Question

Calculate the molar mass of each of the following compounds: a. \(\mathrm{O}_{2}\) b. \(\mathrm{KH}_{2} \mathrm{PO}_{4}\) c. \(\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}\) d. \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{4}\) e. \(\mathrm{Ga}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) f. \(\mathrm{KBrO}_{4}\)

Short answer

1. \(\mathrm{O}_{2}\) = 32 g/mol2. \(\mathrm{KH}_{2}\mathrm{PO}_{4}\) = 136 g/mol3. \(\mathrm{Fe(ClO}_{4})_{3}\) = 354.5 g/mol4. \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{4}\) = 120 g/mol5. \(\mathrm{Ga}_{2}(\mathrm{CO}_{3})_{3}\) = 320 g/mol6. \(\mathrm{KBrO}_{4}\) = 183 g/mol

Step-by-step solution

Identify Atomic Masses

Find the atomic masses of all elements involved. The atomic masses (in g/mol) are: - \(O = 16\)- \(K = 39\)- \(H = 1\)- \(P = 31\)- \(Fe = 56\)- \(Cl = 35.5\)- \(C = 12\)- \(Ga = 70\)- \(Br = 80\)

Calculate Molar Mass of \(\mathrm{O}_{2}\)\

The formula for molecular oxygen is \(\mathrm{O}_{2}\). Since each oxygen atom has a mass of 16 g/mol, the molar mass is: \[\mathrm{O}_{2}: 2 \times 16 = 32\ \mathrm{g/mol}.\]

Calculate Molar Mass of \(\mathrm{KH}_{2}\mathrm{PO}_{4}\)

The formula for potassium dihydrogen phosphate is \(\mathrm{KH}_{2}\mathrm{PO}_{4}\). Calculate the molar mass by summing the masses of all the atoms: \[\mathrm{KH}_{2}\mathrm{PO}_{4}: 39 + (2 \times 1) + 31 + (4 \times 16) = 136\ \mathrm{g/mol}.\]

Calculate Molar Mass of \(\mathrm{Fe(ClO}_{4})_{3}\)

The formula for iron(III) perchlorate is \(\mathrm{Fe(ClO}_{4})_{3}\). Sum the atomic masses of all the atoms: \[\mathrm{Fe(ClO}_{4})_{3}: 56 + 3 \times (35.5 + 4 \times 16) = 56 + 3 \times 99.5 = 354.5\ \mathrm{g/mol}.\]

Calculate Molar Mass of \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{4}\)

The formula for erythritol is \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{4}\). Calculate the molar mass as follows: \[\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{4}: (4 \times 12) + (8 \times 1) + (4 \times 16) = 48 + 8 + 64 = 120\ \mathrm{g/mol}.\]

Calculate Molar Mass of \(\mathrm{Ga}_{2}(\mathrm{CO}_{3})_{3}\)

The formula for gallium carbonate is \(\mathrm{Ga}_{2}(\mathrm{CO}_{3})_{3}\). Calculate the molar mass: \[\mathrm{Ga}_{2}(\mathrm{CO}_{3})_{3}: (2 \times 70) + 3 \times (12 + 3 \times 16) = 140 + 3 \times 60 = 320\ \mathrm{g/mol}.\]

Calculate Molar Mass of \(\mathrm{KBrO}_{4}\)

The formula for potassium perbromate is \(\mathrm{KBrO}_{4}\). Calculate the molar mass: \[\mathrm{KBrO}_{4}: 39 + 80 + (4 \times 16) = 39 + 80 + 64 = 183\ \mathrm{g/mol}.\]

Key concepts

atomic mass

Atomic mass refers to the mass of an individual atom, usually expressed in atomic mass units (amu). One amu is defined as one-twelfth the mass of a carbon-12 atom. This value is almost equal to the mass of one nucleon (proton or neutron). Atomic mass helps us understand the weight of the atoms in a molecule or compound, aiding in the calculation of the molar mass.

For instance, the atomic mass of an oxygen (O) atom is 16 g/mol. This means that one mole of oxygen atoms weighs approximately 16 grams. Knowing atomic masses is crucial for solving many types of chemistry problems, especially those that involve stoichiometry and formulation of chemical compounds.

molecular formula

The molecular formula represents the exact number of each type of atom in a molecule. It gives us a detailed picture of the composition of a given compound.

For example, the molecular formula of oxygen gas is \(\text{O}_{2}\), indicating two oxygen atoms are bonded together. Similarly, potassium dihydrogen phosphate has the molecular formula \(\text{KH}_{2}\text{PO}_{4}\), showing it contains one potassium (K) atom, two hydrogen (H) atoms, one phosphorus (P) atom, and four oxygen (O) atoms. Understanding the molecular formula is essential for calculating molar mass, as it tells exactly how many atoms of each element are present in a compound.

stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It involves using balanced chemical equations to calculate the amounts of different substances involved.

To apply stoichiometry in calculating molar mass, one must know the molecular formula and the atomic masses of the individual elements. For instance, to find the molar mass of \(\text{C}_{4}\text{H}_{8}\text{O}_{4}\), the stoichiometric calculation involves adding up the atomic masses of all carbon, hydrogen, and oxygen atoms present. Hence, stoichiometry forms the backbone of quantitative chemical analysis and measurements.

chemical compounds

Chemical compounds are substances composed of two or more different types of atoms bonded together. They are defined by a unique molecular formula which represents their exact atomic composition.

Take \(\text{Fe(ClO}_{4})_{3} \) as an example. This compound, known as iron(III) perchlorate, is made up of one iron (Fe) atom and three perchlorate (ClO4) groups. Understanding the nature of chemical compounds helps in determining their properties and reactions.

In summary, chemical compounds form the basis of understanding chemical processes and reactions, facilitated by core concepts like atomic mass, molecular formula, and stoichiometry.