Question

Calculate the formula mass for each compound. (a) \(\mathrm{CS}_{2}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (c) \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) (d) \(\mathrm{C}_{7} \mathrm{H}_{16}\)

Short answer

The formula masses are: (a) \text{CS}_2 - 76.13 u, (b) \text{C}_6\text{H}_{12}\text{O}_6 - 180.156 u, (c) \text{Fe}(\text{NO}_3)_3 - 241.88 u, (d) \text{C}_7\text{H}_{16} - 100.198 u.

Step-by-step solution

Calculate the Formula Mass of CS2

To find the formula mass of carbon disulfide (CS2), add the atomic mass of one carbon (C) atom and the atomic mass of two sulfur (S) atoms. The atomic mass of carbon is approximately 12.01 u (atomic mass units) and that of sulfur is approximately 32.06 u. The formula mass of CS2 is calculated as: 1(12.01 u) + 2(32.06 u) = 12.01 u + 64.12 u = 76.13 u.

Calculate the Formula Mass of C6H12O6

To find the formula mass of glucose (C6H12O6), add the atomic mass of six carbon (C) atoms, twelve hydrogen (H) atoms, and six oxygen (O) atoms. The atomic mass of hydrogen is approximately 1.008 u, and that of oxygen is approximately 16.00 u. The formula mass of C6H12O6 is calculated as: 6(12.01 u) + 12(1.008 u) + 6(16.00 u) = 72.06 u + 12.096 u + 96.00 u = 180.156 u.

Calculate the Formula Mass of Fe(NO3)3

Iron (III) nitrate consists of one iron (Fe) atom and three nitrate (NO3) groups. The atomic mass of iron is approximately 55.85 u. Each nitrate group consists of one nitrogen (N) atom with an atomic mass of 14.01 u and three oxygen atoms. The formula mass of Fe(NO3)3 is calculated as: 1(55.85 u) + 3[1(14.01 u) + 3(16.00 u)] = 55.85 u + 3(14.01 u + 48.00 u) = 55.85 u + 3(62.01 u) = 55.85 u + 186.03 u = 241.88 u.

Calculate the Formula Mass of C7H16

To find the formula mass of heptane (C7H16), add the atomic mass of seven carbon (C) atoms and sixteen hydrogen (H) atoms. The formula mass of C7H16 is calculated as: 7(12.01 u) + 16(1.008 u) = 84.07 u + 16.128 u = 100.198 u.

Key concepts

Molecular Weight

Molecular weight, also known as molecular mass, is a critical concept in chemistry that helps us understand the mass of a single molecule of a substance. It is calculated by adding up the atomic masses of all the atoms present in the molecule. The units used for expressing molecular weight are atomic mass units (u), also known as daltons (Da).

In practical terms, knowing the molecular weight of a compound is necessary for a variety of applications, such as calculating the amounts of substances needed in a chemical reaction or understanding the properties of the compound. For instance, when working with chemical reactions, knowing the molecular weight allows chemists to determine the number of moles of each substance involved, thereby enabling precise quantification of reactants and products.

To calculate the molecular weight, one should examine the chemical formula of the compound and apply the known atomic masses of each element, typically found on the periodic table. For example, to calculate the molecular weight of water (H2O), we would add together the atomic masses of two hydrogen atoms and one oxygen atom, using the periodic table as a reference for these values.

Chemical Compound Formulas

Chemical compound formulas provide a concise way to describe the composition of a substance. They indicate the types and numbers of atoms that compose a single molecule of the compound. A proper understanding of chemical formulas is essential for performing formula mass calculations and for predicting the properties and behaviors of the compounds.

For example, the formula for water, H₂O, tells us that each molecule consists of two hydrogen atoms and one oxygen atom. Similarly, the chemical formula C₆H₁₂O₆ represents glucose, indicating it is made of six carbons, twelve hydrogens, and six oxygens. To determine the molecular weight from such a formula, each atom's atomic mass must be multiplied by the number of times it appears in the molecule and then summed.

Understanding the patterns and notations of chemical formulas, such as subscript numbers indicating the quantity of atoms and parentheses denoting groups of atoms, is key to computing the formula mass accurately. Chemical formulas are the language by which chemists communicate the composition of substances and predict their reactivity and interactions with other compounds.

Atomic Mass Units

Atomic mass units (u) are the standard units used to express the weight of atoms and molecules. One atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. The atomic mass unit provides a convenient way for scientists to express and compare the masses of different atoms and elements, which are otherwise incredibly small and difficult to work with.

The atomic masses of elements, as listed on the periodic table, are average values that take into account the relative abundances of different isotopes. For example, the atomic mass of carbon is approximately 12.01 u because it averages the isotopic masses of carbon-12 and carbon-13, the latter having a slightly higher mass due to an additional neutron.

When calculating formula masses or molecular weights, it is important to use the atomic mass unit as a consistent measurement standard, thus allowing for accurate stoichiometric conversions in chemical equations. The formula mass calculation exercise exemplifies how these atomic masses are utilized to determine the mass of a given chemical compound formula.