A sample of \(12.7\) grams of sodium sulfate (Na2SO4) is dissolved in \(672 \mathrm{~mL}\) of distilled water. a. What is the molar concentration of sodium sulfate in the solution? b. What is the concentration of sodium ion in the solution?

Molarity is a measure of the concentration of a solute in a solution. It's defined as the number of moles of solute divided by the total volume of the solution in liters. The unit for molarity is moles per liter (M). For example, if you dissolve a substance into water, the molarity tells you how concentrated that solution is. To calculate molarity, you use the following formula: \( M = \frac{\text{moles of solute}}{\text{volume of solution in L}} \).

Using molarity is useful because it allows chemists to predict how substances will react with one another based on how concentrated they are. Moreover, it's an easy way to measure and communicate the strength of a solution in a laboratory or industrial setting. A greater molarity indicates a higher concentration and vice versa.

Solution concentration is a general term referring to the amount of solute present in a given quantity of solvent or solution. Molarity is one method used to express solution concentration, but there are others such as molality, mass percent, and volume percent. The appropriate method to use often depends on the situation and laboratory requirements. For instance, molarity is temperature-dependent since it involves volume, which can change with temperature.

In the context of our exercise, when we refer to the concentration of sodium sulfate in water, we specifically mean the molarity of that solute within the solution. Higher solution concentrations imply a greater amount of solute dissolved in a fixed amount of solvent.

The concept of moles is fundamental in chemistry, as it allows for a standardized method of quantifying substances. One mole is equal to Avogadro's number of particles, which is approximately \(6.02 \times 10^{23}\) particles. These particles could be atoms, molecules, ions, or electrons.

To calculate the number of moles, you use the substance's molar mass, which is the mass of one mole of that substance. The formula is: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). This calculation is crucial because it helps you transition from the macroscopic world, which deals with grams and liters, to the microscopic world measured in moles, thereby enabling chemists to use the mole concept to balance reactions and find the stoichiometry among reactants and products.

Ionic compounds, such as sodium sulfate (\(Na_2SO_4\)), dissociate in water to form ions. This process is crucial for calculating the concentration of ions in a solution. For every mole of sodium sulfate dissolved, two moles of sodium ions (\(Na^+\)) and one mole of sulfate ions (\(SO_4^{2-}\)) are formed.

To determine the concentration of individual ions, one must consider this dissociation. If the molar concentration of \(Na_2SO_4\) is, say, 1 M, then the concentration of \(Na^+\) ions is 2 M, because each unit of sodium sulfate provides two sodium ions. This same concept applies to other ionic compounds and is vital for understanding properties like electrical conductivity and osmotic pressure in solutions.