The Mole Concept

Introduction to the Particulate Nature of Matter and Chemical Change

• Atoms of different elements combine in fixed ratios, forming compounds with properties differing from their constituent elements.
• Mixtures contain multiple elements or compounds not chemically bonded, retaining individual properties.
• Mixtures can be either homogeneous, with uniform composition, or heterogeneous, with visibly distinct phases.
• Chemical equations are deduced when the reactants and the products are specified.
• The state symbols (s), (l), (g), and (aq) are applied in equations.
• Observable changes are explained in physical properties and temperatures during phase changes.

Particle Nature of Matter

• Matter takes up space and can refer to pure substances or mixtures.
• Pure substances have definite and constant composition.
• From a particle perspective, within a pure substance, all particles appear identical.

Definitions

• Element: Atoms sharing the same number of protons.
• Molecule: Chemically joined two or more elements.
• Compound: Chemically joined two or more different elements in a fixed ratio.
• All compounds are molecules; however, not all molecules are compounds.
• Atoms lose their individual properties upon joining and exhibit different properties than their elements of origin.

Mixtures

• A combination of pure substances
• Mixtures contain elements and/or compounds not chemically bonded, maintaining individual properties.
• Homogeneous mixtures have the same consistency throughout with a uniform composition.
• Heterogeneous mixtures display visibly different substances or phases with a non-uniform composition.

Chemical Equations

• Chemical equations describe what occurs during a chemical reaction.
• Reactants and products are always present in a chemical reaction.
• Reactants are on the left and products on the right; i.e., Reactants → Products
• State symbols are used in chemical equations to denote state
  • (s) solid
  • (l) liquid
  • (g) gas
  • (aq) aqueous solution (dissolved in a solvent)
• Observable changes in physical properties and temperatures occur during changes of state.
• During a change of state. temp remains constant as added energy breaks bonds, which then change a state.

Physical and Chemical Changes

• No new substances are produced in physical change.
  • Melting ice is physical change
• In a chemical change, new chemical substances are formed.
  • Atoms are rearranged to form new products.

The Mole Concept and Avogadro’s Constant

• The mole is a fixed number of particles that indicates the amount, n, of substance.
• Masses of atoms are compared to Carbon-12 and expressed as relative atomic mass (Ar) and relative formula/molecular mass (Mr).
• Molar mass (M) in units of g mol⁻¹.

The Mole

• Mole: Substance amount containing the same number of particles as atoms in 12g of Carbon-12.
• Answers in calculations are expressed in mol to simplify large numbers.
• n is the mole symbol.
• The mole allows correlation of measurable mass with the number of particles.
• Avogadro’s constant (L): 1 mol = 6.02 x 10²³ particles (atoms, molecules, ions).
  • N = n × L
  • N is the number of particles
  • Atoms are simple elements, ions have a charge, and molecules consist of multiple atoms
  • n is the number of moles
  • L is Avogadro's number
• Rearrange this formula to find the number of moles: n = N/L
  • n is the number of moles

Mole relationships

• A chemical formula indicates the mole relationship between individual atoms within a molecule.
• One mol of C + 4 mol of H → 1 mol of CH4, such as methane gas, from a combination of 1 mol of carbon atoms and 4 mol of atoms.
• Calculate the number of mol of an element in a molecule by multiplying it by the amount in mol of that molecule: *nX = i ×*amount of mols.
• Calculate number of atoms of an element by multiplying it by L.
• Calculate total number of atoms by multiplying the amount in mol by the number of atoms.

The Mole Concept

• Masses of atoms are compared against 12C and are expressed as relative atomic and molecular mass.
• A(r): Is the average mass of all isotopes of an element compared to 1/12 the mass of a 12Carbon atom.
• Formula using the relative atomic masses (Ar) of the elements from the periodic table
• Some elements will have a greater atomic mass than others despite their atomic number because heavier isotopes or a greater number of neutrons
• Relative atomic and molecular mass are relative unitless values.
• Molar mass (M) has the units g mol⁻¹.

Amount of Moles

• To find the number of moles: n= m/ M.
  • n is moles
  • m is mass
  • M is molar mass

Percentage Composition

• After the formula is known, molar masses of elements determine percent compositions in compounds.
• Use this equation: % composition by mass of element = (molar mass of x /molar mass of the compound)*100

Empirical Formula

• It is a compound formula showing the lowest whole number ratio of each atom type.
• To calculate:
  • Write the elements that are present.
  • Write each element's % composition or mass.
  • Divide % or mass by the relative atomic mass, then calculate the ratio.
  • Divide each ratio by the smallest ratio to get a whole number ratio.
  • Express as an empirical formula.

Molecular Formula

• This compound formula shows the actual number of each atom type in the molecule.
• Describes the number of different atoms covalently bonded in one molecule.
• Molecular formula is always a whole number multiple of the empirical formula.
• Molecular formula is found when the molar mass is known.

