Chemistry and Matter

What is Chemistry

Chemistry is the science that focuses on the laws, compositions, and interactions between matter. Scientists that partake in this field are known as chemists.

Matter

It is the umbrella term for objects that meet the following criteria:

• Has mass.
• Has volume.

Due to the scientific nature of science, scientists often measure the mass, volume and other properties of matter to have a clear understanding of them.

Units of Measurement

Units of measurements are used in relaying a specific measurement or value. The properties of matter are illustrated and recorded with these units in mind.

Commonly used units

• Mass
  • $kg$ (Fundamental Unit).
• Weight
  • $N$ (Derived Unit) $=kg\times \frac{m}{s^2}$
• Volume
  • $mL$ (Derived Unit) = $c{m}^3$
• Energy
  • $J$ or $Joules$ (Derived Unit). = $Nm=(kg\times \frac{m}{s^2})(m)$

SI Units

The International System of Units, abbreviated to SI Units (from the french: Système international d’unités), also nown as the metric system, is a standard system of units that follows a base10 system of scaling unlike imperial units which uses an outdated and confusing system of conversion.

SI Units have prefixes that denote their scale in relation to their base unit (the below example uses grams ($g$) ).

$kg\leftarrow hc\leftarrow dag\leftarrow g\to dg\to cg\to mg$

• $kg$ - Kilograms
• $hc$ - Hectograms
• $dag$ - Dekagrams
• $g$ - Grams
• $dg$ - Decigrams
• $cg$ - Centigrams
• $mg$ - Milligrams The values above have the corresponding bases as below:

$10^{-3}\leftarrow 10^{-2}\leftarrow 10^{-1}\leftarrow 10^0\to 10^1\to 10^2\to 10^3$

The conversion between SI Units (Metric Units) is as simple as multiplying or dividing your value with the base off your desired unit.

For methods in converting between Imperial/Non-metric units to SI/Metric units, see: Units and Conversions.

Classification

Matter is a large group with a diverse array of different materials; in order for scientist to make sense of matter and the possible relationships and interactions, they classified elements based on key traits.

Phases

Phases is described as the current state in which matter exists. The four states of matter that are observable in everyday life are the following:

• Solid
• Liquid
• Gas
• Plasma

Phase Changes

A piece of matter’s phase can be changed through the manipulation of one or more two variables, notably: temperature and pressure.

Increasing the amount of heat can change matter from one phase to another, the same is true when decreasing the amount of heat. Different materials have different heat requirements to change their current state.

Enthalpy - The amount of energy in a thermodynamic system. Refers also to the total heat content of a system.

Mesophases

As one woulds assume, the change between phases are not instantaneous and is closer to a transition. In Chemistry there is a concept known as a Mesophase, which refers to the intermediate phases between two states of matter. Such as:

• Liquid Crystals (Solid$⟷$Liquid)
• Supercritical Fluids (Liquid$⟷$Gas

Phase Equilibrium

A phase equilibrium is a state in which two states of matter can coexist.

If we were to use Water ($H_{2}O$) as an example. $H_{2}O$ can exist as Ice (Solid), Water (Liquid), or Vapor (Gas).

There is a distinct point known as the Critical Point where water is in a state of a Supercritical Fluid and has both the properties of a liquid and a gas.

There is also another distinct point known as the Triple Point, where— as the name implies, water can be in a state of solid, liquid, and gas at the same time.

Purity

Purity is a property of matter that places it in one of two groups: Pure Substances and Mixtures

Pure Substances

Pure Substances are substances that are composed of a singular element, molecule, or compound.

Element vs Molecule vs Compound

A very common discussion of terminologies, when is something an element, a molecule, or a compound? It depends.

