Solutions: Concentration Calculations and Dilution in Chemistry

Solutions and Their Concentrations

Electrolyte Concentration Calculations

Electrolyte concentrations in solutions are often measured in equivalents (Eq) or milliequivalents (mEq), especially in biological and medical contexts. The calculation of moles of ions from a given volume and concentration involves several conversion factors.

• Given: Volume of solution and concentration in mEq/L

• Need: Moles of the ion (e.g., Ca2+)

• Connect: Use the relationships: 1 Eq = 1000 mEq, and for Ca2+, 1 mole = 2 Eq

The calculation plan involves converting liters of solution to moles of Ca2+ using the provided concentration and conversion factors.

Key conversion factors:

• 1 L solution = 8.8 mEq Ca2+

• 1 Eq = 1000 mEq

• 1 mole Ca2+ = 2 Eq Ca2+

Calculation:

• $0.50\ \mathrm{L} \times \frac{8.8\ \mathrm{mEq}\ \mathrm{Ca}^{2+}}{1\ \mathrm{L}} \times \frac{1\ \mathrm{Eq}\ \mathrm{Ca}^{2+}}{1000\ \mathrm{mEq}\ \mathrm{Ca}^{2+}} \times \frac{1\ \mathrm{mol}\ \mathrm{Ca}^{2+}}{2\ \mathrm{Eq}\ \mathrm{Ca}^{2+}} = 0.0022\ \mathrm{mol}\ \mathrm{Ca}^{2+}$

Example: Calculating moles of Ca2+ in a blood sample using mEq/L.

Saturated Solutions and Solubility

The solubility of a compound in water determines how much of it can dissolve at a given temperature. If more solute is added than can dissolve, the solution is saturated and excess solute remains undissolved.

• Given: Mass of solute and solvent, solubility data

• Need: Maximum mass that can dissolve, and whether the solution is saturated

Calculation:

• $200.\ \mathrm{g}\ \mathrm{H}_2\mathrm{O} \times \frac{34\ \mathrm{g}\ \mathrm{KCl}}{100.\ \mathrm{g}\ \mathrm{H}_2\mathrm{O}} = 68\ \mathrm{g}\ \mathrm{KCl}$

Example: If 75 g KCl is added to 200 g water at 20°C, only 68 g dissolves; the solution is saturated and 7 g remains undissolved.

Mass Percent (m/m) Concentration

Mass percent expresses the concentration of a solution as the mass of solute divided by the total mass of solution, multiplied by 100%.

• Given: Mass of solute and solvent

• Need: Mass percent (m/m)

• Connect: $\frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%$

Formula:

• $\text{Mass percent (m/m)} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 100\%$

Example calculation:

• $\text{Mass percent (m/m)} = \frac{30.0\ \mathrm{g}\ \mathrm{NaOH}}{150.0\ \mathrm{g}\ \text{solution}} \times 100\% = 20.0\%\ \mathrm{NaOH}$

Using Mass Percent to Calculate Mass of Solute

To find the mass of solute in a given mass of solution, use the mass percent as a conversion factor.

• Given: Mass of solution and mass percent

• Need: Grams of solute

• Connect: $\frac{\text{g solute}}{100.\ \text{g solution}}$

Example calculation:

• $64\ \mathrm{g}\ \text{ointment} \times \frac{3.5\ \mathrm{g}\ \text{neomycin}}{100.\ \mathrm{g}\ \text{ointment}} = 2.2\ \mathrm{g}\ \text{neomycin}$

Volume Percent (v/v) Concentration

Volume percent is used for solutions where both solute and solvent are liquids. It is calculated as the volume of solute divided by the total volume of solution, multiplied by 100%.

• Given: Volume of solute and solution

• Need: Volume percent (v/v)

• Connect: $\frac{\text{volume of solute}}{\text{volume of solution}} \times 100\%$

Example calculation:

• $\text{Volume percent (v/v)} = \frac{49\ \mathrm{mL}\ \text{alcohol}}{59\ \mathrm{mL}\ \text{solution}} \times 100\% = 83\%\ \text{alcohol solution}$

Mass/Volume Percent (m/v) Concentration

Mass/volume percent is commonly used in medical and laboratory settings, expressing the mass of solute per 100 mL of solution.

