Problem 61 - Chemistry and Chemical Reactivity

Question

Calculate the mass, in grams, of each the following: (a) 2.5 mol of aluminum (b) \(1.25 \times 10^{-3}\) mol of iron (c) 0.015 mol of calcium (d) 653 mol of neon

Step-by-Step Solution

Answer

Aluminum: 67.5 g; iron: 0.070 g; calcium: 0.601 g; neon: 1.32 × 10⁴ g.

Step 1: Identify the Molar Mass of Each Element

Look up the periodic table to find the molar masses of aluminum (Al), iron (Fe), calcium (Ca), and neon (Ne). These values are needed to convert moles to grams. - Molar mass of aluminum: 26.98 g/mol - Molar mass of iron: 55.85 g/mol - Molar mass of calcium: 40.08 g/mol - Molar mass of neon: 20.18 g/mol.

Step 2: Use the Formula to Find Mass

The mass of a substance in grams can be calculated using the formula: \[\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}\] Apply this formula for each part of the problem.

Step 3: Calculate the Mass for Each Element

Using the formula from Step 2, calculate the mass of each element:(a) For aluminum: \[2.5 \text{ mol} \times 26.98 \text{ g/mol} = 67.45 \text{ g}\](b) For iron: \[(1.25 \times 10^{-3}) \text{ mol} \times 55.85 \text{ g/mol} = 0.0698 \text{ g}\](c) For calcium: \[0.015 \text{ mol} \times 40.08 \text{ g/mol} = 0.6012 \text{ g}\](d) For neon: \[653 \text{ mol} \times 20.18 \text{ g/mol} = 13182.34 \text{ g}\]

Step 4: Round or Format the Answers Appropriately

Round the calculated masses to a reasonable number of significant figures based on the given data: (a) Aluminum: 67.5 g (b) Iron: 0.070 g (c) Calcium: 0.601 g (d) Neon: 1.32 × 10⁴ g

Key Concepts

Molar Mass

In the world of chemistry, molar mass is a key concept that helps bridge the gap between the microscopic and macroscopic. Molar mass is defined as the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and acts as a conversion factor from moles to grams. Every element has its own molar mass, and it can be found on the periodic table. For instance, the molar mass of aluminum is 26.98 g/mol, meaning one mole of aluminum weighs 26.98 grams. When calculating mass using molar mass, remember that precision is crucial, as this basic calculation provides the groundwork for more complex chemical equations.

Conversion of Moles to Grams

Once the molar mass is known, it's fairly straightforward to convert moles to grams. The simple formula for this conversion is:\[ \text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \]This formula allows us to calculate the mass of a substance when the moles and molar mass are known. Let's say you are asked to convert 2.5 moles of aluminum to grams. Using the molar mass of aluminum (26.98 g/mol), the calculation would be:

• 2.5 mol \( \times \) 26.98 g/mol \( = \) 67.45 g

The calculation yields 67.45 grams of aluminum. Converting moles to grams is a fundamental skill when quantifying amounts in chemistry, providing a concrete understanding of molar quantities in a tangible form.

Significant Figures

When dealing with calculations in chemistry, significant figures play a crucial role. Significant figures are the digits in a number that carry meaningful information about its precision. They help ensure that calculations are as accurate as the data allows. In our mass conversion example, the molar masses and given moles determine how many significant figures the final answer should have.Consider the conversion of 1.25 \( \times \) 10\(^{-3}\) moles of iron to grams, where the result is 0.0698 grams. Given that 1.25 has 3 significant figures, the result is rounded to 0.070 grams to reflect the correct precision. Rounded values maintain the integrity and clarity of scientific data, underscoring the importance of significant figures.

Periodic Table Usage

The periodic table is an essential tool in chemistry, serving as a comprehensive reference for elemental information. Each element's square on the table provides insightful data, including the atomic number and the molar mass. Molar mass is particularly useful because it allows chemists to convert between mass and moles—a central aspect of stoichiometry. To find the molar mass of an element such as neon, you simply locate it on the periodic table and note its molar mass, which is 20.18 g/mol. This value is essential for any calculations involving neon, such as determining the mass in grams of 653 moles of neon. By consistently referencing the periodic table, you can quickly gather the necessary data for any elemental mass calculations. Always remember, the periodic table is your guide to unlocking atomic-level mysteries in chemistry.