutions showing positive deviation from Raoult's Law. At a specific composition, the solution has a vapor pressure higher than either pure component, leading to a boiling point lower than either pure component. The ethanol-water mixture is a classic example. Pure ethanol boils at 78.4∘C, pure water boils at 100∘C, but their azeotrope (approximately 95.6% ethanol by mass) boils at 78.2∘C. …
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- CBSE 2026Set 56/1/11 markMCQQ.Assertion (A) : It is not possible to separate the components of an azeotrope by fractional distillation. Reason (R) : Components of an azeotrope have the same composition in liquid and vapour phase and boil at a constant temperature. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
›Reveal solutionSolution
An azeotrope is a constant-boiling mixture whose vapour has the same composition as the liquid, making separation by simple fractional distillation impossible. Both the assertion and the reason are true, and the reason correctly explains the assertion.
Concept and Intuition
Fractional distillation works because, for most liquid mixtures, the vapour is richer in the more volatile component. As you boil the mixture, the vapour is condensed and reboiled repeatedly, gradually enriching the distillate in the lower-boiling component. This process relies on a difference in composition between the liquid and vapour phases at equilibrium.
An azeotrope is a special mixture that defies this. At a specific composition (the azeotropic composition), the liquid and vapour have exactly the same mole fractions. The mixture boils at a constant temperature — either higher or lower than the boiling points of the pure components — and the vapour that comes off is identical in composition to the liquid left behind. No amount of distillation can change the composition of either phase; the mixture simply boils away unchanged.
Therefore, the reason (R) correctly states the defining property of an azeotrope, and the assertion (A) correctly states the consequence: you cannot separate the components by fractional distillation.
Step-by-step reasoning
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Understand the assertion.
Assertion (A) says: “It is not possible to separate the components of an azeotrope by fractional distillation.” This is a well-known fact in chemistry. For example, ethanol and water form a minimum-boiling azeotrope at about 95.6% ethanol by mass. If you try to distill a mixture that is already at that composition, the distillate will also be 95.6% ethanol — you cannot get pure ethanol by simple fractional distillation.
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Understand the reason.
Reason (R) says: “Components of an azeotrope have the same composition in liquid and vapour phase and boil at a constant temperature.” This is the precise definition of an azeotrope. At the azeotropic point, the boiling point is either a maximum or a minimum, and the vapour-liquid equilibrium curve touches the diagonal line (where xliquid=yvapour). Because the compositions are equal, there is no driving force for separation by distillation.
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Check if the reason correctly explains the assertion. …
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- CBSE 2026Set ANNUAL1 markQ.Write the solute and solvent in the gaseous solution of chloroform in nitrogen gas.
›Reveal solutionSolution
In any solution, the component present in a larger proportion is the solvent, and the one present in a smaller proportion is the solute - this also applies to gas-in-gas solutions.
…
- CBSE 2026Set ANNUAL1 markMCQQ.Which of the following is the correct example of a solid solution in which the solute is in gas phase?(a) Copper dissolved in gold(b) Camphor in nitrogen gas(c) Hydrogen in palladium(d) All of the above
›Reveal solutionSolution
Solid solutions are classified by the physical state of the solute dissolved in the solid solvent; hydrogen dissolved in solid palladium is the classic gas-in-solid example.
A solid solution can have solute particles that are themselves solid, liquid, or gaseous, dispersed uniformly in a solid solvent.
- Copper dissolved in gold — both are solids, so this is a solid-in-solid solution (an alloy).
- Camphor in nitrogen gas — this is actually a solid dissolved in a gas (or, read the other way, describes a gas as solvent), not a solid solution with a gaseous solute. …
- CBSE 2026Set ANNUAL1 markMCQQ.The carbonated water is an example of _____.(a) solid in liquid solution(b) liquid in liquid solution(c) gas in liquid solution(d) liquid in gas solution
›Reveal solutionSolution
Carbonated water is CO2 gas dissolved in water — a gas-in-liquid solution.
