Problem 32 - Introductory Chemistry Atoms First

Question

A 1.65-g sample of an acid that has one acidic proton per molecule is dissolved in water to give \(25.00 \mathrm{~mL}\) of solution. It takes \(27.48 \mathrm{~mL}\) of \(1.000 \mathrm{M} \mathrm{NaOH}\) to neutralize the acid. (a) What is the molar concentration of the acid? (b) What is the molar mass of the acid? (c) The empirical formula of the acid is \(\mathrm{CH}_{2} \mathrm{O}\). What are the molecular formula and name of the acid?

Step-by-Step Solution

Answer

The molar concentration of the acid is 1.0992 M. Its molar mass is approximately 60 g/mol, and the molecular formula is C2H4O2. The name of the acid is ethanoic acid or acetic acid.

Step 1: Determine the moles of OH- ions used in neutralization

To understand the amount of the base used to neutralize the acid, start by calculating the moles of OH- ions in NaOH solution. moles of OH- = (Volume of NaOH) × (Concentration of NaOH) =27.48mL x 1.000 mol/L Note that it is necessary to convert the volume of NaOH to liters from milliliters. In this case, 27.48 mL is equal to 0.02748 L. So, the equivalent calculation becomes: moles of OH- = 0.02748 L × 1.000 mol/L moles of OH- = 0.02748 mol

Step 2: Determine the moles of the acid

Since the acid has one acidic proton per molecule, the moles of the acid are equal to the moles of OH- ions: moles of acid = moles of OH- moles of acid = 0.02748 mol

Step 3: Calculate the molar concentration of the acid

The molar concentration of the acid can be calculated using the moles of acid and the volume of the solution (25.00 mL). To calculate the molar concentration, use the following formula: Molar concentration of acid = (moles of acid) / (volume of solution in L) The volume of the solution should be converted to liters first. 25.00 mL is equal to 0.025 L. So, the calculation becomes: Molar concentration of acid = (0.02748 mol) / (0.025 L) Molar concentration of acid = 1.0992 M The molar concentration of the acid is 1.0992 M.

Step 4: Calculate the molar mass of the acid

The molar mass of the acid can be calculated using the mass of the acid and the moles of the acid. Mass = 1.65 g moles = 0.02748 mol molar mass = Mass / moles molar mass = 1.65 g/0.02748 mol molar mass ≈ 60 g/mol The molar mass of the acid is approximately 60 g/mol.

Step 5: Determine the molecular formula and name of the acid

The empirical formula of the acid is given as CH2O, and it has the following masses: C: 12 g/mol H: 1 g/mol (x2) O: 16 g/mol The empirical formula has a total mass of 12 + (2*1) + 16 = 30 g/mol. Next, divide the molar mass of the acid by the empirical formula molar mass: Molecular formula multiple = (Molar mass of the acid) / (Empirical formula molar mass) = 60 g/mol / 30 g/mol = 2 Now multiply the empirical formula by the molecular formula multiple to get the molecular formula: CH2O × 2 = C2H4O2 The molecular formula of the acid is C2H4O2. The name of the acid corresponding to this molecular formula is ethanoic acid, commonly known as acetic acid.

Key Concepts

Molar Concentration

Molar concentration, often simply called 'concentration', is one of the most fundamental concepts in chemistry, especially in solutions-related exercises like acid-base titrations. It has a unit of moles per liter (M or mol/L) and is a measure of how much of a substance (solute) is contained in a certain volume of a solution.

The formula for molar concentration is represented as:
\[ \text{Molar Concentration} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
When performing titrations, understanding the molar concentration of reactants is crucial, as it allows us to calculate how much reactant will react with a given amount of another substance. In our exercise, the molar concentration helped determine how much acid was neutralized by the base.

The concept of molar concentration is widely applicable and especially important when dealing with reactions in aquatic environments or when preparing solutions in a laboratory.

Molar Mass Calculation

Molar mass calculation is a vital process in chemistry that refers to the mass of one mole of a substance. It is typically measured in grams per mole (g/mol) and is equivalent to the atomic or molecular weight of a substance as listed on the periodic table, summed for all atoms in a molecule.

To calculate molar mass, one should:

• Identify the number of moles of each element in the compound.
• Find the atomic mass for each element from the periodic table.
• Multiply the atomic mass by the number of moles for each element.
• Sum all the values to get the total molar mass.

For example, when working out the molar mass of the unknown acid in the exercise, the mass of the sample is divided by the number of moles.

The calculation is simple:
\[ \text{molar mass} = \frac{\text{mass of the compound (in grams)}}{\text{number of moles}} \]

Knowing the molar mass is essential for converting grams to moles and vice versa, which is a common step in stoichiometric calculations and in deducing empirical and molecular formulas.

Empirical and Molecular Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements within it, while the molecular formula indicates the actual number of atoms of each element in a molecule. The empirical formula is the reduced form of the molecular formula. For instance, hydrogen peroxide has an empirical formula of HO, signifying a 1:1 ratio of hydrogen to oxygen, whereas its molecular formula is H2O2, which displays the actual number of atoms present.

To go from an empirical formula to a molecular formula, one must know the molar mass of the compound. The process involves:

• Calculating the molar mass of the empirical formula.
• Dividing the compound's molar mass by the empirical formula's molar mass to get a ratio.
• Multiplying the subscripts in the empirical formula by this ratio to find the molecular formula.

In our acid-base titration problem, the empirical formula is CH2O. The ratio of the molar mass of the unknown acid to the empirical formula molar mass gives the number of empirical units in the molecular formula, leading to the determination of the molecular formula C2H4O2. The name ethanoic acid, or more commonly acetic acid, is derived from the identified molecular formula.