Element is the appropriate term for substances that is comprised of only one type of element. (Ex. $H$)

Compound is the appropriate term for a substance comprised of two or more elements bonded together. (Ex. $H_{2}O$)

Molecules are commonly used to refer to compounds; molecules are any substance that is comprised of two or more elements regardless of the number of unique elements involved. (Ex. $O_2$ is both an element and a molecule, $H_{2}O$ is both a compound and a molecule.)

Mixtures

Mixtures are described as a mixture of two or more pure substances and can be further classified into heterogeneous and homogeneous mixtures.

Heterogeneous Mixtures

These are mixtures where their components are still differentiable from one another (Ex. a mixture of oil and water).

Heterogeneous Mixtures come in different forms such as:

• Suspension (Solid & Liquid) - A fluid that contains solid particle that are insoluble and are sufficiently large for sedimentation.
• Emulsion (Liquid & Liquid) - A mixture of two liquids where the two components are immiscible.
• Solid Sol (Solid & Solid) - A solution wherein both the solute and solvent are solid.
• Aerosol (Solid and/or Liquid & Gas) - A solution where in small liquid and/or solid particles are dispersed in a gas.

Homogeneous Mixtures

These are mixtures where their components are no longer differentiable within the mixture. (Ex. Saltwater)

Homogeneous Mixtures come in different fors such as:

• Gas mixtures (Gas & Gas) - A mixture composed of a variety of gaseS. (Ex. The air we breathe)
• Solutions (Any of the three states & Liquid) - A solution is a mixture composed off a solute (component to be dissolved) and a solvent (component that dissolves). (Ex. Saltwater)
• Alloys (Solid & Solid) - A mixture composed of two or more elements where at least one is a metal. (Ex. Bronze)

Separation Techniques

Scientists have developed many ways to extract specific components from mixtures or to separate both components from a mixture. Chemists primarily employ these methods in their field of study.

The following are the distinct methods of separation:

• Filtration (S in L) - Utilizes the size difference between the solute and the solvent usually through the use of a filtration mesh or filter paper. This method only works for suspensions.
• Evaporation (S in L) - Utilizes the difference in boiling points to separate by allowing one component to evaporate and leaving the other component/s as residue.
• Distillation (S in L) - Similar to evaporation but with the added benefit of preserving both components of the mixture; often used when the first component to evaporate is the desired component.
• Sublimation (S in S) - A method that makes one of the solid components involved sublimate (turn into gas) and leaving the non-sublimable component as residue.
• Crystallization (S in L) - A method that takes advantage of the solid component’s crystallization upon cooling the solution down after heating.
• Separatory Funnel (L in L) - Used to separate two immiscible liquids. (Ex. Oil and Water)
• Chromatograhy (L in L) - Utilizes the solubility-adsorption difference of the components. Can be observed through the separation of black ink into its composite colors (cyan, magenta & yellow).
• Magnetic Separation (S in S) - Separates paramagnetic materials (stronger magnetic behavior) from diamagnetic materials (weaker magnetic force).

Properties of Matter

Thermodynamic Properties

Intensive / Intrinsic

These are mass independent properties.

Example properties:

• Phase transition points - used to determine identity
• Density and Concentration - derived from extensive units
• pH and Color

Extensive / Extrinsic

These are mass dependent properties.

Example properties:

• Length & Volume
• Mass & Weight
• Temperature & Heat content

Physical Properties

Properties that are not under the scope of chemical properties.

• Additive Properties - sum of the parts
  • Molecular Weight
• Constitutive - type and arrangement of bonds
  • Optical rotation (dextro or levo)
• Colligative - amount of solute
  • Vapor Pressure Lowering
  • Boiling Point Elevation
  • Freezing Point Depression
  • Osmostic Pressure
  • Refracative Index (Brix Scale)

Fundamental Laws

Thermodynamic

Law on Conservation of Mass (Lavoisier)

The total mass of all product of a chemical reaction is equal to the total mass of all reactants of that reaction.

