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States of Matter and Separation - States and Properties of Matter

Grade 9IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Kinetic Molecular Theory states that all matter is composed of tiny particles that are in constant, random motion. The average kinetic energy of these particles is directly proportional to the temperature in Kelvin (TT).

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Solids: Particles are tightly packed in a regular arrangement (lattice). They vibrate about fixed positions, have a fixed shape, and a fixed volume. Intermolecular forces are strongest in this state.

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Liquids: Particles are close together but arranged randomly. They can move and slide past each other, allowing liquids to flow and take the shape of the bottom of their container. They have a fixed volume but no fixed shape.

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Gases: Particles are far apart and move rapidly in random directions. They have no fixed shape or volume and are highly compressible because of the large spaces between particles.

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Phase Changes: Changes of state are physical changes. For example, melting occurs at the melting point where solid becomes liquid. During a phase change, the temperature remains constant as the energy is used to overcome intermolecular forces rather than increasing particle speed (KEKE).

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Diffusion: The net movement of particles from a region of higher concentration to a region of lower concentration. The rate of diffusion depends on temperature (TT) and the mass of the particles (mm). At higher temperatures, particles move faster (v∝Tv \propto \sqrt{T}), increasing the rate of diffusion.

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Density is a property defined as mass per unit volume. It determines whether a substance will float or sink in another fluid. The density of a substance generally decreases as it changes from solid to liquid to gas, with the notable exception of water near 4∘C4^{\circ}C.

📐Formulae

ρ=mV\rho = \frac{m}{V}

T(K)=T(∘C)+273.15T(K) = T(^{\circ}C) + 273.15

P=FAP = \frac{F}{A}

vrms≈3kBTmv_{rms} \approx \sqrt{\frac{3k_{B}T}{m}}

💡Examples

Problem 1:

A sample of an unknown metal has a mass of 135135 g and occupies a volume of 5050 cm3\text{cm}^3. Calculate the density of the metal and identify if it will float on mercury (density of mercury ≈13.6\approx 13.6 g/cm3\text{g/cm}^3).

Solution:

Density ρ=mV=13550=2.7\rho = \frac{m}{V} = \frac{135}{50} = 2.7 g/cm3\text{g/cm}^3. Since 2.72.7 g/cm3<13.6\text{g/cm}^3 < 13.6 g/cm3\text{g/cm}^3, the metal will float on mercury.

Explanation:

Density is calculated by dividing mass by volume. Because the metal is less dense than the liquid mercury, it experiences an upward buoyant force greater than its weight per unit volume.

Problem 2:

Convert the boiling point of liquid nitrogen, which is −196∘C-196^{\circ}C, into Kelvin (KK).

Solution:

T(K)=−196+273.15=77.15 KT(K) = -196 + 273.15 = 77.15 \text{ K}

Explanation:

To convert from Celsius to Kelvin, we add 273.15273.15 to the Celsius temperature. The Kelvin scale is the absolute temperature scale used in gas law calculations.

Problem 3:

Two gas jars, one containing Bromine vapor (molar mass ≈160\approx 160 g/mol\text{g/mol}) and one containing Hydrogen gas (molar mass ≈2\approx 2 g/mol\text{g/mol}), are opened. Which gas will diffuse faster and why?

Solution:

Hydrogen gas will diffuse faster than Bromine vapor.

Explanation:

According to the kinetic theory, at the same temperature, lighter particles move at higher average speeds than heavier particles. Since MH2<MBr2M_{H_2} < M_{Br_2}, Hydrogen particles travel faster and thus diffuse more rapidly.