Question

Common salt obtained from sea-water contains \(8.775 \% \mathrm{NaCl}\) by mass. The number of formula units of \(\mathrm{NaCl}\) present in \(25 \mathrm{~g}\) of this salt is : (a) \(3.367 \times 10^{23}\) formula units (b) \(2.258 \times 10^{22}\) formula units \(8^{3}\) (c) \(3.176 \times 10^{23}\) formula units (d) \(4.73 \times 10^{25}\) formula units

Short answer

The number of formula units of NaCl is approximately \(3.367 \times 10^{23}\text{ formula units}\).

Step-by-step solution

Calculate the mass of NaCl in the sample

To find the mass of NaCl in the 25g salt sample, multiply the total mass by the percentage of NaCl (as a decimal).

Convert the mass of NaCl to moles

Use the molar mass of NaCl to convert the mass of NaCl to moles. The molar mass of NaCl (sodium chloride) is approximately 58.44 g/mol.

Calculate the number of formula units

Multiply the number of moles of NaCl by Avogadro's number (\(6.022 \times 10^{23}\text{ formula units/mol}\) ) to find the number of formula units of NaCl.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that helps us relate the mass of a substance to the number of particles it contains. It's like a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. A mole represents a specific number of particles, which is known as Avogadro's number, or about 6.022 x 10²³.
This concept allows us to convert between the mass of a substance and the amount of substance in moles. For instance, if we know the number of moles of a compound, we can calculate how many molecules or formula units it contains, and vice versa.

• A mole is simply a unit of measurement in chemistry.
• Specifically, 1 mole is equal to 6.022 x 10²³ particles (atoms, molecules, or formula units).
• The mole concept links mass (grams) with the number of particles.

Molar Mass

Molar mass is the mass of one mole of a substance. It's the combined weight of all the atoms in a molecule of the substance. You find it by adding up the atomic masses of all the atoms in a molecular formula.
Think of it as the 'atomic weight' for a bunch of molecules rather than just one. In our example, the molar mass of NaCl (sodium chloride) is about 58.44 grams per mole. We use the molar mass to convert between grams and moles of a substance.

• The molar mass of an element is found on the periodic table and is usually listed in grams per mole (g/mol).
• Compounds' molar masses are calculated by adding the molar masses of the constituent elements based on the chemical formula.
• Knowing the molar mass allows us to translate mass (from a scale) into moles, which relates to the number of particles.

Avogadro's Number

Avogadro's number is supremely important because it's at the heart of the mole concept. It is the number of particles in exactly one mole of a substance. This value helps chemists convert between the macroscopic and microscopic worlds by relating physical quantities to amounts of atoms or molecules.
Named after the scientist Amedeo Avogadro, this number is approximately 6.022 x 10²³. When we perform calculations like finding the number of formula units in a given mass, as in our exercise, Avogadro's number is crucial.

Key Points About Avogadro's Number

• It is a fixed number: 6.022 x 10²³ particles per mole.
• Used to convert moles to particles (like atoms, ions, or formula units) and vice versa.

Percent Composition

Percent composition describes the percentage by mass of each element in a compound. In our original exercise, the sea-water salt contains 8.775% NaCl. This tells us that in every 100 grams of this salt, 8.775 grams are NaCl. It's a way of expressing the concentration of an element in a compound.
The percent composition is also useful when calculating the mass of each individual element within a sample of a compound. Here's how it works in our exercise:

Understanding Percent Composition

• It is calculated by dividing the mass of each element in a compound by the total mass of the compound and multiplying by 100.
• You can use this percentage to figure out the mass of a particular element in any given amount of the compound.
• This quantitative information is essential when doing any kind of stoichiometric calculations in chemistry.