Question

What is the molarity of \(\mathrm{NaCl}(\mathrm{aq})\) if a solution has 1.52 ppm Na? Assume that NaCl is the only source of Na and that the solution density is \(1.00 \mathrm{g} / \mathrm{mL}\) (The unit \(p p m\) is parts per million; here it can be taken to mean g Na per million grams of solution.)

Short answer

The molarity of the NaCl solution is \(6.61*10^{-5} M\).

Step-by-step solution

Convert ppm into g Na

To start, ppm is parts per million, which can be understood as grams of Na per million grams of solution. Therefore, 1.52 ppm Na means there are 1.52 grams of Na in 1 million grams of the solution. (As one million grams is 1000 kg or 1000 L, considering the density of the solution = 1 g/mL).

Convert g Na into Na moles

Since Na is the only source of Na+, the amount of Na is equal to the amount of NaCl in the solution. The molar mass of Na is approximately 23 g/mol. To convert the amount of Na from grams into moles, divide it by the molar mass of Na. This gives, \( \frac{1.52 \, \text{g}}{23 \, \text{g/mol}} = 0.0661 \, \text{moles}\).

Calculate Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Given that the solution volume is 1000 L (since 1 million grams is equal 1 million mL or 1000 L, the density of the solution = 1 g/mL), the molarity is, \( M = \frac{0.0661 \, \text{moles}}{1000 \, \text{L}} = 6.61*10^{-5} M \).

Key concepts

ppm (parts per million)

Understanding ppm (parts per million) is crucial when dealing with very dilute solutions, as it measures concentration on a much finer scale. To visualize this, imagine a huge room where out of a million balls, just one is red. That's similar to how ppm works. It quantifies how many parts of a solute, like sodium in this case, exist per million parts of the whole solution.

In the exercise, 1.52 ppm Na means there are 1.52 grams of sodium dispersed throughout one million grams (or 1000 kilograms) of solution. Essentially, you're looking at how one very small substance stands out against a vast background of solvent. This concept is particularly handy when the solute is present in tiny amounts, making it simpler to calculate moles and other measurements without confusing tiny fractions.

• 1 ppm is equivalent to 1 mg/L, which simplifies many conversions, especially when the density is approximately 1 g/mL.
• The ppm unit is particularly favored in environmental science and chemistry for expressing trace amounts of substances.

sodium chloride (NaCl)

Sodium Chloride, commonly known as table salt, is a crucial compound in chemistry. It consists of equal numbers of sodium ions (Na⁺) and chloride ions (Cl⁻). When dissolved in water, NaCl dissociates completely into its ions, making it an ideal subject for calculating molarity.

In this exercise, NaCl is the only source of sodium ions in the solution. Thus, analyzing sodium directly gives us direct insight into the amount of sodium chloride present. By knowing the ppm concentration of sodium, we can deduce the concentration of NaCl. As Na+ ions originate solely from NaCl, the number of moles calculated from sodium's mass directly translates to the moles of sodium chloride in solution.

• Each molecule of NaCl contributes one sodium ion (Na⁺) and one chloride ion (Cl⁻)
• Being a strong electrolyte, NaCl fully ionizes in water, simplifying the stoichiometry in solutions.

molar mass conversion

Converting from mass to moles is a fundamental step in chemistry. It allows us to translate between the amount of substance and its corresponding mass. The molar mass of an element, like sodium in the discussion here, represents the mass of one mole of that element and is expressed in grams per mole (g/mol).

Given sodium's molar mass of approximately 23 g/mol, you can find moles by dividing the substance's mass by its molar mass. For instance, in this exercise, 1.52 grams of sodium is divided by 23 g/mol, yielding 0.0661 moles of sodium. This conversion is essential for further calculations, such as determining molarity.

• Always check and use the correct molar masses: Periodic tables are your best friend here.
• Remember, moles act as a bridge in chemical reactions, connecting mass and volume to the number of particles.