• Given: Mass of solute and volume of solution

• Need: Mass/volume percent (m/v)

• Connect: $\frac{\text{mass of solute}}{\text{volume of solution}} \times 100\%$

Example calculation:

• $\text{Mass/volume percent (m/v)} = \frac{5.0\ \mathrm{g}\ \mathrm{KI}}{250\ \mathrm{mL}\ \text{solution}} \times 100\% = 2.0\%\ \mathrm{KI}$

Using Mass/Volume Percent to Calculate Mass of Solute

To determine the mass of solute in a given volume of solution, use the (m/v) percent as a conversion factor.

• Given: Volume of solution and (m/v) percent

• Need: Grams of solute

• Connect: $\frac{\text{g solute}}{100\ \text{mL solution}}$

Example calculation:

• $60.\ \mathrm{mL}\ \text{solution} \times \frac{1.0\ \mathrm{g}\ \text{clindamycin}}{100.\ \mathrm{mL}\ \text{solution}} = 0.60\ \mathrm{g}\ \text{clindamycin}$

Molarity (M) Calculations

Molarity is a measure of concentration, defined as moles of solute per liter of solution. It is widely used in chemistry for solution preparation and stoichiometric calculations.

• Given: Mass of solute and volume of solution

• Need: Molarity (M)

• Connect: Use molar mass to convert grams to moles, then divide by liters of solution

Example calculation:

• $M = \frac{1.50\ \text{moles NaOH}}{0.250\ \text{L solution}} = 6.00\ \text{M NaOH}$

Using Molarity to Calculate Volume of Solution

To find the volume of solution needed to provide a specific mass of solute, use the molarity and molar mass as conversion factors.

• Given: Mass of solute and molarity

• Need: Volume of solution

• Connect: Use molar mass to convert grams to moles, then use molarity to convert moles to liters

Example calculation:

• $67.3\ \mathrm{g}\ \mathrm{NaCl} \times \frac{1\ \mathrm{mol}\ \mathrm{NaCl}}{58.44\ \mathrm{g}\ \mathrm{NaCl}} \times \frac{1\ \mathrm{L}\ \text{solution}}{2.00\ \mathrm{mol}\ \mathrm{NaCl}} = 0.576\ \mathrm{L}\ \text{solution}$

Molarity of a Diluted Solution

Dilution involves adding solvent to a solution, decreasing its concentration. The relationship is given by $C_1V_1 = C_2V_2$, where $C$ is concentration and $V$ is volume.

• Given: Initial concentration and volume, final volume

• Need: Final concentration

• Connect: $C_1V_1 = C_2V_2$

Example calculation:

• $C_2 = 4.00\ \mathrm{M} \times \frac{75.0\ \mathrm{mL}}{500.\ \mathrm{mL}} = 0.600\ \mathrm{M}$

Dilution of a Solution (Percent Concentration)

When diluting solutions with concentrations expressed as percent (m/v), the same dilution equation applies: $C_1V_1 = C_2V_2$.

• Given: Initial and final concentrations, final volume

• Need: Initial volume required

• Connect: $V_1 = V_2 \times \frac{C_2}{C_1}$

Example calculation:

• $V_1 = 1000.\ \mathrm{mL} \times \frac{35.0\%}{50.0\%} = 700.\ \mathrm{mL}$

Summary Table: Common Concentration Units

Unit	Expression	Typical Use
Mass percent (m/m)	grams solute / grams solution × 100%	Solid in solid/liquid
Volume percent (v/v)	mL solute / mL solution × 100%	Liquid in liquid
Mass/volume percent (m/v)	grams solute / mL solution × 100%	Medical/lab solutions
Molarity (M)	moles solute / liters solution	Chemical reactions