Problem 149 - Chemistry Matter and Change

Question

Calculate the number of sodium ions present in 25.0 \(\mathrm{g}\) of sodium chloride.

Step-by-Step Solution

Answer

There are approximately 2.57 x 10^{23} sodium ions in 25.0 g of sodium chloride.

Step 1: Understand the Molecular Composition

Sodium chloride (NaCl) is composed of sodium ions (Na\(^+\)) and chloride ions (Cl\(^-\)). For every formula unit of NaCl, there is one sodium ion.

Step 2: Calculate the Molar Mass of NaCl

To find the molar mass of NaCl, add the atomic masses of sodium (Na, approximately 23.0 g/mol) and chlorine (Cl, approximately 35.5 g/mol):\[\text{Molar mass of NaCl} = 23.0 \, \text{g/mol} + 35.5 \, \text{g/mol} = 58.5 \, \text{g/mol}\]

Step 3: Determine Moles of NaCl

Use the given mass of NaCl (25.0 g) and its molar mass to calculate the number of moles:\[\text{Moles of NaCl} = \frac{25.0 \, \text{g}}{58.5 \, \text{g/mol}}\]Calculate this value to find the moles of NaCl.

Step 4: Calculate the Number of Sodium Ions

Using Avogadro's number \(6.022 \times 10^{23}\) ions/mol, calculate the number of sodium ions in the moles of NaCl:\[\text{Number of Na ions} = \text{Moles of NaCl} \times 6.022 \times 10^{23} \, \text{ions/mol}\]This gives the total number of sodium ions.

Key Concepts

Molar Mass Calculation

When dealing with chemical compounds, understanding molar mass is crucial. Molar mass is simply the mass of one mole of a substance, and it is usually expressed in grams per mole (g/mol). To calculate the molar mass, you need to add up the atomic masses of each element in a compound. These atomic masses are found on the periodic table.

For example, in sodium chloride (NaCl), you find the molar mass by adding the atomic mass of sodium (Na) which is approximately 23.0 g/mol, to the atomic mass of chlorine (Cl) which is about 35.5 g/mol. Therefore, the molar mass of NaCl is 58.5 g/mol. Knowing the molar mass allows you to convert between grams of a compound and moles, which is essential in stoichiometric calculations.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry. It provides a link between the macroscopic and microscopic worlds by defining the number of particles in one mole of a substance. Avogadro's number is approximately 6.022 x 10^23 particles/mol. It can apply to atoms, molecules, ions, or any other entities.

This number is extremely large because atoms and molecules are incredibly small. Avogadro's number is used to convert between the amount of substance measured in moles and the number of constituent particles. For instance, when you calculate the number of sodium ions in a sample of sodium chloride, you multiply the moles of sodium chloride by Avogadro's number to determine the total number of individual sodium ions present.

Moles of Substances

The concept of a mole is a cornerstone in chemistry. A mole is a unit that measures the quantity of a substance, akin to how a dozen represents twelve items. It allows chemists to count atoms, ions, and molecules in a given sample by weighing it, since direct counting is impossible due to their small size.

To find the moles of a substance, you divide the mass of the sample by its molar mass. This conversion is extremely useful in stoichiometry, where you can predict how different substances react and in what proportions. For instance, if you have 25.0 g of sodium chloride, you can calculate the moles of NaCl by using its molar mass (58.5 g/mol). This calculation facilitates further conversion to determine how many sodium or chloride ions are present in your sample.