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