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?

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 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.

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.