Dimensional analysis is a systematic way to convert a measurement from one unit to another without losing track of what the number means. In chemistry, it is used constantly for grams, moles, liters, particles, concentrations, densities, and energies. The method matters because chemical calculations often require several unit changes before the final answer is useful.
By treating units like algebraic factors, you can check your work as you go.
Key Facts
- A conversion factor is a fraction equal to 1, such as 1000 mL / 1 L or 1 mol / 6.022 x 10^23 particles.
- Set up conversion factors so unwanted units cancel and the desired unit remains.
- General setup: given quantity x conversion factor 1 x conversion factor 2 = desired quantity.
- Molar mass converts between grams and moles: moles = grams / molar mass and grams = moles x molar mass.
- Avogadro's number converts between moles and particles: 1 mol = 6.022 x 10^23 particles.
- For solutions, molarity relates moles and volume: M = mol / L.
Vocabulary
- Dimensional analysis
- A problem-solving method that uses units and conversion factors to change a quantity into an equivalent quantity with different units.
- Factor-label method
- Another name for dimensional analysis in which each number is labeled with units and multiplied by factors that cancel units.
- Conversion factor
- A ratio of equal quantities in different units that can be multiplied by a measurement without changing its actual value.
- Unit cancellation
- The process of placing the same unit in the numerator and denominator so it divides out of a calculation.
- Molar mass
- The mass in grams of one mole of a substance, usually found from the periodic table.
Common Mistakes to Avoid
- Putting the conversion factor upside down. This is wrong because the starting unit will not cancel, so the final unit will not match the question.
- Canceling numbers instead of units. The units guide the setup, while the numbers are only multiplied or divided after the unit pathway is correct.
- Skipping units in intermediate steps. This removes the main error-checking tool and makes it easier to mix up grams, moles, liters, or particles.
- Rounding too early in a multi-step conversion. This can create avoidable error, so keep extra digits until the final answer and then round to the correct significant figures.
Practice Questions
- 1 Convert 2.50 L of water to milliliters using 1 L = 1000 mL.
- 2 How many molecules are in 18.0 g of H2O? Use molar mass H2O = 18.02 g/mol and 1 mol = 6.022 x 10^23 molecules.
- 3 A student wants to convert grams of CO2 to molecules of CO2. Explain which conversion factors should be used and why the units must be arranged in that order.