Carbonated water is prepared by dissolving carbon dioxide gas (CO2) under pressure in water. Here the solute (CO2) is a gas and the solvent (water) is a liquid, s …
- CBSE 2025Set 56/6/11 markMCQQ.A solution of acetone in ethanol : (A) obeys Raoult's law. (B) forms an ideal solution. (C) shows a positive deviation from Raoult's law. (D) shows a negative deviation from Raoult's law.
›Reveal solutionSolution
Acetone–ethanol mixtures form hydrogen bonds weaker than those in pure ethanol, making escape easier and raising vapor pressure above the ideal prediction. The solution shows a positive deviation from Raoult's law — option (C).
Types of Solutions: Understanding Deviations from Ideality
Raoult's law predicts that the partial vapor pressure of each component in a solution is proportional to its mole fraction: Pi=xiPi0. This holds perfectly only for ideal solutions, where the intermolecular forces between unlike molecules (A–B) are identical in strength to those between like molecules (A–A and B–B). When these forces differ, the solution deviates from Raoult's law.
Positive deviation occurs when A–B interactions are weaker than the average of A–A and B–B interactions. Molecules escape more easily into the vapor phase, so the total vapor pressure exceeds the ideal prediction.
Negative deviation occurs when A–B interactions are stronger than those in the pure components. Molecules are held more tightly in the liquid, reducing vapor pressure below the ideal value.
The key is to compare the intermolecular forces in the mixture with those in the pure liquids.
Step-by-Step Analysis
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Identify the intermolecular forces in pure ethanol
Ethanol (CX2HX5OH) has a hydroxyl group that forms strong hydrogen bonds between molecules. These O–H···O interactions are quite robust, holding ethanol molecules together tightly in the liquid phase.
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Identify the intermolecular forces in pure acetone
Acetone (CHX3COCHX3) is a polar molecule with a carbonyl group, but it cannot donate hydrogen bonds (no O–H or N–H). It can only accept hydrogen bonds. In pure acetone, the dominant forces are dipole–dipole interactions, which are weaker than hydrogen bonds.
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Examine the acetone–ethanol interaction
When acetone and ethanol mix, ethanol can donate a hydrogen bond to the oxygen of acetone's carbonyl group, forming an O–H···O=C interaction. However, this hydrogen bond is weaker than the O–H···O–H hydrogen bonds present in pure ethanol, because the carbonyl oxygen is a less effective hydrogen-bond acceptor than the hydroxyl oxygen.
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Compare net intermolecular forces
- In pure ethanol: strong H-bonds (O–H···O–H)
- In the mixture: weaker H-bonds (O–H···O=C) plus dipole–dipole forces …
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- CBSE 2025Set X11 markMCQQ.Camphor in nitrogen gas, is an example of ______.(a) liquid solution(b) solid solution(c) gaseous solution(d) aqueous solution
›Reveal solutionSolution
Solvent = nitrogen gas, solute = solid camphor → a solid-in-gas solution, classified as a gaseous solution.
A solution is classified by the physical state of the solvent (the component present in larger amount / the medium). Here the medium is nitrogen gas, so the solution is a gaseous solution, with solid camphor as the solute dispersed in it. …
- CBSE 2025Set JZ1 markMCQQ.Give an example of such solid solution in which solute is gas.(a) Oxygen dissolved in water.(b) Solution of camphor in nitrogen.(c) Solution of hydrogen in palladium.(d) Glucose dissolved in water.
›Reveal solutionSolution
A solid solvent holding a gaseous solute → hydrogen dissolved in palladium, option (c).
Concept. A solution is a homogeneous mixture; it is classified by the physical state of the solvent (the component in excess), and separately by the state of the solute. A solid solution therefore has a solid as its solvent. The question asks for a solid solution in which the solute is a gas.
Checking the options:
- (a) Oxygen (gas) in water (liquid) → this is a liquid solution, not solid.
