☰ Contents · Chemistry (General chemistry)

Relations between percent, molar and normal concentration

Lessons 20–21 · 2 lessons · S. Masharipov, A. Mutalibov, E. Murodov, H. Islomova. General chemistry, Grade 11, 1st edition. G‘afur G‘ulom Publishing and Printing House, Tashkent, 2018
20

Relation between percent and molar concentration

Textbook: pp. 92–94
GoalDerive and use the conversion formulas between percent and molar concentration (C_M = C%·ρ·10/M).
New words
conversion formula · o‘tish formulasidensity of the solution · eritma zichligimolar mass · molyar massapercent concentration · foiz konsentratsiya
Explanation

1 L of solution has a mass of 1000·ρ grams (ρ in g/mL), the mass of solute in it is 1000·ρ·C%/100 = 10·ρ·C% grams, and the number of moles is 10·ρ·C%/M. Hence C_M = C%·ρ·10/M. The reverse conversion is C% = C_M·M/(ρ·10). The same formulas give the density ρ = C_M·M/(C%·10) and the molar mass of the solute M = C%·10·ρ/C_M, so an unknown substance can be identified. In the formulas ρ is the density of the solution in g/mL, M is the molar mass of the solute (g/mol) and C% is taken as a number (20 for 20 %). The factor 10 comes from converting percent and litres to millilitres. Check the result for sense: concentrated acid solutions can have C_M above 10, while dilute ones have values near or below 1.

Worked examples
98 % H₂SO₄ (ρ = 1.84 g/mL): C_M = 98·1.84·10/98 = 18.4 mol/L.
2 M H₂SO₄ (ρ = 1.12 g/mL): C% = C_M·M/(ρ·10) = 2·98/(1.12·10) = 17.5 %.
Class activity

Derivation: in class write m(solution), m(solute) and n(solute) in turn for 1 L of solution and derive C_M = C%·ρ·10/M on the board yourselves.

Practice
1
A 49 % H₂SO₄ solution has a density of 1.4 g/mL. What is its molar concentration in M?
2
A 5 M NaOH solution has a density of 1.25 g/mL. Find the percent concentration (M = 40 g/mol).
3
A 12 % solution has a density of 1.2 g/mL and a molar concentration of 2 M. Find the molar mass of the solute.
4
Why does the formula C_M = C%·ρ·10/M contain the factor 10?