Question

Give the name and calculate the molar mass for each of the following substances. a. \(\mathrm{KHCO}_{3}\) b. \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\) c. \(\mathrm{H}_{2} \mathrm{O}_{2}\) d. \(\mathrm{BeCl}_{2}\) e. \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) f. \(\mathrm{KClO}_{3}\)

Short answer

The molar masses of the given substances are as follows: a. \(KHCO_3\): Potassium hydrogen carbonate (100.12 g/mol) b. \(Hg_2Cl_2\): Mercury(I) chloride (472.08 g/mol) c. \(H_2O_2\): Hydrogen peroxide (34.02 g/mol) d. \(BeCl_2\): Beryllium chloride (79.91 g/mol) e. \(Al_2(SO_4)_3\): Aluminum sulfate (342.14 g/mol) f. \(KClO_3\): Potassium chlorate (122.55 g/mol)

Step-by-step solution

a. Finding the molar mass of \(\mathrm{KHCO}_{3}\)

: First, determine the elements in \(\mathrm{KHCO}_{3}\) and their respective numbers: - 1 potassium atoms (K) - 1 hydrogen atoms (H) - 1 carbon atoms (C) - 3 oxygen atoms (O) Next, find their atomic masses from the periodic table: - K: 39.10 g/mol - H: 1.01 g/mol - C: 12.01 g/mol - O: 16.00 g/mol Now multiply the atomic mass of each element by its count in the formula and sum the results: Molar mass = (1 × 39.10) + (1 × 1.01) + (1 × 12.01) + (3 × 16.00) = 39.10 + 1.01 + 12.01 + 48.00 = 100.12 g/mol

b. Finding the molar mass of \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\)

: - 2 mercury atoms (Hg) - 2 chlorine atoms (Cl) Atomic masses: - Hg: 200.59 g/mol - Cl: 35.45 g/mol Molar mass = (2 × 200.59) + (2 × 35.45) = 401.18 + 70.90 = 472.08 g/mol

c. Finding the molar mass of \(\mathrm{H}_{2}\mathrm{O}_{2}\)

: - 2 hydrogen atoms (H) - 2 oxygen atoms (O) Atomic masses: - H: 1.01 g/mol - O: 16.00 g/mol Molar mass = (2 × 1.01) + (2 × 16.00) = 2.02 + 32.00 = 34.02 g/mol

d. Finding the molar mass of \(\mathrm{BeCl}_{2}\)

: - 1 beryllium atom (Be) - 2 chlorine atoms (Cl) Atomic masses: - Be: 9.01 g/mol - Cl: 35.45 g/mol Molar mass = (1 × 9.01) + (2 × 35.45) = 9.01 + 70.90 = 79.91 g/mol

e. Finding the molar mass of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)

: - 2 aluminum atoms (Al) - 3 sulfate ions (SO4), each with: - 1 sulfur atom (S) - 4 oxygen atoms (O) Atomic masses: - Al: 26.98 g/mol - S: 32.06 g/mol - O: 16.00 g/mol Molar mass = (2 × 26.98) + (3 × ((1 × 32.06) + (4 × 16.00))) = 53.96 + 3 × (32.06 + 64.00) = 53.96 + 3 × 96.06 = 53.96 + 288.18 = 342.14 g/mol

f. Finding the molar mass of \(\mathrm{KClO}_{3}\)

: - 1 potassium atom (K) - 1 chlorine atom (Cl) - 3 oxygen atoms (O) Atomic masses: - K: 39.10 g/mol - Cl: 35.45 g/mol - O: 16.00 g/mol Molar mass = (1 × 39.10) + (1 × 35.45) + (3 × 16.00) = 39.10 + 35.45 + 48.00 = 122.55 g/mol

Key concepts

Atomic Masses

The concept of atomic masses is fundamental to understanding how to calculate molar mass. Atomic mass, often referred to as atomic weight, is the average mass of atoms of an element, measured in atomic mass units (amu). This value accounts for the mixture of isotopes that occur in nature and is not simply the mass of a single atom. For instance, hydrogen has an atomic mass of approximately 1.01 amu.

A crucial step in computing the molar mass of a compound is identifying the atomic masses of its individual elements. These can be without difficulty found on the periodic table or in a list of elements. For example, in the step by step solution provided, we see elements like potassium (K) with an atomic mass of 39.10 g/mol and carbon (C) with 12.01 g/mol. Remember that these values are the building blocks for the full molar mass equation of any chemical compound.

Chemical Formula

The chemical formula of a substance provides the proportions of each element within a compound and is integral to calculating its molar mass. The formula is composed of the elemental symbols and numbers that indicate the number of atoms of each element in a molecule. For instance, \(\mathrm{H}_{2}\mathrm{O}_{2}\) represents a molecule of hydrogen peroxide, with two hydrogen atoms and two oxygen atoms.

Understanding the formula is critical because it determines the quantity of each element's atomic mass that must be counted in the molar mass calculation. For exersice a, \(\mathrm{KHCO}_{3}\) includes one potassium atom, one hydrogen atom, one carbon atom, and three oxygen atoms. Their atomic masses are then used with their respective atom count to calculate the compound's total molar mass. When encountering formulas with polyatomic ions, such as sulfate \(\mathrm{SO}_{4}\), it's important to consider the mass of the entire group as one unit like shown in step 5 of the solution.

Periodic Table Elements

The periodic table is a comprehensive chart containing all the chemical elements organized by increasing atomic number. It is indispensable for finding atomic masses required for molar mass calculations. Each element's box typically includes its atomic number, symbol, name, and atomic mass. For chemistry students and professionals alike, the periodic table is an essential tool for understanding the properties of elements and their relationships to one another.

As seen in the provided solution, the periodic table is the reference point to obtain the atomic masses of elements like beryllium (Be) or aluminum (Al). Once you have these values, you can proceed with the molar mass computation, as you will know how much each atom adds to the total weight of a compound. When calculating the molar mass of substances, such as \(\mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}\), familiarity with the periodic table helps in promptly identifying each component element and its corresponding atomic mass.