Solutions and Concentration - Solution Composition

Chemical reactions often take place in aqueous solutions. To perform stoichiometric calculations in such cases the amounts of chemicals present in solution – the concentration of solution - must be known.

Concentration of a solution is a measurement stating the amount of a solute present in a known amount of solution:

Concentration = amount of solute / amount of solution

The terms solute and solution are usually used for liquid samples but they can be extended to gaseous and solid samples.

The most common units of concentration are given in Table I.1:

Common Units of Concentration
Name	Symbol	Units
molarity	moles solute / liters of solution	M
molality	moles solute / kg solvent	m
normality	number of equivalent weights of solute / liters of solution	N
formality	number of formal weights of solute / liters of solution	F
weight %	g solute / 100 g of solution	% w/w
volume %	ml solute / 100 ml solution	% v/v
weight-to-volume %	g solute / 100 ml solution	% w/v
parts per million	g solute / 106 g solution	ppm
parts per billion	g solute / 109 g solution	ppb

Note: Another way of describing solution concentration is the mole fraction (xi)

Molarity (M) is defined as the number of moles of solute per liter of solution.

i.e by dissolving 0.1 mol NaOH in 1 l of H₂O gives a solution that contains 0.1 mol Na⁺ and 0.1 mol of OH^- in 1 l. The concentration of the solution is [Na⁺] = 0.1 M and [OH^-] = 0.1 M.  

Since molarity depends on the volume of the solution it changes slightly with temperature.

Another way of describing solution concentration is molality (m) which is the number of moles of solute per kilogram of solvent.

Molality is independent of temperature since it depends on mass.

In very dilute aqueous solutions the molarity (M) and molality (m) are nearly the same.

Example #1

A solution of 1M H₂SO₄ has density 1.04 g/cm³. Calculate the (%w/w) concentration of the solution.

Given	[H2SO4] = 1M d = 1.04 g/cm3 PH2O = 41 mmHg MW H2SO4 = 98 g/mole
Asked for	(%w/w) = ?

 From the definition of  (%w/w) = g solute / 100 g of solution    (1)

The mass of solute (g solute) is unknown but it can be calculated.

Since [H₂SO₄] = 1M ⇒ 1000 cm³ of H₂SO₄ solution contain 1 mole “pure” H₂SO₄    (2)

The mass of 1 mole “pure” H₂SO₄ can be calculated as shown below:

mass (g) = mole * MW = 1 mole * 98 g/mole = 98 g    (3)

 

From (2) and d = m/V = 1.04 g/cm³   the mass of 1000 cm³ of H₂SO₄can be calculated:

m = d * V = 1.04 g/cm³  * 1000 cm³ = 1040 g of H₂SO₄ solution  (4)

From (2), (3) and (4):

Mass of 1040 g of H₂SO₄ solution contain 98 g of “pure” H₂SO₄

              Mass of 100  g of H₂SO₄ solution contain   x = ? g of “pure” H₂SO₄

x = 98 g “pure” H₂SO₄ * (100g of H₂SO₄ / 1040g of H₂SO₄) = 9.42 g of “pure” H₂SO₄

Therefore, (%w/w) = 9.42

Provided that the theory and the definitions of solution concentration units is understood a % solution calculator can be used.

Meant to be used in both the teaching and research laboratory, a % solution calculator  can be utilized to perform a number of different calculations for preparing percent (%) solutions when starting with the solid or liquid material.


An additional solved example regarding solutions and concentration is shown in the following video

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 Relevant Posts

Properties of solutions - Henry's-law - Effect of Pressure on Solubility 

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 References

David W. Oxtoby, H.P. Gillis, Alan Campion, “Principles of Modern Chemistry”, Sixth Edition, Thomson Brooks/Cole, 2008

Steven S. Zumdahl, “Chemical Principles”  6^th Edition, Houghton Mifflin Company, 2009

Ralph H. Petrucci, “General Chemistry”, 3^rd Edition, Macmillan Publishing Co., 1982

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Key Terms

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