Question

The concentration of a certain sodium hydroxide solution was determined by using the solution to titrate a sample of potassium hydrogen phthalate (abbreviated as KHP). KHP is an acid with one acidic hydrogen and a molar mass of \(204.22 \mathrm{~g} / \mathrm{mol}\). In the titration, \(34.67 \mathrm{~mL}\) of the sodium hydroxide solution was required to react with \(0.1082\) g KHP. Calculate the molarity of the sodium hydroxide.

Short answer

The concentration of the sodium hydroxide solution is approximately \(0.0153 \mathrm{M}\).

Step-by-step solution

Calculate moles of KHP

Using the given mass of KHP (\(0.1082 \mathrm{~g}\)) and its molar mass (\(204.22 \mathrm{~g/mol}\)), we can calculate the moles of KHP reacted in the titration. To do this, use the formula: moles of KHP = \(\frac{\text{mass of KHP}}{\text{molar mass of KHP}}\)

Find the moles of NaOH reacting with KHP

In the reaction, one mole of KHP reacts with one mole of sodium hydroxide (NaOH). Therefore, the moles of NaOH reacting with KHP will be the same as the moles of KHP. Moles of NaOH = Moles of KHP

Calculate the molarity of sodium hydroxide

Now that we have the moles of NaOH, we can calculate the molarity using the formula: Molarity = \(\frac{\text{moles of solute}}{\text{volume of solution in liters}}\) Since we have the volume of sodium hydroxide solution in milliliters (\(34.67 \mathrm{~mL}\)), we can convert it to liters by dividing by 1000. Now, let's put all the steps together and find the molarity of the sodium hydroxide solution.

Step 1

moles of KHP = \(\frac{0.1082 \mathrm{~g}}{204.22 \mathrm{~g/mol}} = 0.00053 \mathrm{~mol}\)

Step 2

Since Moles of NaOH = Moles of KHP: moles of NaOH = \(0.00053 \mathrm{~mol}\)

Step 3

First, convert the volume of sodium hydroxide solution to liters: Volume of NaOH solution = \(\frac{34.67 \mathrm{~mL}}{1000} = 0.03467 \mathrm{~L}\) Now, calculate the molarity of sodium hydroxide: Molarity of NaOH = \(\frac{0.00053 \mathrm{~mol}}{0.03467 \mathrm{~L}} = 0.0153 \mathrm{~M}\) Therefore, the concentration of the sodium hydroxide solution is approximately \(0.0153 \mathrm{M}\).

Key concepts

Molarity

Molarity is a vital concept in chemistry, representing the concentration of a solute in a solution. It is defined as the number of moles of a substance per liter of solution. When measuring molarity, the formula
\( M = \frac{\text{moles of solute}}{\text{volume of solution (L)}} \)
is used. This is a critical unit of concentration since it allows chemists to relate the volume of a solution to the amount of substance dissolved in it. Understanding molarity also helps determine how solutions will react when mixed, as seen in titration procedures. Molarity is especially useful because it provides a direct measure of the number of reacting particles in a given volume, which is essential for predicting the outcome of reactions.

Stoichiometry

Stoichiometry is the backbone of chemical reactions. It refers to the quantitative relationship between reactants and products in a chemical reaction. This aspect of chemistry enables scientists to predict the amounts of substances consumed and produced in a reaction, based on the balanced chemical equation. In a stoichiometric calculation, we use the coefficients of the balanced equation to understand the molar ratios of the reactants and products. For example, if a reaction indicates that one mole of substance A reacts with one mole of substance B, stoichiometry allows us to calculate how much of A is needed to fully react with a certain amount of B, or vice versa. It ensures the correct proportions are used for the reactants to avoid wasting materials and to predict the yield of the reaction.

Acid-Base Titration

Acid-base titration is a practical application of the concept of stoichiometry in analytical chemistry. In this process, a solution of known concentration (titrant) is gradually added to a solution of unknown concentration (analyte) until the chemical reaction between the two is complete – indicated by a color change or a pH meter reading.

Endpoint and Equivalence Point

An endpoint of a titration is when the indicator changes color, while the equivalence point is when the moles of acid equal the moles of base in the solution. These two points help chemists establish the point of complete neutralization, allowing for the calculation of the unknown concentration.
Titration calculations require precise measurement, a balanced reaction equation, and a thorough understanding of molarity and the stoichiometry of the reaction. By applying these principles, one can accurately determine the concentration of an unknown solution, vital in fields such as pharmaceuticals, environmental monitoring, and the food industry.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is a fundamental property of substances that bridges the gap between the microscopic world of atoms and molecules and the macroscopic world that we can measure.
In chemistry, knowing the molar mass of a compound is crucial as it is used to convert between grams and moles, a key step in stoichiometry. The molar mass can be calculated by summing the masses of all the atoms in a molecule as given by the periodic table. For instance, to find the molar mass of a compound like KHP, we would add up the masses of potassium (K), hydrogen (H), and phthalate, a more complex group whose molar mass we would find by adding the masses of its constituent carbon, hydrogen, and oxygen atoms. An accurate molar mass allows for precise calculations in titrations and other quantitative analytical techniques.