$\text{Mass of reactants}=\text{Mass of products}$

Mass can neither be created nor destroyed

This law is the basis of Stoichiometry, the practice of balancing the number of atoms of a chemical reaction to adhere to the law on conservation of mass.

Chemical Reactions

Law of Definitive/Constant Proportions (Proust) (Outdated)

A chemical compound always contains exactly the same proportion of elements by mass.

Example: $C+O⟶C_1{O}_2$

Law of Multiple Proportions (Dalton)

When chemical elements combine, they do so in a ratio of small whole numbers.

Example: $C+O⟶C{O}_2$

Law of Reciprocal Proportion (Richter)

Also known as the Law of Combining Weights or the Law of Equivalents.

Elements combine in the ratio of their combining weights or chemical equivalents; or is some cases multiple or sub-multiple of that ratio.

Gas Laws

Combined Gas Laws

This is a law combined from Boyle’s Law, Gay-Lussac’s Law, and Charles’ Law; it states that the variables for volume and pressure are inversely related to each other, and that they both are directly related to temperature.

Combined Gas Law Formula

• Use case:
  • When one of the following variables are desired, while the rest are given:
    • Pressure ($P$)
    • Temperature ($T$)
    • Volume ($V$)
• Variables:
  • $P_1$ - First / Initial Pressure
  • $P_2$ - Second / Final Pressure
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $T_1$ - First / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second / Final Temperature ( $\text{K}$ )
• Formula: $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

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Boyle’s Law

This law states that the variables for volume and pressure are inversely related to each other.

Boyle’s Law Formula

• Use Case:
  • Temperature is constant / Isothermal
  • Temperature is not given or will not be used.
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $P_1$ - First / Initial Pressure
  • $P_2$ - Second / Final Pressure
• Formula: $V_1{P}_1=V_2{P}_2$

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Gay-Lussac’s Law

This law states that the variables for temperature and pressure are directly related to each other.

Gay-Lussac’s Law Formula

• Use case:
  • Volume is constant / Isovolumetric
  • Volume is not given
• Variables:
  • $P_1$ - First Pressure / Initial Pressure
  • $P_2$ - Second Pressure / Final PressurE
  • $T_1$ - First Temperature / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second Temperature / Final Temperature ( $\text{K}$ )
• Formula: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

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Charles’s Law

This law states that the variables for temperature and volume are directly related to each other.

Charles’ Law Formula

• Use case:
  • Pressure is constant / Isobaric
  • Pressure is not given.
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $T_1$ - First / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second / Final Temperature ( $\text{K}$ )
• Formula: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

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Avogadro’s Law Formula

This law states that when temperature and pressure are the same, the same number of molecules are found in equal volumes of different gases.

Avogadro’s Law Formula

• Use case:
  • Pressure and Temperature are constant / Isobaric and Isothermal
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $n_1$ - First / Initial Number of Moles ( $\text{mol}$ )
  • $n_2$ - Second / Final Number of Moles ( $\text{mol}$ )
• Formula: $\frac{V_1}{n_1}=\frac{V_2}{n_2}$

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Ideal vs Real Gas Law

In reality, Real gases do not behave well like how the Ideal Gas Law states.

For a gas to behave in an ideal state the following must be met:

• Low Pressure$⟶$Repulsion
• High Temperature$⟶$Attraction
• Large Volume$⟶$Negligible atomic size

To calculate the behavior of real gases, one must use Van der Waals Equation.

Van der Waal’s Real Gas Formula

• Use case:
  • When the problem concerns real gases
• Variables:
  • $R$ - Gas Constant ( $0.08206L\cdot atm/mol\cdot K$ )
  • $P$ - Pressure ( $\text{atm}$ )
  • $n$ - Number of moles of the given gas ( $\text{mol}$ )
  • $a{n}^2$ - Internal Pressure per mole ( ${\text{L}}^2\cdot \text{atm}$ )
  • $nb$ - Incompressibility ( $\text{L}/\text{mol}$ )
  • $V$ - Volume ( $\text{L}$ )
  • $T$ - Temperature ( $\text{K}$ )
• Formula: $(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$

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Gas Interactions (in mixtures)

Dalton’s Law of Partial Pressure (Gas in Gas)

Total pressure in a mixture is equal to the sum of the partial pressure of each gas.

