Solution Concentrations, Stoichiometry, and Titration in General Chemistry

Solution Concentrations

Units of Solution Concentration

Understanding how to express the concentration of solutions is fundamental in chemistry. The most common units include molarity, mass percent, and others.

• Molarity (M): The number of moles of solute per liter of solution. Formula: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Mass Percent: The mass of solute divided by the total mass of the solution, multiplied by 100%. Formula: $\text{Mass \%} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%$

Dilutions

Dilution involves reducing the concentration of a solution by adding more solvent. The relationship between the initial and final concentrations and volumes is given by:

• Formula: $M_1 V_1 = M_2 V_2$ where $M_1$ and $V_1$ are the initial molarity and volume, and $M_2$ and $V_2$ are the final molarity and volume.

• Example: If 18.0 M H2SO4 is available, what volume is needed to prepare 1.25 L of 2.50 M H2SO4? Use $M_1 V_1 = M_2 V_2$ to solve for $V_1$.

Solutions Prepared by Mixing Two Liquids

When two solutions are mixed, the total moles of solute is the sum of the moles from each solution. Molarity can be used to determine the final concentration.

• Strategy: Calculate moles of solute in each solution, sum them, and divide by the total volume.

• Example: Mixing 25.6 mL C2H5OH (d = 0.789 g/mL, 95% by mass) with 48.9 mL H2O. Find the molarity of ethanol in the solution.

Stoichiometry and Limiting Reactants

Stoichiometry in Solution Reactions

Stoichiometry allows chemists to predict the amounts of products and reactants in chemical reactions, including those in solution.

• General Steps:

  1. Balance the chemical equation.

  2. Convert masses to moles.

  3. Determine the limiting reactant (the reactant that is completely consumed first).

  4. Use mole ratios to calculate the amount of desired product or reactant.

• Example: For the reaction $3Ba(NO_3)_2 + 2Al_2(SO_4)_3 \rightarrow 3BaSO_4 + 4Al(NO_3)_3$, determine the limiting reactant and calculate the mass of BaSO4 produced.

Yields of Chemical Reactions

Theoretical, Actual, and Percent Yield

Yields are used to measure the efficiency of a chemical reaction.

• Theoretical Yield: The maximum amount of product that can be formed from the given reactants, based on stoichiometry.

• Actual Yield: The measured amount of product actually obtained from a reaction.

• Percent Yield: The ratio of actual yield to theoretical yield, expressed as a percentage. Formula: $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

• Example: If 48.5 g BaSO4 is produced but the theoretical yield is 55.0 g, percent yield is $\frac{48.5}{55.0} \times 100\% = 88.2\%$.

Titrations

Simple Titration

Titration is a technique to determine the concentration of a solution by reacting it with a solution of known concentration.

• Equivalence Point: The point at which the amount of titrant added is stoichiometrically equivalent to the amount of analyte in the sample.

• Indicator: A substance that changes color at (or near) the equivalence point.

• End Point: The point at which the indicator changes color, signaling the completion of the reaction.

• Example: Titrating HCl with NaOH to determine the concentration of HCl.

Standardization

Standardization is the process of determining the exact concentration of a solution (often an acid or base) using a primary standard.

• Primary Standard: A highly pure chemical used to determine the concentration of another solution.

• Example: KHP (potassium hydrogen phthalate) is commonly used to standardize NaOH solutions.

Back Titration

Principle and Application

Back titration is used when the analyte is not easily titrated directly. An excess of a standard reagent is added to react with the analyte, and the remaining excess is titrated with another reagent.

• Example: Determining the mass of BaCO3 in a sample by reacting it with excess HCl, then titrating the remaining HCl with NaOH.

• Relevant equations: $\text{BaCO}_3 + 2\text{HCl} \rightarrow \text{BaCl}_2 + \text{H}_2\text{O} + \text{CO}_2$ $\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$

Tables

Comparison of Yield Types

The following table summarizes the differences between theoretical, actual, and percent yield:

Yield Type	Definition	Formula
Theoretical Yield	Maximum possible amount of product, calculated from stoichiometry	Based on balanced equation
Actual Yield	Measured amount of product obtained from experiment	Measured in lab
Percent Yield	Efficiency of reaction	$\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Additional Info

• When performing stoichiometric calculations, always ensure the chemical equation is balanced.

• For titrations, the use of indicators is essential to accurately determine the end point.

• Back titration is especially useful for substances that are insoluble or react slowly with the titrant.