Convert mass and moles using m = n × M
Quantitative chemistry • Concentration of solutions
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Key concepts
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Definition of mole and molar mass
The mole represents a fixed number of particles: 6.02 × 10^23 entities (Avogadro's number). Molar mass (M) equals the mass of one mole of a substance and uses units of g mol-1. Elemental molar mass uses relative atomic mass values from the periodic table; compound molar mass equals the sum of the atomic masses of its constituent atoms.
Core formula and algebraic rearrangement
The core equation m = n × M links mass (m), amount in moles (n) and molar mass (M). Rearrangement yields n = m ÷ M for mass to moles and m = n × M for moles to mass. Correct algebraic manipulation allows accurate conversion in both directions.
Unit handling and common unit conversions
Mass must be in grams when using molar mass in g mol-1. Kilograms and milligrams require conversion to grams before substitution. Amount (n) uses the unit mol. Molar mass uses g mol-1; cancelation of units in n = m ÷ M leaves mol as the resulting unit. Incorrect units cause numerically wrong answers.
Procedure: step-by-step conversion
To convert mass to moles: (1) Convert mass to grams if necessary, (2) calculate the molar mass of the substance from atomic masses, (3) substitute into n = m ÷ M and compute, remembering units. To convert moles to mass: multiply the number of moles by the molar mass using m = n × M. Clear intermediate steps reduce arithmetic errors.
Limiting factors and significant figures
Molar masses from the periodic table are typically quoted to two decimal places; the final answer should reflect the precision of input data. Extremely large or small masses may require expression in scientific notation. The mole concept applies to atoms, ions and molecules alike; the same method applies whether the substance is an element or a compound.
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