Concentration

Concentration tells us how much of one component (in a mixture) we have relative the mixture (or another component in the mixture). That is, for a mixture of sugar and water, a concentration can specify how much water we have relative to the solution (water and sugar), or how much water we have relative to the other component (sugar). These concentrations can be expressed using units of amount (mols, molecules, ...), mass (kg, lb, ...), and volume (m³, L, ...). The following are some ways to express concentration, where the numerator signifies the solute and the denominator signifies the solution.

Mass Concentration: g / cm³, lb_m / ft³, kg / in³

Molar Concentration: kmol / m³, lb-mol / ft³, g-mol / L

The last molar concentration listed, g-mol/L is the Molarity of the solute in the mixture. Thus, the definition of molarity follows:

Molarity of component A, M_A = g-mol_A / L_total

Mass and mole fractions will be used frequently in material and energy balance problems. The notation used throghout the majority of this course and in this online textbook differs from the notation introduced in chapter 3. Here, x designates a liquid or solid mass or mole fraction, and y designates mass or mole fraction for a gas. Here are the definitions for mass and mole fractions:

Equation 1: x_A = m_A / m_total

Equation 2: x_A = n_A / n_total

Equation 3: y_A = m_A / m_total

Equation 4: y_A = n_A / n_total

x_A, y_A - mass or mole fraction of component A.
m_A - the mass of component A in the mixture
n_A - the mole of component A in the mixture
m_total - the mass of the total mixture
n_total - the moles of the total mixture

"x" is used for liquids and solids, thus the first two equations are the mass and mole fractions for liquids and solids. Accordingly, the last two equations refer to gases. As you can see, "x_A" can donote several different things. For example, x_H2O can refer to either the mass or mole fraction of water or ice in a mixture. It will be up to the problem solver to keep track of how "x_A" is defined in working a problem.

Related to the mass and mole fractions are the definitions for parts per million (ppm) and the parts per billion (ppb). Here, we simply multiply the mass or mole fraction by 10⁶ for ppm, and by 10⁹ for ppb.

Parts Per Million (ppm) = x_A*10⁶ or y_A*10⁶

Parts Per Billion (ppb) = x_A*10⁹ or y_A*10⁹

note #1: The mole and mass fractions must always be unitless, so the mole/mass of the component (numerator) and the total mole/mass (denominator) must both have the same units.

note #2: Mass ratios are usually used for liquids and solids, while mole rations are usually used for gases.

Example 1

A mixture of gases has the following composition by mass:

Example 2

Air is approximately 79 mole% N₂ and 21 mole% O₂. Calculate the average molecular weight of air by using the following formula:

MW_avg = y_N2 * MW_N2 + y_O2 * MW_O2

Example 3

Check your calculated Mole Fractions:

O2 N2 CO2 H2O		O2 N2 CO2
	H2O