Problem 108 - Chemistry Matter and Change

Question

Calculate the mass of each element. \begin{equation}\begin{array}{ll}{\text { a. } 5.22 \text { mol of } \mathrm{He}} & {\text { c. } 2.22 \mathrm{mol} \text { of Ti }} \\ {\text { b. } 0.0455 \text { mol of } \mathrm{Ni}} & {\text { d. } 0.00566 \mathrm{mol} \text { of Ge }}\end{array}\end{equation}

Step-by-Step Solution

Answer

He: 20.88 g, Ni: 2.67 g, Ti: 106.27 g, Ge: 0.411 g.

Step 1: Identify Element Mass

Collect the atomic masses of the elements from the periodic table: Helium (He) is 4.00 g/mol, Nickel (Ni) is 58.69 g/mol, Titanium (Ti) is 47.87 g/mol, and Germanium (Ge) is 72.63 g/mol.

Step 1: Calculate Mass of Helium

Use the formula: mass = moles × molar mass. For Helium: Mass = 5.22 mol × 4.00 g/mol = 20.88 g.

Step 2: Calculate Mass of Nickel

Use the formula: mass = moles × molar mass. For Nickel: Mass = 0.0455 mol × 58.69 g/mol = 2.67 g.

Step 3: Calculate Mass of Titanium

Use the formula: mass = moles × molar mass. For Titanium: Mass = 2.22 mol × 47.87 g/mol = 106.27 g.

Step 4: Calculate Mass of Germanium

Use the formula: mass = moles × molar mass. For Germanium: Mass = 0.00566 mol × 72.63 g/mol = 0.411 g.

Key Concepts

Understanding Atomic Mass

Atomic mass is a crucial concept in chemistry, representing the mass of a single atom of an element, usually expressed in atomic mass units (amu).
This measurement reflects the total number of protons and neutrons in the atomic nucleus since electrons have almost no mass compared to these particles.

• It's an average, factoring in the different isotopes of the element found in nature.
• For example, Helium (He) has an atomic mass of about 4.00, indicating that it typically has two protons and two neutrons.

In chemical calculations, the atomic mass provided by the periodic table helps determine the molar mass, which is used to convert between moles and grams.

The Concept of Moles

The mole is a central unit in chemistry that measures the amount of a substance. It's similar to a dozen, but instead of 12, a mole represents Avogadro's number, approximately 6.022 x 10²³ entities.

• Moles allow chemists to count atoms, molecules, or formula units in a given sample without counting each individual particle.
• One mole of any element or compound contains Avogadro's number of atoms or molecules.

This unit simplifies mass calculations, converting between the atomic scale (like the atomic mass unit) and the macroscopic scale, where we deal with measurable masses of substances.

How to Use the Periodic Table

The periodic table is a comprehensive chart listing all known elements organized by their atomic properties, such as atomic mass and number.
It is an essential tool for chemists and provides quick access to the atomic masses necessary for mass determination.

• Elements are arranged in order of increasing atomic number, from left to right, and tell you the number of protons in an atom's nucleus.
• Columns, known as groups, contain elements with similar chemical behaviors, while rows, known as periods, indicate energy levels of an element's electrons.

Utilizing the periodic table allows for easy identification of molar masses, which are indispensable for performing molecular and stoichiometric calculations.

Understanding Mass Calculation Using Molar Mass

Mass calculation in chemistry often involves using the concept of molar mass, which connects the atomic or molecular scale to the practical scale of grams.
To calculate the mass of a substance:

• First, identify the molar mass from the periodic table. For example, Nickel (Ni) has a molar mass of 58.69 g/mol.
• Multiply the number of moles of the substance by its molar mass.

This formula, mass = moles × molar mass, allows you to determine how much a certain number of moles of a substance weighs.
Understanding this concept is key to accurately preparing solutions and reactions in a laboratory or industrial setting.