Question

A diprotic acid, \(\mathrm{H}_{2} \mathrm{~B}(\mathrm{MM}=126 \mathrm{~g} / \mathrm{mol})\), is determined to be a hydrate, \(\mathrm{H}_{2} \mathrm{~B} \cdot x \mathrm{H}_{2} \mathrm{O} .\) A \(10.00-\mathrm{g}\) sample of this hydrate is dissolved in enough water to make \(150.0 \mathrm{~mL}\) of solution. Twenty-five milliliters of this solution requires \(48.5 \mathrm{~mL}\) of \(0.425 \mathrm{M} \mathrm{NaOH}\) to reach the equivalence point. What is \(x\) ?

Short answer

The molar mass of H2B is 126 g/mol. Answer: In the hydrate H2B·xH2O, the value of 'x' is approximately 2.

Step-by-step solution

Calculate moles of NaOH used in titration

Given the volume and concentration of the NaOH solution, we can determine the moles of NaOH used in titration. Use the formula: Moles of NaOH = Volume × Concentration Moles of NaOH = 48.5 mL × 0.425 mol/L Convert mL to L Moles of NaOH = 0.0485 L × 0.425 mol/L = 0.0206125 mol

Calculate moles of H2B in the titrated sample

Since H2B is a diprotic acid, there are two moles of H+ ions to be neutralized by NaOH. Therefore, moles of H2B in the titrated sample = moles of NaOH / 2: Moles of H2B = 0.0206125 mol / 2 = 0.01030625 mol

Determine moles of H2B in the initial sample

We used 25 mL of the 150 mL solution for titration. Therefore, to get the moles of H2B in the initial sample, we need to multiply moles of H2B in the titrated sample by the ratio of the total volume to the titrated volume: Moles of H2B (initial sample) = 0.01030625 mol × (150 mL/ 25 mL) = 0.0618375 mol

Calculate the mass of H2B

To determine the mass of H2B, multiply the moles of H2B (initial sample) by the molar mass of H2B: Mass of H2B = 0.0618375 mol × 126 g/mol = 7.79192 g

Calculate the mass of water in the hydrate

Now, we can find the mass of water in the entire hydrate sample: Mass of water = Total sample mass (hydrate) - Mass of H2B Mass of water = 10.00 g - 7.79192 g = 2.20808 g

Calculate moles of water in the hydrate

Using the molar mass of water (18 g/mol), determine the moles of water in the hydrate: Moles of water = Mass of water / Molar mass of water Moles of water = 2.20808 g / 18 g/mol = 0.122671 mol

Calculate the value of 'x'

To find the value of 'x,' we must determine the mole ratio of water molecules (H2O) to H2B in the hydrate. Divide the moles of water by moles of H2B: x = Moles of water / Moles of H2B x = 0.122671 mol / 0.0618375 mol ≈ 1.986 Since 'x' must be an integer, we can round it to the nearest whole number: x ≈ 2 Thus, in the hydrate H2B·xH2O, the value of 'x' is approximately 2.

Key concepts

Understanding Acid-Base Titration

Acid-base titration is a laboratory procedure used to determine the concentration of an unknown acid or base solution by reacting it with a base or acid of known concentration, respectively. During the titration, an indicator or a pH meter can be used to identify the equivalence point—the stage at which the amount of acid equals the amount of base, neutralizing each other.

As a diprotic acid has two ionizable hydrogen atoms per molecule, it can accept two hydroxide ions (OH⁻) from a base such as sodium hydroxide (NaOH) to reach the equivalence point. In the given exercise, the titration process helps us figure out the composition of the hydrate by utilizing the stochiometric relationship between the acid and the base.

Stoichiometry in Action

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's used to calculate amounts in reactions, based on the balanced chemical equations.

In the context of the exercise with a diprotic acid, stoichiometry allows for the calculation of the moles of the acid after determining the moles of NaOH used. Understanding that each mole of a diprotic acid reacts with two moles of NaOH is crucial for solving this exercise—the stoichiometric ratio being 1:2. Therefore, dividing the moles of NaOH by two gives the moles of the acid in the titrated portion of the solution.

Calculating Molar Mass

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). It is a fundamental concept in chemistry that allows for conversions between mass and moles of a substance.

In the solution steps, the molar mass of the acid (126 g/mol) is given, which facilitates the determination of the mass of the H2B present in the hydrate. By multiplying the moles of H2B by the molar mass, the mass of the acid in the sample is obtained. Establishing molar mass relations is essential for stoichiometry and conversions throughout chemistry.

Understanding Hydrate Composition

Hydrate compounds are substances that contain water molecules integrated into their molecular structure. The 'x' in the hydrate ‘H2B·xH2O’ signifies the number of water molecules associated with each formula unit of the non-water compound. Calculating the hydrate composition involves determining the mass and moles of water and the moles of the dry compound.

In the final steps of the given solution, the mass of water is found by subtracting the mass of H2B from the total sample mass. Dividing this mass by the molar mass of water yields the moles of water, which when divided by the moles of H2B, gives 'x', the number of water molecules per H2B molecule in the hydrate. The result is rounded to the nearest whole number because 'x' must represent a discrete number of water molecules.