General Chemistry: Measurement, Moles, and Chemical Calculations Study Guide

Measurement and Precision in Chemistry

Accuracy and Precision

In chemistry, it is essential to distinguish between accuracy and precision when making measurements and reporting data.

• Accuracy: How close a measured value is to the true or accepted value.

• Precision: How close repeated measurements are to each other, regardless of their closeness to the true value.

Example: If you weigh a sample three times and get 5.01 g, 5.00 g, and 5.02 g, your measurements are precise. If the true mass is 5.00 g, they are also accurate.

Relative Mass and Molar Mass

Relative Mass

Relative mass compares the mass of one substance to another, often using atomic mass units (amu) for atoms.

• The atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom.

• Relative atomic masses are found on the periodic table.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, usually expressed in grams per mole (g/mol).

• To calculate molar mass, sum the atomic masses of all atoms in a molecule or formula unit.

Formula:

$\text{Molar Mass} = \sum (\text{number of atoms of each element} \times \text{atomic mass of element})$

Example: The molar mass of H2O is $2 \times 1.01\ \text{g/mol} + 16.00\ \text{g/mol} = 18.02\ \text{g/mol}$.

The Mole Concept

Definition and Use

The mole is a fundamental unit in chemistry that represents $6.022 \times 10^{23}$ particles (Avogadro's number) of a substance.

• Used to count atoms, molecules, ions, or other entities in a given sample.

• Links the mass of a substance to the number of particles it contains.

Formula:

$\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

Empirical and Molecular Formulas

Empirical Formula

The empirical formula gives the simplest whole-number ratio of atoms in a compound.

• Determined from experimental data, such as percent composition.

Example: The empirical formula of hydrogen peroxide (H2O2) is HO.

Molecular Formula

The molecular formula shows the actual number of each type of atom in a molecule.

• It is a whole-number multiple of the empirical formula.

Formula:

$\text{Molecular Formula} = (\text{Empirical Formula})_n$

where $n = \frac{\text{Molar Mass of Compound}}{\text{Molar Mass of Empirical Formula}}$

Significant Figures in Measurements

Rules for Significant Figures

Significant figures (sig figs) indicate the precision of a measured or calculated quantity.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant only if there is a decimal point.

Example: 0.00450 has three significant figures.

Lab Calculations and Data Analysis

Common Calculations

In laboratory settings, students often perform calculations involving mass, moles, and empirical formulas.

• Use significant figures appropriately in all calculations.

• Convert between grams, moles, and number of particles using molar mass and Avogadro's number.

Example: To find the number of molecules in 5.00 g of CO2:

• Calculate moles: $\frac{5.00\ \text{g}}{44.01\ \text{g/mol}} = 0.1136\ \text{mol}$

• Calculate molecules: $0.1136\ \text{mol} \times 6.022 \times 10^{23}\ \text{molecules/mol} = 6.84 \times 10^{22}\ \text{molecules}$

Key Vocabulary

• Accuracy

• Precision

• Hypothesis

• Relative Mass

• Molar Mass

• Mole

• Empirical Formula

• Molecular Formula

Summary Table: Key Calculations and Concepts

Concept	Definition	Key Formula
Accuracy	Closeness to true value	—
Precision	Closeness of repeated measurements	—
Mole	6.022 × 1023 particles	$\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$
Molar Mass	Mass of 1 mole of substance	$\sum (\text{atoms} \times \text{atomic mass})$
Empirical Formula	Simplest ratio of atoms	—
Molecular Formula	Actual number of atoms	$n = \frac{\text{Molar Mass (compound)}}{\text{Molar Mass (empirical formula)}}$

Additional info: These notes are based on a checklist and reference to class/lab activities, with academic context added for completeness and clarity.