Problem 29 - Chemistry and Chemical Reactivity

Question

Calculate the amount (moles) represented by each of the following: (a) \(127.08 \mathrm{g}\) of \(\mathrm{Cu}\) (b) 0.012 g of lithium (c) 5.0 mg of americium (d) \(6.75 \mathrm{g}\) of \(\mathrm{Al}\)

Step-by-Step Solution

Answer

(a) 2.0 moles, (b) 0.0017 moles, (c) 2.06×10⁻⁵ moles, (d) 0.250 moles.

Step 1: Understand the Problem

The problem requires converting mass (in grams or milligrams) of different elements to the amount in moles. We will use the formula: \( ext{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). First, we'll need to know the molar mass of each element: Copper (Cu) \(= 63.55 \text{ g/mol}\), Lithium (Li) \(= 6.94 \text{ g/mol}\), Americium (Am) \(= 243.0 \text{ g/mol}\), and Aluminum (Al) \(= 26.98 \text{ g/mol}\).

Step 2: Calculate Moles of Copper

For copper, the mass is given as 127.08 g. Use the formula for moles:\[\text{moles of Cu} = \frac{127.08 \text{ g}}{63.55 \text{ g/mol}} \approx 2.0 \text{ moles}\]

Step 3: Calculate Moles of Lithium

For lithium, the mass is 0.012 g. Use the formula for moles:\[\text{moles of Li} = \frac{0.012 \text{ g}}{6.94 \text{ g/mol}} \approx 0.0017 \text{ moles}\]

Step 4: Calculate Moles of Americium

For americium, the mass is 5.0 mg. First, convert mg to g: \(5.0 \text{ mg} = 0.005 \text{ g}\). Now use the formula for moles:\[\text{moles of Am} = \frac{0.005 \text{ g}}{243.0 \text{ g/mol}} \approx 2.06 \times 10^{-5} \text{ moles}\]

Step 5: Calculate Moles of Aluminum

For aluminum, the mass is 6.75 g. Use the formula for moles:\[\text{moles of Al} = \frac{6.75 \text{ g}}{26.98 \text{ g/mol}} \approx 0.250 \text{ moles}\]

Key Concepts

Mole Calculations

Understanding how to perform mole calculations is a key concept in chemistry. A mole is a unit of measurement used to express amounts of a chemical substance. The central formula for calculating moles is:

• \[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]

To apply this formula, you simply need the mass of the substance and its molar mass (which can be found on the periodic table). By dividing the mass by the molar mass, you can find how many moles of a substance you have. This formula effectively allows conversion from mass to moles, which is helpful for stoichiometric calculations in chemical reactions. Calculating moles in different scenarios, whether in grams, milligrams, or other units, is fundamental in performing accurate laboratory work. Always ensure the units are consistent, typically converting milligrams to grams if needed to avoid errors.

Molar Mass

Molar mass is an essential property of chemical substances, crucial for stoichiometry. It tells us how much one mole of a substance weighs in grams. Molar mass is expressed in units of grams per mole (g/mol). For instance:

• Copper (Cu) has a molar mass of 63.55 g/mol.
• Lithium (Li) has a molar mass of 6.94 g/mol.
• Americium (Am) has a molar mass of 243.0 g/mol.
• Aluminum (Al) has a molar mass of 26.98 g/mol.

To find the molar mass of an element or compound, refer to the periodic table for elements or sum up the atomic masses for compounds. Molar mass acts as a bridge, allowing conversion between the mass of a sample and the number of moles, which is critical in performing accurate and meaningful calculations in chemistry. Properly knowing how to handle molar mass is vital for tasks ranging from simple lab exercises to industrial chemical manufacturing.

Chemical Elements

Chemical elements are the basic building blocks of matter. Each element is defined by the number of protons in its nucleus, known as the atomic number. Recognizing elements and their symbols is foundational in understanding chemistry and how substances interact. For the exercise we are discussing, the elements involved are:

• Copper (Cu)
• Lithium (Li)
• Americium (Am)
• Aluminum (Al)

Each element has distinct chemical and physical properties and they form the basis for calculations involving compounds and reactions. Elements combine in specific ratios to form compounds, governed by their valencies and the principles of stoichiometry. Understanding these elements' individual characteristics is essential in predicting reaction outcomes and behaviors in various environments. This knowledge is foundational for anyone studying or working within the chemical sciences.

Mass to Moles Conversion

The conversion of mass to moles is a common practice in chemistry, enabling scientists to relate macroscopic measurements with microscopic chemical equations. This conversion relies on the foundational equation:

• \[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]

Let's break down the process using an example. Suppose you have a known mass of copper, say 127.08 g. To find the amount of copper in moles, you'd use copper's molar mass (63.55 g/mol) in the equation above. This is how you get the answer:

• \[\text{moles of Cu} = \frac{127.08}{63.55} \approx 2.0 \text{ moles}\]

For effective conversion, always ensure consistency in your units, converting them to grams if necessary before plugging them into the formula. This process is crucial for preparing solutions, reagents, and determining reactants/products in chemical reactions. Mastering mass to moles conversion allows for precise and efficient laboratory work and is a core skill for chemistry students and professionals alike.