Problem 116 - Chemistry Matter and Change

Question

Determine the molar mass for the foloowing compounds. (Chapter 10\()\) \begin{equation}\begin{array}{l}{\text { a. } \operatorname{Co}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}} \\ {\text { b. } \mathrm{Fe}(\mathrm{OH})_{3}}\end{array}\end{equation}

Step-by-Step Solution

Answer

The molar mass of Co(NO3)2 · 6H2O is 291.046 g/mol, and Fe(OH)3 is 106.874 g/mol.

Step 1: Understanding the Molar Mass Calculation

The molar mass of a compound is the sum of the atomic masses of all atoms in its formula. Atomic masses can be found on the periodic table.

Step 2: Calculate Molar Mass for Co(NO3)2 · 6H2O

First, identify the atomic masses: Co = 58.93 g/mol, N = 14.01 g/mol, O = 16.00 g/mol, H = 1.008 g/mol. Then, calculate each part: - Co: 1 58.93 = 58.93 g/mol - N: 2 14.01 = 28.02 g/mol - O: 6 16.00 = 96.00 g/mol - 6H2O: (6 2 1.008) + (6 16.00) = 108.096 g/mol Add these together: 58.93 + 28.02 + 96.00 + 108.096 = 291.046 g/mol.

Step 3: Calculate Molar Mass for Fe(OH)3

Identify the atomic masses: Fe = 55.85 g/mol, O = 16.00 g/mol, H = 1.008 g/mol. Calculate each part: - Fe: 1 55.85 = 55.85 g/mol - O: 3 16.00 = 48.00 g/mol - H: 3 1.008 = 3.024 g/mol Add these together: 55.85 + 48.00 + 3.024 = 106.874 g/mol.

Key Concepts

Atomic Mass

Atomic mass is an essential concept in chemistry that influences how we calculate the molar mass of compounds. Atomic mass refers to the mass of an individual atom expressed in atomic mass units (amu), and it is typically found on the periodic table. It's important to note that atomic mass considers the weighted average of all naturally occurring isotopes of an element. This is why it includes decimal values.

When calculating the molar mass, you sum up the atomic masses of all atoms present in the compound. For example, if you look at cobalt in the compound Co(NO3)2 · 6H2O, the atomic mass of Co is 58.93 g/mol. Using the periodic table provides you these values, ensuring precise calculations.

Chemical Formulas

Chemical formulas represent the types and numbers of atoms in a chemical compound. Each element in a compound is represented by its chemical symbol, accompanied by subscripts indicating the number of atoms of each element. For instance, in the chemical formula Fe(OH)3, Fe represents iron, O represents oxygen, and H stands for hydrogen. The subscripts tell us there are three hydroxide (OH) groups in this compound.

• Chemical formulas help in calculating the molar mass of the compound as they provide the exact proportions of elements present.
• Reading a chemical formula correctly is crucial for determining how many atoms of each element are present in the compound.

This knowledge leads to precise calculations and a better understanding of the compound's composition.

Periodic Table

The periodic table is a comprehensive chart that categorizes all known elements based on increasing atomic number. It is an invaluable tool for chemists as it provides essential information about the elements, including their atomic masses, which are crucial in molar mass calculations. Each element's atomic mass can usually be found as a decimal below the element symbol.

• The periodic table displays elements in specific groups and periods, which reflect their atomic structure and properties.
• The elements are arranged such that those with similar chemical and physical properties reside in the same groups.

Using the periodic table, one can identify and utilize atomic masses for molar mass calculations, as shown in the exercises involving both Co(NO3)2 · 6H2O and Fe(OH)3.

Hydrated Compounds

Hydrated compounds include water molecules within their structure, which must be considered when calculating their molar mass. These compounds are typically written with a dot followed by a number of water molecules, e.g., Co(NO3)2 · 6H2O. The dot indicates that each formula unit of the compound is associated with six water molecules in this case.

• To find the molar mass of hydrated compounds, include the mass of the water molecules as well as the other components of the compound.
• The calculation involves breaking down both the anhydrous part and the water component separately, then summing their masses.

The presence of water molecules affects both the mass and sometimes the physical properties of the compound, making it important to consider this extra mass in calculations.