Question

Calculate the formula mass for each compound. (a) \(\mathrm{HNO}_{3}\) (b) \(\mathrm{CaBr}_{2}\) (c) \(\mathrm{CCl}_{4}\) (d) \(\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2}\)

Short answer

The formula masses are: (a) 63.01 amu for HNO3, (b) 199.88 amu for CaBr2, (c) 153.81 amu for CCl4, and (d) 211.64 amu for Sr(NO3)2.

Step-by-step solution

Find Atomic Masses for HNO3

Locate the atomic masses of hydrogen (H), nitrogen (N), and oxygen (O) on the periodic table. For H, the atomic mass is approximately 1.008 amu; for N, it's about 14.01 amu; and for O, it's roughly 16.00 amu.

Calculate the Formula Mass for HNO3

Multiply the atomic mass of each element by the number of atoms of that element in the molecule and add the values together: Formula mass of \(\mathrm{HNO}_{3}\) = (1 \times 1.008 amu) + (1 \times 14.01 amu) + (3 \times 16.00 amu).

Find Atomic Masses for CaBr2

Locate the atomic masses of calcium (Ca) and bromine (Br) on the periodic table. For Ca, the atomic mass is approximately 40.08 amu; and for Br, it's about 79.90 amu.

Calculate the Formula Mass for CaBr2

Multiply the atomic mass of each element by the number of atoms of that element in the molecule and add the values together: Formula mass of \(\mathrm{CaBr}_{2}\) = (1 \times 40.08 amu) + (2 \times 79.90 amu).

Find Atomic Masses for CCl4

Locate the atomic masses of carbon (C) and chlorine (Cl) on the periodic table. For C, the atomic mass is approximately 12.01 amu; and for Cl, it's about 35.45 amu.

Calculate the Formula Mass for CCl4

Multiply the atomic mass of each element by the number of atoms of that element in the molecule and add the values together: Formula mass of \(\mathrm{CCl}_{4}\) = (1 \times 12.01 amu) + (4 \times 35.45 amu).

Find Atomic Masses for Sr(NO3)2

Locate the atomic masses of strontium (Sr), nitrogen (N), and oxygen (O) on the periodic table. For Sr, the atomic mass is approximately 87.62 amu; for N, it's about 14.01 amu; and for O, it's roughly 16.00 amu.

Calculate the Formula Mass for Sr(NO3)2

Multiply the atomic mass of each element by the number of atoms of that element in the compound and add the values together: Formula mass of \(\mathrm{Sr(NO}_{3})_{2}\) = (1 \times 87.62 amu) + (2 \times 14.01 amu) + (6 \times 16.00 amu).

Key concepts

Atomic Mass Unit

The atomic mass unit (amu) is a small unit of mass used to express atomic and molecular weights. It's defined as one-twelfth of the mass of a carbon-12 atom, which is approximately 1.66 x 10^-24 grams. When looking at a periodic table, each element's atomic weight, typically listed below the element's symbol, is expressed in amu. For instance, hydrogen has an atomic mass of approximately 1.008 amu, meaning a single hydrogen atom weighs almost one amu. This standardized measurement is crucial because it allows chemists and students alike to compare the relative masses of different atoms and molecules on an equal footing. Understanding amu and how it relates to atomic mass is the foundation for calculating the formula mass of chemical compounds.

Molecular Weight Determination

Determining the molecular weight of a compound, also known as its formula mass, involves the use of atomic mass units. This calculation is straightforward once you grasp the concept of amu. The molecular weight is the sum of the atomic masses of all the atoms in a molecule. For example, the molecular weight of a water molecule (H₂O) is calculated by adding twice the atomic mass of hydrogen (2 x 1.008 amu) to the atomic mass of oxygen (16.00 amu), giving us approximately 18.02 amu. To accurately determine molecular weights, it's essential to know the exact composition of the molecule and have accurate atomic masses for each element involved. This process is vital in stoichiometry for balancing chemical reactions and calculating reactant or product quantities.

Chemical Compound Formulas

Chemical compound formulas provide a concise way to represent the composition of molecules and ionic compounds. They consist of chemical symbols from the periodic table and numerical subscripts indicating the number of atoms of each element present. Understanding how to read and interpret these formulas is necessary for calculating formula mass. As seen in exercises like the ones for CaBr₂ and Sr(NO₃)₂, the subscripts tell you how many of each atom are in the compound. In Sr(NO₃)₂, the formula suggests one strontium atom, two nitrogen atoms, and six oxygen atoms, based on the subscript outside the parentheses. Reading and interpreting compound formulas accurately ensure proper stoichiometric calculations and chemical analysis.

Stoichiometry

Stoichiometry is the area of chemistry that concerns the quantitative relationships between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles. The stoichiometric calculations rely heavily on the molecular weights determined from chemical compound formulas. For instance, if we are reacting hydrochloric acid (HCl) with sodium hydroxide (NaOH) to produce water (H₂O) and sodium chloride (NaCl), stoichiometry allows us to calculate how much reactant is needed to completely react and how much product will be formed. Balanced chemical equations and mole ratios, derived from the molecular weights, serve as the roadmap for these calculations. Grasping stoichiometry is essential for understanding and predicting the outcomes of chemical reactions, as well as for scaling up reactions from the laboratory to industrial production.