Problem 71 - Chemistry The Molecular Science

Question

Calculate the mass of (a) 6.03 mol gold (b) 0.045 mol uranium (c) \(15.6 \mathrm{~mol} \mathrm{Ne}\) (d) \(3.63 \times 10^{-4} \mathrm{~mol}\) plutonium

Step-by-Step Solution

Answer

(a) 1187.91 g, (b) 10.71 g, (c) 314.808 g, (d) 0.088692 g.

Step 1: Understanding Moles to Mass Calculation

To calculate the mass of a substance from moles, you use the formula: \[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \] where the molar mass is the mass of one mole of the substance and is usually given in grams per mole (g/mol). Look up the molar mass of each element from the periodic table. For this exercise, consider: - Gold (Au): 197.0 g/mol- Uranium (U): 238.0 g/mol- Neon (Ne): 20.18 g/mol- Plutonium (Pu): 244.0 g/mol.

Step 2: Calculate the Mass of Gold (Au)

Using the formula from Step 1: \[ \text{Mass of Au} = 6.03 \text{ mol} \times 197.0 \text{ g/mol} \] Perform the multiplication:\[ \text{Mass of Au} = 1187.91 \text{ g} \] Therefore, the mass of 6.03 mol of gold is 1187.91 grams.

Step 3: Calculate the Mass of Uranium (U)

Using the formula from Step 1: \[ \text{Mass of U} = 0.045 \text{ mol} \times 238.0 \text{ g/mol} \] Perform the multiplication:\[ \text{Mass of U} = 10.71 \text{ g} \] Thus, the mass of 0.045 mol of uranium is 10.71 grams.

Step 4: Calculate the Mass of Neon (Ne)

Using the formula from Step 1: \[ \text{Mass of Ne} = 15.6 \text{ mol} \times 20.18 \text{ g/mol} \] Perform the multiplication:\[ \text{Mass of Ne} = 314.808 \text{ g} \] Therefore, the mass of 15.6 mol of neon is 314.808 grams.

Step 5: Calculate the Mass of Plutonium (Pu)

Using the formula from Step 1: \[ \text{Mass of Pu} = 3.63 \times 10^{-4} \text{ mol} \times 244.0 \text{ g/mol} \] Perform the multiplication:\[ \text{Mass of Pu} = 0.088692 \text{ g} \] So, the mass of \(3.63 \times 10^{-4}\) mol of plutonium is 0.088692 grams.

Key Concepts

Chemistry Calculations

Chemistry is full of exciting calculations that help us understand how the world works at a molecular level. In this context, moving from moles to mass is crucial. The formula to convert moles to mass is \( \text{Mass} = \text{Moles} \times \text{Molar Mass} \). This equation tells us that to find the mass of a substance, we need to know the number of moles and the molar mass. Moles measure the amount of a substance, similar to "dozen" but for atoms or molecules. Molar mass, on the other hand, is the mass of one mole of a substance, measured in grams per mole (g/mol). Understanding how to use this formula is a basic yet vital skill in chemistry, enabling scientists to quantify and experiment with substances accurately.
By using this formula, we can easily calculate the mass of any element if we know its amount in moles and its molar mass.

Molar Mass

The molar mass of a substance is an essential piece of information you can generally retrieve from the periodic table. It's the mass of one mole of a given substance, expressed in grams per mole (g/mol). To find the molar mass of an element, you simply look at its atomic mass number on the periodic table. This number is usually located under the element symbol. For example:

• Gold (Au) has a molar mass of 197.0 g/mol.
• Uranium (U) is 238.0 g/mol.
• Neon (Ne) is 20.18 g/mol.
• Plutonium (Pu) is 244.0 g/mol.

By knowing the molar mass, you can figure out how much one mole of that substance weighs. Therefore, calculating the mass of several moles simply becomes a question of multiplying the moles by the molar mass. This is crucial for precisely measuring and mixing elements in chemical reactions.

Periodic Table Elements

The periodic table is a fundamental tool for anyone dealing with chemistry. It organizes all known elements according to increasing atomic number, and groups them based upon similar chemical properties. Each element's block provides useful details, including the atomic number, element symbol, and atomic mass. For converting moles to mass, the atomic mass is crucial because it effectively represents the element's molar mass.
When tackling chemistry problems, the table allows quick access to an element's molar mass, ensuring efficient and accurate calculations. For instance, if you need the molar mass of gold for a problem, you simply find gold in the table, note its atomic mass (197.0), and use it in your calculations. Being familiar with where to find and how to use these numbers is vital for any chemistry student.