- (b) Camphor (solid) in nitrogen (gas) → solvent is a gas, so this is a gaseous solution. …
- CBSE 2025Set A1 markMCQQ.Homogeneous mixtures of two or more than two components is —(a) Solution(b) Liquid solute(c) Liquid solvent(d) Solvent
›Reveal solutionSolution
A solution is a homogeneous mixture of two or more non-reacting substances.
A mixture is homogeneous when its composition and properties are uniform throughout — no individual component can be distinguished by eye, and any sample taken from any part of it is identical. A solution (made of a solute dissolved in a solvent) is exactly this kind of mixture. Options (b) 'liquid solute', (c) 'liquid solvent' and (d) 'solvent' each name onl …
- CBSE 2024Set 56/2/11 markMCQQ.An azeotropic solution of two liquids has boiling point lower than either of them when it : (A) is saturated (B) shows positive deviation from Raoult's law (C) shows negative deviation from Raoult's law (D) shows no deviation from Raoult's law
›Reveal solutionSolution
An azeotrope with a boiling point lower than either pure component forms when the mixture shows positive deviation from Raoult's law, because the components "want to escape" the liquid phase more readily than ideal behavior predicts. The answer is (B).
Understanding Azeotropes and Deviations from Ideality
An azeotrope is a constant-boiling mixture where the vapor has the same composition as the liquid. This means you cannot separate the components by simple distillation at that composition. The key to understanding which type of azeotrope forms lies in how the solution deviates from Raoult's law.
Raoult's law for an ideal solution states that the partial vapor pressure of each component is proportional to its mole fraction:
Pi=xiPi0
where Pi0 is the vapor pressure of the pure component. Real solutions often deviate from this ideal behavior due to intermolecular forces between unlike molecules differing from those between like molecules.
The Connection Between Deviation and Boiling Point
The boiling point of a liquid is reached when its total vapor pressure equals atmospheric pressure. If a mixture has a higher total vapor pressure than predicted by Raoult's law, it will boil at a lower temperature. Conversely, if the vapor pressure is lower than ideal, the boiling point rises.
Step-by-Step Analysis
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Positive Deviation from Raoult's Law
When A-B interactions are weaker than A-A and B-B interactions, molecules escape the liquid phase more easily than in an ideal solution. The total vapor pressure is:
Ptotal>xAPA0+xBPB0
This increased vapor pressure means the mixture reaches atmospheric pressure at a lower temperature than either pure component. The azeotrope formed is a minimum-boiling azeotrope.
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Negative Deviation from Raoult's Law
When A-B interactions are stronger than A-A and B-B interactions (hydrogen bonding, for example), molecules are held more tightly in the liquid phase:
Ptotal<xAPA0+xBPB0
The reduced vapor pressure means a higher boiling point than either pure component. This forms a maximum-boiling azeotrope.
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No Deviation (Ideal Solution)
An ideal solution follows Raoult's law exactly. No azeotrope forms because the vapor composition continuously changes with liquid composition during distillation. Complete separation is possible.
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Saturation …
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- CBSE 2024Set ANNUAL1 markQ.Define saturated solution.
›Reveal solutionSolution
A saturated solution has reached the maximum solute concentration possible at that temperature; dissolution and crystallisation occur at equal rates.
When a solute is added to a solvent, it keeps dissolving until a point is reached where the solution can hold no additional solute (at a fixed temperature and pressure) - at this point a dynamic equilibrium is established between the solute molecules going into solution and those coming out of solution (if excess undissolved solute is present). …
- CBSE 2024Set ANNUAL1 markQ.Write names of solute and solvent present in sodium amalgam solution.
›Reveal solutionSolution
Sodium amalgam is a solution of sodium metal dissolved in mercury; since mercury is present in the larger amount and is the medium, it is the solvent, while sodium (the dissolved component) is the solute.
An amalgam is an alloy/solution of a metal dissolved in mercury. …
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