Problem 49 - Chemistry Matter and Change

Question

Explain how you can determine the number of atoms or ions in a given mass of a compound.

Step-by-Step Solution

Answer

To determine the number of atoms or ions in a given mass of a compound, follow these steps: (1) Identify the compound and its molecular formula. (2) Calculate the molar mass of the compound. (3) Use the given mass and the molar mass to determine the number of moles. (4) Finally, use Avogadro's number (approximately \(6.022 \times 10^{23}\) particles/mol) to find the number of atoms or ions in the sample. For example, in a 29.22 gram sample of NaCl, there are approximately \(3.011 \times 10^{23}\) Na+ ions and \(3.011 \times 10^{23}\) Cl- ions.

Step 1: Identify the compound and its molecular formula

Determine the molecular formula of the compound. The molecular formula provides information about the types and number of atoms present in a single molecule of the compound. To illustrate the process, let's consider an example with a sample of NaCl (sodium chloride).

Step 2: Calculate the molar mass of the compound

Next, determine the molar mass of the compound. The molar mass is the mass of one mole of a substance, which is equal to the sum of the atomic masses of its constituent atoms multiplied by their frequency in the molecular formula. For NaCl, the molar mass is: Molar mass = (Mass of Na) + (Mass of Cl) Molar mass = (22.99 g/mol) + (35.45 g/mol) = 58.44 g/mol

Step 3: Calculate the number of moles

Now, use the given mass of the compound and its molar mass to calculate the number of moles present. The formula to find the number of moles is: Number of moles = (Given mass) / (Molar mass) Assuming we have a 29.22 gram sample of NaCl, the number of moles would be: Number of moles = (29.22 g) / (58.44 g/mol) = 0.5 mol

Step 4: Use Avogadro's number to find the number of atoms or ions

Finally, use Avogadro's number (6.022 × 10^23 particles/mol) to determine the number of atoms or ions in the sample. Since NaCl is an ionic compound, it consists of equal numbers of Na+ and Cl- ions. Hence, we will multiply the number of moles by Avogadro's number for both ions to find the total number of particles. Number of Na+ ions = Number of moles × Avogadro's number Number of Na+ ions = 0.5 mol × (6.022 × 10^23 ions/mol) = 3.011 × 10^23 Na+ ions Number of Cl- ions = Number of moles × Avogadro's number Number of Cl- ions = 0.5 mol × (6.022 × 10^23 ions/mol) = 3.011 × 10^23 Cl- ions So, in the 29.22 gram sample of NaCl, there are approximately 3.011 × 10^23 Na+ ions and 3.011 × 10^23 Cl- ions.

Key Concepts

Molar Mass

Molar mass is a key concept in stoichiometry, helping us understand the amount of matter in a compound. It is the mass of one mole of a substance and is expressed in grams per mole (g/mol). To determine the molar mass of a compound, one must sum the atomic masses of all the atoms present in its molecular formula. Each element in the periodic table has an atomic mass, typically found below the chemical symbol.For example, in sodium chloride (NaCl), we have one sodium atom and one chlorine atom. Sodium (Na) has an atomic mass of approximately 22.99 g/mol and chlorine (Cl) about 35.45 g/mol. Therefore, the molar mass of NaCl is:\[ \text{Molar mass of NaCl} = 22.99 \, \text{g/mol} + 35.45 \, \text{g/mol} = 58.44 \, \text{g/mol} \]Molar mass is essential for converting between grams and moles, allowing us to measure amounts of substances precisely for chemical reactions.

Avogadro's Number

Avogadro's number is a cornerstone in the world of chemistry, bridging the macroscopic and microscopic worlds. It is defined as the number of atoms, ions, or molecules in one mole of a substance.Avogadro's number is approximately \( 6.022 \times 10^{23} \) particles per mole. This huge number helps chemists work with the measurable amounts of substances when dealing with countless tiny atoms or molecules. Using Avogadro's number, we convert moles into the actual number of particles. For example, if you have 1 mole of NaCl, it contains:- \( 6.022 \times 10^{23} \) sodium ions (Na\(^+\))- \( 6.022 \times 10^{23} \) chloride ions (Cl\(^-\))This concept is crucial for understanding chemical reactions, as it allows us to calculate how many particles are involved in reactions or are present in a given sample.

Molecular Formula

The molecular formula of a compound provides the exact number and type of atoms in a single molecule of that compound. It serves as a chemical 'recipe', detailing the components required to form the substance. Take NaCl, for instance. Its molecular formula tells us there is one sodium (Na) atom and one chlorine (Cl) atom in each molecule of sodium chloride. Molecular formulas are important when determining the molar mass of compounds, as they reveal the exact count of each type of atom present. Moreover, they are crucial for detecting stoichiometric ratios in reactions, identifying what combinations of elements result in specific substances. Understanding molecular formulas allows chemists to plan and balance chemical reactions efficiently, ensuring precise quantities of reactants and products.

Ionic Compounds

Ionic compounds are a vital category of chemical compounds, characterized by their formation from positively charged ions (cations) and negatively charged ions (anions). This union arises through the electrostatic force of attraction between these oppositely charged particles.Sodium chloride (NaCl) is an example of an ionic compound. It is formed when sodium (Na), a metal, donates an electron to chlorine (Cl), a non-metal, generating ions Na\(^+\) and Cl\(^-\), respectively.Key characteristics of ionic compounds include:

• High melting and boiling points, due to the strong attraction between ions
• Good electrical conductivity when dissolved in water, as the ions are free to move
• Generally solid at room temperature

Understanding ionic compounds is crucial for comprehending not only the basic principles of chemistry but also the real-world applications, like electrolysis or the functionality of salts in different processes.