Question

The density of sodium chloride is \(2.164 \mathrm{~g} \mathrm{~cm}^{-3}\). What is the molar concentration of \(\mathrm{NaCl}\) in a \(12.0 \mathrm{~cm}^{3}\) sample of pure \(\mathrm{NaCl}\) ? What is the molar concentration of \(\mathrm{NaCl}\) in a \(25.0 \mathrm{~g}\) sample of pure \(\mathrm{NaCl}\) ?

Short answer

The molar concentration of NaCl in a 12.0 cm^3 sample of pure NaCl is 37.0 M. The molar concentration of NaCl in a 25.0 g sample of pure NaCl is 37.1 M.

Step-by-step solution

Calculate mass of the 12.0 cm^3 sample

To find the mass of the 12.0 cm^3 sample of NaCl, use the density formula: mass = density * volume. Mass = (2.164 g/cm^3) * (12.0 cm^3) = 25.968 g.

Calculate the moles of NaCl in the 12.0 cm^3 sample

Molar mass of NaCl is approximately 58.44 g/mol. Use the formula: moles = mass / molar mass.Moles of NaCl = 25.968 g / 58.44 g/mol = 0.444 mol.

Calculate molar concentration of the 12.0 cm^3 sample

Molar concentration is given by moles of solute per volume of solution in liters. The volume of the sample in liters is 12.0 cm^3 x (1 L/1000 cm^3) = 0.012 L.Molar concentration = 0.444 mol / 0.012 L = 37.0 M.

Calculate the moles of NaCl in the 25.0 g sample

Use the same molar mass of NaCl to calculate moles: moles = mass / molar mass.Moles of NaCl = 25.0 g / 58.44 g/mol = 0.428 mol.

Calculate molar concentration of the 25.0 g sample

Since we are not given the final volume of solution for the 25.0 g sample, it is assumed that the volume of NaCl itself is used as the sample volume. Calculate the volume using density.Volume = mass / density = 25.0 g / 2.164 g/cm^3 = 11.54 cm^3 or 0.01154 L.Molar concentration = 0.428 mol / 0.01154 L = 37.1 M.

Key concepts

Density of Sodium Chloride

The density of a substance like sodium chloride (table salt) is a measure of its mass per unit volume. In more tangible terms, it tells us how much a certain volume of the substance weighs. Knowing the density is essential in many scientific calculations because it allows us to relate a substance's mass and volume.

For example, if the density of sodium chloride is given as \(2.164 \mathrm{~g} \mathrm{~cm}^{-3}\), it means that a cube of sodium chloride with a volume of one cubic centimeter (cc or cm³) weighs \(2.164\) grams. In practical use, if we have a larger volume, we can simply multiply the volume by the density to find out how much our sample weighs.

To deepen your understanding, consider that the density of a substance can change with temperature and pressure. However, in most classroom problems, we assume standard conditions when using the density for calculations.

Molar Mass of NaCl

The molar mass of a compound, such as sodium chloride (NaCl), is the mass in grams of one mole of that compound. One mole represents \(6.022 \times 10^{23}\) entities (atoms, molecules, ions, etc.) of that substance, often referred to as Avogadro's number. For NaCl, the molar mass is the sum of the atomic masses of sodium (Na) and chlorine (Cl), which are approximately 22.99 g/mol and 35.45 g/mol respectively.

Therefore, the molar mass of NaCl is approximately \(22.99 \mathrm g/mol + 35.45 \mathrm g/mol = 58.44 \mathrm g/mol\). This value is crucial for converting between the mass of a substance and the number of moles, as seen in our exercises. Understanding the concept of molar mass allows us to interpret how much of a substance is present on a molecular level.

Moles and Molar Concentration

Moles are a fundamental concept in chemistry that quantifies the amount of substance. When we talk about the molar concentration, also known as molarity, we are referring to the number of moles of a substance in one liter of solution. The molar concentration is expressed in moles per liter (mol/L or M).

This concept is vital in preparing solutions and performing stoichiometric calculations in reactions. To find the molar concentration, you divide the moles of the solute by the volume of the solution in liters. For dense solids like sodium chloride, if not dissolved, we may consider the volume of the solid itself when it is entirely pure, as is done in the second part of the exercise.

Understanding moles and molar concentration is key to comprehending the quantitative relationships in chemical reactions and processes. It allows chemists to predict how much product will result from a given amount of reactants, and to compare the concentrations of different solutions.