Formulae & Mass in Chemistry

• Atom: An atom is the smallest indivisible unit of an element that retains the chemical properties of that element. It consists of a nucleus containing protons and neutrons, surrounded by electrons, and is the fundamental building block of all matter.

• Element: An element is a pure substance consisting only of atoms that all have the same number of protons in their atomic nuclei. Elements cannot be broken down into simpler substances by chemical means, and they are organized in the Periodic Table based on their atomic number.

• Ion: An ion is an atom or a group of atoms that has gained or lost one or more electrons, resulting in a net electrical charge. Cations are positively charged ions (lost electrons), while anions are negatively charged ions (gained electrons).

• Molecule: A molecule is formed when two or more atoms are chemically bonded together, which can be atoms of the same element (e.g., $O_2$) or different elements (e.g., $H_2O$). Molecules are the smallest units of a compound that retain the chemical properties of that compound.

• Compound: A compound is a substance formed when two or more different elements are chemically bonded together in fixed proportions. Unlike mixtures, compounds have distinct chemical and physical properties from their constituent elements and can only be separated by chemical reactions.

• Empirical Formula: The empirical formula represents the simplest whole-number ratio of atoms of each element present in a compound. It provides the most reduced form of the chemical composition, indicating the relative number of atoms rather than their absolute count.

• Molecular Formula: The molecular formula indicates the exact number of atoms of each element present in a single molecule of a compound. It is a multiple of the empirical formula and provides the actual composition of a discrete molecular unit.

• Relative Isotopic Mass: This is the mass of a specific isotope of an element relative to $1/12$ of the mass of a carbon-12 atom. It is typically a whole number close to the mass number of the isotope, but more precise values account for the mass defect.

• Relative Atomic Mass ($A_r$): The relative atomic mass is the weighted average mass of an atom of an element, taking into account the relative abundances of all its naturally occurring isotopes, compared to $1/12$ of the mass of a carbon-12 atom. This value is found on the periodic table and is rarely a whole number due to isotopic averaging.

• Relative Molecular Mass ($M_r$): This term is used for substances that exist as discrete molecules (covalent compounds) and represents the sum of the relative atomic masses of all atoms in one molecule. It is calculated by adding the $A_r$ values of all constituent atoms according to the molecular formula.

• Relative Formula Mass ($M_r$): This term is used for compounds that do not exist as discrete molecules, such as ionic compounds or giant covalent structures, and represents the sum of the relative atomic masses of all atoms in one formula unit. While technically distinct from relative molecular mass, the calculation method is identical, and it is often used as a general term for both molecular and ionic compounds.

• Methodology: To calculate the relative formula mass ($M_r$) of a substance, one must sum the relative atomic masses ($A_r$) of all atoms present in its chemical formula. Each $A_r$ value is multiplied by the number of times that atom appears in the formula.

• Example: For water ($H_2O$), the $M_r$ is calculated as $(2 \times A_r(H)) + (1 \times A_r(O))$. Using $A_r(H) \approx 1.0$ and $A_r(O) \approx 16.0$, the $M_r(H_2O) = (2 \times 1.0) + (1 \times 16.0) = 18.0$.

• Source of $A_r$ values: It is standard practice to use the relative atomic mass values provided in the Periodic Table for these calculations, as they are typically more accurate than rounded whole numbers.

Determining Empirical Formula

• From Mass Composition: The empirical formula can be determined from the masses of each element in a compound. This involves converting the mass of each element to moles by dividing by its relative atomic mass, then finding the simplest whole-number ratio of these moles.

• From Percentage Composition: If given the percentage composition by mass, assume a 100g sample, which converts percentages directly into masses. Then, follow the same steps as determining from mass composition: convert to moles, and find the simplest whole-number ratio.

• Steps for Empirical Formula:

  1. List the mass (or percentage) of each element.
  2. Divide each mass by its respective relative atomic mass ($A_r$) to find the number of moles.
  3. Divide all mole values by the smallest mole value obtained to get a ratio.
  4. If necessary, multiply the ratios by a small whole number to obtain the simplest whole-number ratio, which gives the subscripts in the empirical formula.

Determining Molecular Formula

• Relationship to Empirical Formula: The molecular formula is always a whole-number multiple of the empirical formula. This means that the ratio of the molecular formula's relative molecular mass ($M_r$) to the empirical formula's relative empirical mass will be a whole number.

• Calculation Steps:

  1. First, determine the empirical formula of the compound.
  2. Calculate the relative empirical mass by summing the $A_r$ values in the empirical formula.
  3. Obtain the relative molecular mass ($M_r$) of the compound (this is usually given experimentally, e.g., from mass spectrometry or ideal gas law calculations).
  4. Divide the relative molecular mass by the relative empirical mass to find the whole-number multiplier ($n$).
  5. Multiply all the subscripts in the empirical formula by this multiplier ($n$) to obtain the molecular formula.

Key Relationship: $Molecular \, Formula = n \times Empirical \, Formula$, where $n = \frac{Relative \, Molecular \, Mass}{Relative \, Empirical \, Mass}$

• Use Periodic Table Values: Always use the relative atomic mass ($A_r$) values provided in the Periodic Table for calculations, as these are typically more precise than rounded whole numbers. This ensures accuracy in your final answers, especially for multi-step problems.

• Relative Formula Mass as General Term: When in doubt about whether to use 'relative molecular mass' or 'relative formula mass', it is safer to use 'relative formula mass' ($M_r$). This term is universally applicable to all compounds, whether they are molecular (covalent) or ionic, avoiding potential misclassification.

• Show All Working: For calculations involving empirical or molecular formulae, clearly show each step, including the conversion to moles, the division to find ratios, and any multiplication to achieve whole numbers. This allows for partial credit even if a minor arithmetic error occurs.

• Check for Simplest Ratio: When determining empirical formulae, always double-check that the ratios obtained are indeed the simplest whole numbers. If they are not, divide or multiply by a common factor to simplify them.

• Units and Significant Figures: Pay attention to units (e.g., grams for mass, g/mol for molar mass) and significant figures throughout your calculations. Final answers should generally be reported to an appropriate number of significant figures, often dictated by the least precise measurement given in the problem.

• Confusing Empirical and Molecular Formulae: A common mistake is to assume the empirical formula is always the molecular formula. Remember that the empirical formula is the simplest ratio, while the molecular formula is the actual number of atoms, which can be the same or a whole-number multiple.

• Incorrectly Rounding Ratios: When determining empirical formulae, students sometimes round mole ratios prematurely or incorrectly. It's crucial to divide by the smallest mole value and then, if necessary, multiply by a small integer to get whole numbers, rather than rounding decimals that are not very close to whole numbers.

• Using Mass Numbers Instead of Relative Atomic Masses: For $M_r$ calculations, using the integer mass number (protons + neutrons) instead of the precise relative atomic mass from the periodic table can lead to inaccuracies. Always refer to the periodic table for $A_r$ values.

• Misinterpreting 'Relative': The term 'relative' signifies a comparison to the carbon-12 standard, not an absolute mass. Forgetting this can lead to conceptual confusion about the meaning of $A_r$ or $M_r$ values.

• Calculation Errors with Multipliers: When converting from empirical to molecular formula, ensure the multiplier 'n' is calculated correctly and applied to all subscripts in the empirical formula, not just one or two.