Question

Calculate the molar mass of the following substances: (a) \(\mathrm{Li}_{2} \mathrm{CO}_{3},(\mathrm{~b}) \mathrm{CS}_{2},\) (c) \(\mathrm{CHCl}_{3}\) (chloroform), (d) \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) (ascorbic acid, or vitamin \(\mathrm{C}\) ), (e) \(\mathrm{KNO}_{3}\), (f) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}\).

Short answer

(a) 73.89 g/mol, (b) 76.15 g/mol, (c) 119.37 g/mol, (d) 176.14 g/mol, (e) 101.11 g/mol, (f) 100.95 g/mol.

Step-by-step solution

Calculate Molar Mass of Li2CO3

To calculate the molar mass of \( \mathrm{Li}_2\mathrm{CO}_3 \), first find the atomic mass for each element: Li (6.94 g/mol), C (12.01 g/mol), and O (16.00 g/mol). Using the chemical formula, calculate its molar mass:\[2(6.94) + 1(12.01) + 3(16.00) = 13.88 + 12.01 + 48.00 = 73.89 \text{ g/mol}\]

Calculate Molar Mass of CS2

For \( \mathrm{CS}_2 \), determine the atomic masses: C (12.01 g/mol) and S (32.07 g/mol). Then calculate:\[1(12.01) + 2(32.07) = 12.01 + 64.14 = 76.15 \text{ g/mol}\]

Calculate Molar Mass of CHCl3 (Chloroform)

For \( \mathrm{CHCl}_3 \), calculate using these atomic masses: C (12.01 g/mol), H (1.01 g/mol), and Cl (35.45 g/mol):\[1(12.01) + 1(1.01) + 3(35.45) = 12.01 + 1.01 + 106.35 = 119.37 \text{ g/mol}\]

Calculate Molar Mass of C6H8O6 (Ascorbic Acid)

Using atomic masses: C (12.01 g/mol), H (1.01 g/mol), and O (16.00 g/mol), calculate:\[6(12.01) + 8(1.01) + 6(16.00) = 72.06 + 8.08 + 96.00 = 176.14 \text{ g/mol}\]

Calculate Molar Mass of KNO3

For \( \mathrm{KNO}_3 \), find the atomic masses: K (39.10 g/mol), N (14.01 g/mol), and O (16.00 g/mol):\[1(39.10) + 1(14.01) + 3(16.00) = 39.10 + 14.01 + 48.00 = 101.11 \text{ g/mol}\]

Calculate Molar Mass of Mg3N2

Determine using these atomic masses: Mg (24.31 g/mol) and N (14.01 g/mol):\[3(24.31) + 2(14.01) = 72.93 + 28.02 = 100.95 \text{ g/mol}\]

Key concepts

Chemical Formulas

A chemical formula represents a chemical compound using symbols for the elements and subscripts indicating the number of atoms of each element present. Understanding how to read and interpret chemical formulas is crucial when calculating molar masses. For example, in the formula \( \mathrm{Li}_2\mathrm{CO}_3 \), the subscript \( 2 \) after \( \mathrm{Li} \) means there are two lithium atoms, and \( \mathrm{CO}_3 \) indicates that the compound also contains one carbon and three oxygen atoms. Thus, a chemical formula provides a concise way of representing detailed information about the chemical composition of a substance.

Atomic Mass

Atomic mass is the mass of an atom expressed in atomic mass units (amu). It is approximately equivalent to the number of protons and neutrons in the atom, which is also known as the atomic weight. For calculations involving molar masses, atomic masses are usually given in grams per mole (g/mol). Each element on the periodic table has a specific atomic mass, which one can use to calculate the mass of molecules or compounds. For instance, lithium (Li) has an atomic mass of 6.94 g/mol, carbon (C) is 12.01 g/mol, and oxygen (O) is 16.00 g/mol. These values are essential when determining the molar mass of compounds like \( \mathrm{Li}_2\mathrm{CO}_3 \) or \( \mathrm{KNO}_3 \).

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is a fundamental concept in chemistry that helps understand how substances interact in their respective ratios. When calculating the molar mass of a compound, stoichiometry comes into play as you use the proportions of each element in the chemical formula. For example, in \( \mathrm{C}_6\mathrm{H}_8\mathrm{O}_6 \) (ascorbic acid), stoichiometry tells us there are six carbons, eight hydrogens, and six oxygens in each molecule. It teaches us how to balance equations and how quantities relate to each other in chemical processes. By calculating the total mass using stoichiometric ratios, you achieve the correct molar mass for the compound.

Compounds

Compounds are substances formed when two or more chemical elements are chemically bonded together. Each compound has distinct properties different from the elements it is composed of. For example, carbon dioxide \( \mathrm{CO}_2 \) is a compound resulting from a chemical reaction between carbon and oxygen. The properties of a compound reflect the nature of the chemical bonds and the arrangement of its atoms. Compounds like \( \mathrm{Mg}_3\mathrm{N}_2 \) can have complex structures, and understanding these structural details helps chemists predict how compounds will behave in different scenarios. It is also important because knowing the exact molecular composition is key to determining the compound's molar mass.

Chemical Elements

Chemical elements are pure substances consisting entirely of one type of atom. Each element has unique properties and is defined by its number of protons, represented by its atomic number on the periodic table. Elements are the building blocks of matter, both within compounds and individually. They determine the atomic mass of a substance, which further dictates how much of each is needed to form compounds of specific masses. Elements like lithium, carbon, and oxygen play a significant role in forming numerous compounds. Familiarizing oneself with the elements and their typical chemical behaviors is vital because they are foundational in understanding how compounds form and react.