Dalton’s Law Formula

• Use case:
  • When asked the partial pressure of a gas
  • Mole fraction is given
  • Total pressure is given
• Variables:
  • $P_T$ - Total Pressure ( $\text{atm}$ )
  • $\chi$ - Mole fraction ( $\frac{n_x}{n_T}$ )
    • $n_x$ - Moles of a particular gas ( $\text{mol}$ )
    • $n_T$ - Total moles within a gas ( $\text{mol}$ )
  • $P_x,P_y,P_z$ - Partial pressure of a particular gas ( $\text{atm}$ )
• Formula for total pressure: $P_T=P_z+P_y+\cdots P_x$
• Formula for partial pressure: $P_x=P_T\chi$

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Raoult’s Law (Vapor Pressure of Solvent)

The Vapor Pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent

Raoult’s Law Formula

• Use case:
  • For calculating the vapor pressure of a solution
  • Solvent pressure is given
  • Solvent mole fraction is given
• Variables:
  • $P_{\text{solution}}$ - Vapor pressure of the solution ( $\text{atm}$ )
  • ${\chi }_{\text{solvent}}$ - Mole fraction of the solvent ( $\frac{n_{\text{solvent}}}{n_{\text{solvent}}+n_{\text{solute}}}$ )
    • $n_{\text{solvent}}$ - Moles of the solvent ( $\text{mol}$ )
    • $n_{\text{solute}}$ - Moles of the solute ( $\text{mol}$ )
  • $P_{\text{solvent}}^0$ - Vapor pressure of the pure solvent ( $\text{atm}$ )
• Formula: $P_{\text{solution}}=({\chi }_{\text{solvent}})(P_{\text{solvent}}^0)$

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Henry’s Law on Solubility (Gas in Liquid)

Increasing the vessel pressure of your gas will increase its solubility in a liquid solvent.

Solubility and Pressure are directly proportional in the context of gas ( $S\propto P$ ) while being inversely proportional to temperature ( $S\propto \frac{1}{T}$)

Movement

Graham’s Law (Molecular Weight)

The rate of diffusion and speed of are inversely proportional to the square root of their density.

The heavier the gas the slower its rate of movement.

${\text{Rate}}_{\text{diffusion}}\propto \frac{1}{\sqrt{\text{density}}}$

Diffusion is the movement of a molecule from an area of high concentration towards an area of low concentration. Osmosis is an example of diffusion specific to the movement of water ($H_{2}O$).

Graham’s Law Formula

• Use case:
  • To compare the rates of diffusion between two gases
• Variables:
  • ${\text{Rate}}_1$ - Rate of the first gas ( ${\text{m}}^2/\text{s}$ )
  • ${\text{Rate}}_2$ - Rate of the second gas ( ${\text{m}}^2/\text{s}$ )
  • $M{W}_1$ - Molecular weight of the first gas
  • $M{W}_2$ - Molecular weight of the second gas
• Formula: $\frac{{\text{Rate}}_1}{{\text{Rate}}_2}=\sqrt{\frac{M{W}_2}{M{W}_1}}$

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Fick’s First Law Formula

Movement of particles (diffusion flux) is proportional to the concentration gradient (from high concentration to low concentraion)

Fick’s 1st Law Formula

• Use case:
  • When asked the flux of a given gas
• Variables:
  • $J$ - Flux; amount of substance per unit area per unit of time
  • $D$ - Diffusivity; diffusion coefficient
  • $\phi$ - Concentration gradient; difference in concentration
  • $x$ - Path length
• Formula: $J=-D\frac{d\phi }{dx}$

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