Worked concentration calculation examples and reversals

Quantitative chemistry • Concentration of solutions

Flashcards

Test your knowledge with interactive flashcards

Find mass required to obtain 0.50 mol dm−3 solution of substance Mr = 84 in 250 cm3.

Click to reveal answer

Volume = 0.250 dm3. Moles = 0.50 × 0.250 = 0.125 mol. Mass = 0.125 × 84 = 10.5 g.

Key concepts

What you'll likely be quizzed about

Definition and units for concentration

Concentration measures the amount of substance per unit volume of solution. Concentration commonly appears as mass concentration in grams per decimetre cubed (g dm−3) and as molar concentration in moles per decimetre cubed (mol dm−3). The symbol for molar concentration is c and the standard unit is mol dm−3. Exact units must appear in the final answer to indicate whether the concentration refers to mass or amount of substance.

Core formulae for calculations

Mass concentration uses the formula concentration (g dm−3) = mass of solute (g) / volume of solution (dm3). Molar concentration uses the formula concentration (mol dm−3) = amount in moles (mol) / volume (dm3). Amount in moles uses the formula amount (mol) = mass (g) / relative formula mass (Mr). Rearrangement of these formulae allows calculation of unknown mass or volume when concentration and the other quantities are known.

Unit conversion: cm3 to dm3

Volume often appears in cubic centimetres (cm3) in practical problems and requires conversion to decimetres cubed (dm3) for the standard concentration formulas. One decimetre cubed equals 1000 cubic centimetres, so volume in dm3 = volume in cm3 ÷ 1000. Failure to convert cm3 to dm3 leads to answers that are off by a factor of 1000 and produces incorrect concentration values.

Reverse calculations: finding mass or volume

Rearrangement of the core formulae enables reverse calculations. Mass from mass concentration uses mass (g) = concentration (g dm−3) × volume (dm3). Mass from molar concentration uses mass (g) = concentration (mol dm−3) × volume (dm3) × Mr. Volume from a given concentration uses volume (dm3) = mass (g) / concentration (g dm−3) or volume (dm3) = amount (mol) / concentration (mol dm−3). Clear algebraic manipulation and unit tracking produce correct rearranged expressions.

Key notes

Important points to keep in mind

Always convert cm3 to dm3 before using concentration formulae.

Track units at every step to prevent factor-of-1000 errors.

Use amount (mol) = mass ÷ Mr when calculating molar concentration from mass.

Rearrange formulae algebraically to solve reverse problems for mass or volume.

Round only the final answer to the appropriate number of significant figures.

Include the correct unit (g dm−3 or mol dm−3) with the numeric answer.

Use consistent units for all quantities before performing arithmetic.

Check calculations by substituting the result back into the original formula where possible.