A 4.36-g sample of an unknown alkali metal hydroxide is dissolved in 100.0 mL of water. An acid–base indicator is added, and the resulting solution is titrated with 2.50 M HCl(aq) solution. The indicator changes color, signaling that the equivalence point has been reached, after 17.0 mL of the hydrochloric acid solution has been added. (a) What is the molar mass of the metal hydroxide?

Verified step by step guidance

1. Step 1: Calculate the moles of HCl used in the titration. The molarity of a solution is defined as the number of moles of solute per liter of solution. Therefore, the moles of HCl can be calculated by multiplying the volume of the HCl solution (in liters) by its molarity. In this case, convert 17.0 mL to liters by dividing by 1000, then multiply by the molarity of 2.50 M.
2. Step 2: Determine the stoichiometry of the reaction. Since HCl and the alkali metal hydroxide (M(OH)) react in a 1:1 ratio to produce water and a salt, the moles of HCl used in the titration is equal to the moles of M(OH) in the original solution.
3. Step 3: Calculate the molar mass of the alkali metal hydroxide. The molar mass is the mass of the substance divided by the number of moles. In this case, divide the mass of the M(OH) sample (4.36 g) by the number of moles calculated in Step 2.
4. Step 4: The result from Step 3 is the molar mass of the alkali metal hydroxide in g/mol.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry is essential for relating the moles of HCl used in the titration to the moles of the alkali metal hydroxide present in the sample.

Titration

Titration is a laboratory technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (in this case, HCl) to a solution until the reaction reaches the equivalence point, indicated by a color change from the acid-base indicator. Understanding the titration process is crucial for calculating the amount of hydroxide in the sample based on the volume and concentration of the titrant used.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule. In this problem, determining the molar mass of the unknown alkali metal hydroxide requires knowing the moles of hydroxide ions that reacted with the titrant, which can be derived from the titration data.