Question

Calculate the molar mass (in grams/mol) of (a) osmium metal, the densest naturally occurring element. (b) baking soda, \(\mathrm{NaHCO}_{3}\). (c) vitamin \(\mathrm{D}, \mathrm{C}_{28} \mathrm{H}_{44} \mathrm{O},\) required for healthy bones and teeth.

Short answer

Answer: (a) The molar mass of Osmium is 190.23 g/mol. (b) The molar mass of Baking soda (NaHCO₃) is 84.01 g/mol. (c) The molar mass of Vitamin D (C₂₈H₄₄O) is 396.72 g/mol.

Step-by-step solution

Identify the elements present in each compound

For each compound, we will list the individual elements: (a) Osmium: \(\mathrm{Os}\) (b) Baking soda: \(\mathrm{Na, H, C, O}\) (c) Vitamin D: \(\mathrm{C, H, O}\)

Determine the atomic mass of each element

Using a Periodic Table, we can find the atomic mass of each element: (a) Osmium: \(190.23\,\mathrm{g/mol}\) (b) Baking soda: - \(\mathrm{Na}\): \(22.99\,\mathrm{g/mol}\) - \(\mathrm{H}\): \(1.01\,\mathrm{g/mol}\) - \(\mathrm{C}\): \(12.01\,\mathrm{g/mol}\) - \(\mathrm{O}\): \(16.00\,\mathrm{g/mol}\) (c) Vitamin D: - \(\mathrm{C}\): \(12.01\,\mathrm{g/mol}\) - \(\mathrm{H}\): \(1.01\,\mathrm{g/mol}\) - \(\mathrm{O}\): \(16.00\,\mathrm{g/mol}\)

Multiply the atomic mass of each element by the number of atoms

Now, we will multiply the atomic mass of each element by the number of atoms present in the chemical formula: (a) Osmium: \(190.23\,\mathrm{g/mol} \times 1 = 190.23\,\mathrm{g/mol}\) (b) Baking soda: - \(\mathrm{Na}\): \(22.99\,\mathrm{g/mol} \times 1 = 22.99\,\mathrm{g/mol}\) - \(\mathrm{H}\): \(1.01\,\mathrm{g/mol} \times 1 = 1.01\,\mathrm{g/mol}\) - \(\mathrm{C}\): \(12.01\,\mathrm{g/mol} \times 1 = 12.01\,\mathrm{g/mol}\) - \(\mathrm{O}\): \(16.00\,\mathrm{g/mol} \times 3 = 48.00\,\mathrm{g/mol}\) (c) Vitamin D: - \(\mathrm{C}\): \(12.01\,\mathrm{g/mol} \times 28 = 336.28\,\mathrm{g/mol}\) - \(\mathrm{H}\): \(1.01\,\mathrm{g/mol} \times 44 = 44.44\,\mathrm{g/mol}\) - \(\mathrm{O}\): \(16.00\,\mathrm{g/mol} \times 1 = 16.00\,\mathrm{g/mol}\)

Add the masses obtained in step 3 to calculate the molar mass

Finally, we will add the masses obtained in step 3 to calculate the molar mass of each compound: (a) Osmium: \(190.23\,\mathrm{g/mol}\) (b) Baking soda: \(22.99\,\mathrm{g/mol} + 1.01\,\mathrm{g/mol} + 12.01\,\mathrm{g/mol} + 48.00\,\mathrm{g/mol} = 84.01\,\mathrm{g/mol}\) (c) Vitamin D: \(336.28\,\mathrm{g/mol} + 44.44\,\mathrm{g/mol} + 16.00\,\mathrm{g/mol} = 396.72\,\mathrm{g/mol}\)

Key concepts

Atomic Mass

Understanding the concept of atomic mass is crucial when diving into the realm of chemistry. Each element on the periodic table has a unique mass that essentially represents the average weight of a single atom of that element, taking into account all of its naturally occurring isotopes. It's measured in atomic mass units (amu), but for practical applications in chemistry, particularly in calculating the mass of substances, we use the unit grams per mole (g/mol).

When you look at the periodic table, the atomic mass is usually located beneath the chemical symbol of each element. For example, the atomic mass of hydrogen (H) is approximately 1.01 g/mol, and for carbon (C), it's around 12.01 g/mol. These values are pivotal for calculating the molar mass of compounds, as they allow you to determine how much one mole of a substance weighs.

Chemical Formula

Chemical formulas provide a concise way of expressing information about the atoms that constitute a particular chemical compound. It identifies each element by its chemical symbol and indicates the number of atoms of each element found in one discrete molecule of the substance. This is important for a process called stoichiometry, which involves ratios and calculations based on these precise numbers.

For instance, the chemical formula of baking soda is \(\mathrm{NaHCO}_{3}\), which tells us that in one molecule of baking soda, there is one sodium (Na), one hydrogen (H), one carbon (C), and three oxygen (O) atoms. These numbers are not arbitrary but instead reflect a fixed ratio that defines the composition of the substance, allowing chemists to calculate the total weight or the molar mass of the substance.

Periodic Table

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties. This structure shows periodic trends, such as elements with similar behavior in the same column. It's an indispensable tool for chemists, providing a wealth of information at a glance.

For our discussion on molar mass, the periodic table is the go-to source for finding the atomic masses needed for calculations. By knowing where to look on the table (usually under the element's symbol), students and chemists alike can find the atomic mass and use it along with the chemical formula to calculate the molar mass of any given substance. This relationship between the chemical elements and their weights is foundational to many aspects of chemistry.

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the conservation of mass where the total mass of the reactants equals the total mass of the products. Central to this concept is the mole, which is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles.

One aspect of stoichiometry is the molar mass calculation, which combines the atomic mass of individual atoms (from the periodic table) and their proportions in the substance (as indicated by the chemical formula) to determine the mass of one mole of a substance. This plays a key role in predicting how much reactants are needed or how much of a product will be formed in a chemical reaction.