Question

Calculate the molar mass of each of the following compounds. (a) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\) (c) \(\mathrm{Cl}_{2} \mathrm{O}_{5}\) (b) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NaHSO}_{4}\)

Short answer

The molar masses of the compounds are: \( \mathrm{Hg}_{2} \mathrm{Cl}_{2} \) = 472.08 g/mol, \( \mathrm{Cl}_{2} \mathrm{O}_{5} \) = 160.9 g/mol, \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \) = 172.17 g/mol and \( \mathrm{NaHSO}_{4} \) = 120.06 g/mol.

Step-by-step solution

Calculate Molar Mass of Hg2Cl2

Identify that \( \mathrm{Hg}_{2} \mathrm{Cl}_{2} \) consists of Mercury(Hg) and Chlorine(Cl). There are 2 atoms of Mercury and 2 atoms of Chlorine. From the periodic table, we find that the atomic weight of Hg is 200.59 g/mol and that of Cl is 35.45 g/mol. So, molar mass of \( \mathrm{Hg}_{2} \mathrm{Cl}_{2} \) = 2*(200.59 g/mol) + 2*(35.45 g/mol) = 472.08 g/mol.

Calculate Molar Mass of Cl2O5

Identify that \( \mathrm{Cl}_{2} \mathrm{O}_{5} \) consists of Chlorine(Cl) and Oxygen(O). There are 2 atoms of Chlorine and 5 atoms of Oxygen. The atomic weight of Cl is 35.45 g/mol and that of O is 16.00 g/mol. So, molar mass of \( \mathrm{Cl}_{2} \mathrm{O}_{5} \) = 2*(35.45 g/mol) + 5*(16.00 g/mol) =160.9 g/mol.

Calculate Molar Mass of CaSO4.2H2O

Identify that \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \) is a hydrated compound consisting of Arsenic(Ca), Sulfur(S), Oxygen(O) and Water(H2O). There are 1 atom of Ca, 1 atom of S, 4+2*2=8 atoms of O and 2*2=4 atoms of Hydrogen(H). The atomic weight of Ca is 40.08 g/mol, S is 32.06 g/mol, O is 16.00 g/mol and H is 1.01 g/mol. So, molar mass of \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \) = 1*(40.08 g/mol) + 1*(32.06 g/mol) + 8*(16.00 g/mol) + 4*(1.01 g/mol) = 172.17 g/mol.

Calculate Molar Mass of NaHSO4

Identify that \( \mathrm{NaHSO}_{4} \) consists of Sodium(Na), Hydrogen(H), Sulfur(S) and Oxygen(O). There are 1 atom of Na, 1 atom of H, 1 atom of S, 4 atoms of O. The atomic weight of Na is 22.99 g/mol, H is 1.01 g/mol, S is 32.06 g/mol and O is 16.00 g/mol. So, molar mass of \( \mathrm{NaHSO}_{4} \) = 1*(22.99 g/mol) + 1*(1.01 g/mol) + 1*(32.06 g/mol) + 4*(16.00 g/mol) = 120.06 g/mol.

Key concepts

Atomic Weight

Atomic weight, also known as atomic mass, is the average mass of an atom of an element, measured in atomic mass units (amu). This value considers the relative abundance of different isotopes of an element found in nature, making it a significant factor when calculating the properties of chemical compounds.
For example, in the problem above, the atomic weight of elements like Mercury (Hg), Chlorine (Cl), and Oxygen (O) are crucial for determining the molar mass of compounds such as \( \mathrm{Hg}_{2} \mathrm{Cl}_{2} \) and \( \mathrm{Cl}_{2} \mathrm{O}_{5} \).
It is essential to use the correct atomic weights obtained from a reliable source such as the periodic table of elements. Only by doing so can precise calculations and predictions about a compound's characteristics be accurately completed.

Periodic Table

The periodic table is an organized chart of elements, arranged by increasing atomic number and grouped by similar chemical properties. Each element's atomic weight is also listed in the table, making it an indispensable tool in chemistry for finding important details quickly.
The table aids in understanding how each element will react in chemical compounds. It provides a straightforward pathway to find the atomic weights needed for calculating the molar mass of compounds. For example, to find the molar mass of \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \), you would reference the atomic weights of Calcium (Ca), Sulfur (S), Oxygen (O), and Hydrogen (H) in the periodic table.

• Always confirm the atomic weights from a current periodic table
  to ensure the most accurate molar mass calculations.

Chemical Compounds

Chemical compounds are substances formed by the bonding of different elements in specific ratios. The compound's formula reflects its composition, indicating the kinds and numbers of atoms present. For instance, \( \mathrm{NaHSO}_{4} \) reflects the components of one Sodium (Na) atom, one Hydrogen (H) atom, one Sulfur (S) atom, and four Oxygen (O) atoms.
Understanding the formula is vital for calculating molar mass because it enables you to multiply the atomic weight of each element by the number of times it appears within the compound. This is apparent in the step-by-step solutions to determine the molar masses of complex compounds.
Knowing the basics of chemical compounds helps in predicting their behavior, ways they combine, and how they may decompose or react with other substances.

Molar Mass Concept

The molar mass concept is a key idea in chemistry used to determine the mass of a given amount, typically one mole, of a compound. Expressed in grams per mole (g/mol), molar mass provides a bridge between the atomic world and the macroscopic quantities we encounter in real life.
To find a compound's molar mass, you sum up the total atomic weights of all atoms in its molecular formula. In the solutions shown, this is done systematically for each compound, like \( \mathrm{Hg}_{2} \mathrm{Cl}_{2} \) or \( \mathrm{Cl}_{2} \mathrm{O}_{5} \).
Molar mass allows chemists to convert between the amount of substance (in moles) and mass (in grams), a process that is crucial when carrying out chemical reactions and determining reactant and product amounts. This concept simplifies many results, making stoichiometric calculations more manageable.