Atom Economy

• Chemical reaction measure with the amount of starting materials that become products
• A high atom economy indicates less waste with a higher efficiency.

Reacting Masses and Volumes

• Reactants exist in limited or excess quantities.
• Experimental yield can differ from theoretical yield.
• Avogadro’s Law determines reacting gases' mole ratio from volume.
• At a specified temp and press, molar volume for an gas is constant.
• Solution of problems relating to reacting quantities, limiting and excess reactants, theoretical, experimental and percentage yield
• Calculate molar concentration using solution amount and volume.
• Standard solution is one of known concentration
• Calculate reacting volumes of gases using Avogadro’s equation.
• Solve and analyze graphs to find the relationships between temp, pressure and volume, for a fixed mass of an ideal gas.
• Deviation is explained for real gases and ideal behavior in high pressure and low temps.
• Values are experimentally obtained and used to calculate molar mass of a gas, from the ideal gas equation.
• Issues are solved related to molar concentration, solute amount and solution vol.
• With reference to a standard solution, use the experimental method of titration to calculate the concentration.

Limiting/Excess Reactants

• Reactants can be limiting, or excess:
  • Limiting reagents are used up first in a chemical reaction.
  • Excess reagents are left over after the limiting reactant is used up.
• Divide by the leading coefficient to find the limiting reactant.
• The reactant having the lower number of moles is the limiting reactant

Percentage Yield

• Experimental yield can differ from theoretical yield. The yield of the product is the actual mass
• The percentage yield is the amount of product produced experimentally compared to the theoretical
• Use this equation: Percentage yield % = (actual yield/theoretical yield) × 100
• Percentage yield is always greater between 0 and 100 %

Theory of an Ideal Gas

• The kinetic molecular theory to explains the behavior of gases.
  • Gaseous particles move continuously and randomly, in straight lines, not curved.
  • Perfect elastic collision
  • Average kinetic energy is directly proportional to temperature
  • Volume of gas is negligible
  • No intermolecular forces (no attraction between particles)
• No gas is perfectly ideal

Ideal Gas Equation

• PV=nRT:
  • P is pressure in Pascals (Pa)
  • V is volume in m³
  • n is the number of moles
  • T is temp in Kelvin
  • R is the universal gas constant (8.31)

Combined Gas Equation

• Three gas laws applied to fixed gas mass:
  • P ∝ (1/V) (constant temp)
  • V ∝ T (constant press)
  • P ∝ T (constant volume)
• Law, Result, Formula
  • Combined Gas law, (PV/T) =k, P1V1/T1 = P2V2/ T2
  • Gay-Lussac Law, (P /T) =k, P1/T1 = P2/ T2
  • Boyle’s Law PV=k, P1V1=P2V2
  • Charles' Law (V/T) =k, V1 /T1 = V2/ T2
• Ideal gas will have the greatest volume at a high temperature and a low pressure

Real vs Ideal Gases

• At high temperature and low pressure a gas behaves more like an ideal gas.
  • A high temperature indicates potential energy from intermolecular forces becomes insignificant, as compared with particles kinetic energy.
  • A low pressure indicates that molecule size becomes insignificant compared molecules in empty space.
  • Ideal gases have particles that do not have volume. Real gases have particles with volume
  • Ideal gases have there are no attractive forces between particles. Real gases have attractive forces.

Molar Volume

• An ideal gas molar volume is constant at specified temperature and pressure.
  • Volume (Vm): volume occupied by one mole of a subs (chemical element or chemical compound) given its temperature and pressure.
• 22.7 dm³ is Avogadro’s Law, one mol of gas measured at STP.
  • Standard temp and press. (STP) are: 273 K and 100kPa
• The mole ratio of the gases with volumes of gases determined via Avogadro’s law.
• n= Vm/ V
  • n is the number of moles, V is used to calculate the gas volume at STP and Vm is the gas’ molar volume.

Molar Concentrations

• Solute- the smallest component mixed into a solution.
• Solvent- component of a solution that is the largest.
• Solution- combination of both the solute and the solvent, in a homogenous mix.
• Solution concentration measurement (moles) for each solution (dm³).
• Concerntration is calculated using the formula concertation= mole os solute/ volume of solution= n

Addition of Solutions

• Add moles from individual solution to calculate the new amount of moles, then find new volume.

Dilution

• A process which adds more solvent to a solution, with solute particles which are widely spread.
• Between the volume and the concentration, there exists a direct relationship .
• The dilution formula is then: C1V1=C2V2

Explore the mole concept, its symbol, and its significance in correlating mass to the number of atoms or molecules. Understand Avogadro's constant and apply the formula to calculate the number of particles in a given number of moles.