Question

Calculate the molar mass for each of the following compounds: a. ${\mathrm{KC}}_4{\mathrm{H}}_5{\mathrm{O}}_6$ (cream of tartar) b. ${\mathrm{Fe}}_2{\mathrm{O}}_3$ (rust) c. ${\mathrm{C}}_{19}{\mathrm{H}}_{20}{\mathrm{FNO}}_3$ (Paxil, an antidepressant) d. ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ (antiperspirant) e. $\mathrm{Mg}(\mathrm{OH}{)}_2$ (antacid) f. ${\mathrm{C}}_{16}{\mathrm{H}}_{19}{\mathrm{N}}_3{\mathrm{O}}_5\mathrm{S}$ (amoxicillin, an antibiotic)

Short answer

a. 188.19 g/molb. 159.70 g/molc. 329.40 g/mold. 342.17 g/mole. 58.33 g/molf. 365.45 g/mol

Step-by-step solution

Determine Atomic Masses

Identify the atomic masses (in amu) of each element present in the compounds using the periodic table. For example: K = 39.10, C = 12.01, H = 1.01, O = 16.00, Fe = 55.85, S = 32.07, Al = 26.98, Mg = 24.31, F = 19.00, N = 14.01.

Calculate for Compound \mathrm{KC}_{4} \mathrm{H}_{5} \mathrm{O}_{6} (Cream of Tartar)

Sum the atomic masses multiplied by their respective counts: 39.10 (K) + 4*12.01 (C) + 5*1.01 (H) + 6*16.00 (O). $=39.10+48.04+5.05+96.00=188.19\mathrm{g}/\mathrm{mol}$

Calculate for Compound Fe_2O_3 (Rust)

Sum the atomic masses multiplied by their respective counts: 2*55.85 (Fe) + 3*16.00 (O). $=111.70+48.00=159.70\mathrm{g}/\mathrm{mol}$

Calculate for Compound \mathrm{C}_{19} \mathrm{H}_{20} \mathrm{FNO}_{3} (Paxil)

Sum the atomic masses multiplied by their respective counts: 19*12.01 (C) + 20*1.01 (H) + 1*19.00 (F) + 1*14.01 (N) + 3*16.00 (O). $=228.19+20.20+19.00+14.01+48.00=329.40\mathrm{g}/\mathrm{mol}$

Calculate for Compound Al_2(SO_4)_3 (Antiperspirant)

Sum the atomic masses multiplied by their respective counts: 2*26.98 (Al) + 3*(32.07 (S) + 4*16.00 (O)). $=53.96+3\ast (32.07+64.00)=53.96+3\ast 96.07=53.96+288.21=342.17\mathrm{g}/\mathrm{mol}$

Calculate for Compound \mathrm{Mg}(\mathrm{OH})_2 (Antacid)

Sum the atomic masses multiplied by their respective counts: 24.31 (Mg) + 2*(1.01 (H) + 16.00 (O)). $=24.31+2\ast (1.01+16.00)=24.31+2\ast 17.01=24.31+34.02=58.33\mathrm{g}/\mathrm{mol}$

Calculate for Compound \mathrm{C}_{16} \mathrm{H}_{19} \mathrm{N}_3 \mathrm{O}_5 \mathrm{S} (Amoxicillin)

Sum the atomic masses multiplied by their respective counts: 16*12.01 (C) + 19*1.01 (H) + 3*14.01 (N) + 5*16.00 (O) + 1*32.07 (S). $=192.16+19.19+42.03+80.00+32.07=365.45\mathrm{g}/\mathrm{mol}$

Key concepts

atomic mass

Understanding atomic mass is crucial for calculating the molar mass of a compound. Atomic mass is the mass of an atom, typically expressed in atomic mass units (amu). Each element on the periodic table has an atomic mass that represents the average mass of its atoms, accounting for different isotopes. For example, the atomic mass of carbon (C) is 12.01 amu, while the atomic mass of oxygen (O) is 16.00 amu. These values are used to compute the total mass of a molecule by summing up the masses of all the atoms in the molecule’s chemical formula.

molar mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is measured in grams per mole (g/mol). To calculate the molar mass of a compound, you sum the atomic masses of all atoms in the compound's formula. For instance, if you have a compound such as ${\text{KC}}_4{\text{H}}_5{\text{O}}_6$ (cream of tartar), you multiply the atomic masses by the number of each atom present. Here, the molar mass would be calculated as: 39.10 (K) + 4*12.01 (C) + 5*1.01 (H) + 6*16.00 (O) = 188.19 g/mol. This ensures you understand the quantity of each type of atom and how their weights contribute to the overall mass of the molecule.

compound formula

A compound formula represents the elements that make up the molecule and the number of atoms of each element. For example, the formula for rust is ${\text{Fe}}_2{\text{O}}_3$. This indicates the molecule contains two iron (Fe) atoms and three oxygen (O) atoms. Recognizing the compound formula is the first step in calculating its molar mass. Each element's atoms are accounted for by using their atomic masses from the periodic table and multiplying them by the number of atoms present in the formula.

periodic table

The periodic table is an essential tool in chemistry for finding the atomic mass of elements used in molar mass calculations. Each element on the table is displayed with its atomic number and atomic mass. The atomic mass helps in determining the total mass contribution of that element in a chemical compound. For instance, the atomic mass of aluminum (Al) is 26.98 amu. When calculating the molar mass of ${\text{Al}}_2({\text{SO}}_4{)}_3$ (antiperspirant), you would use the atomic masses: 2*26.98 for Al, 3*32.07 for sulfur (S), and 12*16.00 for oxygen (O), leading to a total molar mass of 342.17 g/mol. The periodic table provides a quick reference for all needed atomic masses.