Problem 37 - Chemistry The Central Science

Question

What is the molarity of \(\mathrm{Na}^{+}\) in a solution of \(\mathrm{NaCl}\) whose salinity is 5.6 if the solution has a density of 1.03 \(\mathrm{g} / \mathrm{mL}\) ?

Step-by-Step Solution

Answer

The molarity of \(\mathrm{Na}^{+}\) in the solution of NaCl with 5.6 salinity and 1.03 g/mL density is 0.959 M.

Step 1: Calculate the mass of NaCl

The salinity of the solution is given as 5.6, which means there are 5.6 grams of NaCl dissolved in 100 mL of the solution. Thus, the amount of NaCl dissolved in the solution can be calculated as: Mass of NaCl = 5.6 g

Step 2: Convert mass of NaCl to moles

To find the number of moles of NaCl, we need to divide the mass of NaCl by its molar mass. The molar mass of NaCl is approximately 58.44 g/mol. Thus, Moles of NaCl = \(\frac{5.6 \text{ g}}{58.44 \text{ g/mol}}\) = 0.0959 mol

Step 3: Calculate the volume of the solution

The solution has a density of 1.03 g/mL. As we know the mass of NaCl in 100 mL of the solution, we can find the mass of 100 mL of the solution: Mass of 100 mL solution = (100 mL x 1.03 g/mL) = 103 g Now, as we know the mass and density of the solution, we can calculate the volume as: Volume = \(\frac{\text{mass}}{\text{density}} = \frac{103 \text{ g}}{1.03 \text{ g/mL}}\) = 100 mL = 0.100 L

Step 4: Calculate the molarity of Na+

The molarity of Na+ in the solution can be calculated by dividing the moles of NaCl by the volume of the solution. Since NaCl dissociates into equal amounts of Na+ and Cl- ions, the moles of Na+ will be the same as the moles of NaCl: Molarity of Na+ = \(\frac{\text{moles of NaCl}}{\text{volume of solution}} = \frac{0.0959 \text{ mol}}{0.100 \text{ L}}\) = 0.959 M So, the molarity of \(\mathrm{Na}^{+}\) in the given solution is 0.959 M.

Key Concepts

NaCl dissociation

When table salt, or sodium chloride (NaCl), is added to water, it undergoes a process called dissociation. This process is essential in understanding how the dissolved substances behave in a solution.
NaCl is composed of sodium (Na\(^+\)) and chloride (Cl\(^-\)) ions. In solid form, they are held together by ionic bonds. However, when NaCl is dissolved in water, these ionic bonds break due to the interaction with water molecules.
The water molecules, which are polar in nature, attract the oppositely charged ions in NaCl, effectively separating them.

• Sodium ions (Na\(^+\)) are attracted to the oxygen end of water molecules, which is negatively charged.
• Chloride ions (Cl\(^-\)) are attracted to the hydrogen end, which is positively charged.

Thus, in a solution, NaCl dissociates completely into Na\(^+\) and Cl\(^-\) ions. In stoichiometric terms, for every mole of NaCl added to the solution, one mole of Na\(^+\) ions and one mole of Cl\(^-\) ions are released. This makes the number of Na\(^+\) ions equivalent to the amount of dissolved NaCl.

Solution density

Density is a fundamental property of a solution, defined as the mass of the solution per unit volume. It is often expressed in grams per milliliter (g/mL). Understanding solution density helps in determining other properties such as concentration.
In this context, the given solution has a density of 1.03 g/mL. This means that every milliliter of this solution has a mass of 1.03 grams. Knowing this density is instrumental in calculating other quantities, such as the volume of the solution from a given mass, or vice versa.
For instance, if you have a specific mass of the solution, you can determine the corresponding volume using the formula: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}}\] This relationship is particularly useful when preparing or analyzing solutions, as it provides a direct way to convert between mass and volume, helping in accurate calculations of concentration and molarity.

Mole calculation

The concept of a mole is central to chemistry, acting as a bridge between the mass of a substance and its amount in terms of particles, such as atoms or molecules. One mole consists of approximately 6.022 x 10\(^{23}\) particles, known as Avogadro's number.
To calculate the number of moles from a given mass, you use the formula: \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\] In the context of the original problem, with NaCl having a molar mass of 58.44 g/mol, you can determine how many moles are present in a given mass of the compound.

• For example, if you have 5.6 g of NaCl, the number of moles is calculated as: \(\frac{5.6\, \text{g}}{58.44\, \text{g/mol}} = 0.0959\, \text{mol}\).

By understanding how to calculate moles, you can determine concentrations, which are expressed in terms of molarity (moles per liter) in solutions. This is crucial in various chemical calculations and practical applications, from laboratory experiments to industrial chemical processes.