Question

Determine the molar masses of these compounds: (a) \(\mathrm{NaOH}\) (f) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) (b) \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\) (g) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (c) \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) (h) \(\mathrm{K}_{4} \mathrm{Fe}(\mathrm{CN})_{6}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) (i) \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}\)

Short answer

NaOH = 40.00 g/mol, Ag2CO3 = 275.75 g/mol, Cr2O3 = 152.00 g/mol, (NH4)2CO3 = 96.11 g/mol, Mg(HCO3)2 = 146.34 g/mol, C6H5COOH = 122.13 g/mol, C6H12O6 = 180.18 g/mol, K4Fe(CN)6 = 368.41 g/mol, BaCl2·2H2O = 244.26 g/mol.

Step-by-step solution

Find the Atomic Masses

Look up the atomic masses of each element in the periodic table. For instance, the atomic masses of some key elements are: Na = 22.99, O = 16.00, H = 1.01, Ag = 107.87, C = 12.01, Cr = 52.00, N = 14.01, K = 39.10, Fe = 55.85, Ba = 137.34, Cl = 35.45, Mg = 24.31.

Calculate the Molar Mass of \(\text{NaOH}\)

Add the atomic masses of one sodium (Na), one oxygen (O), and one hydrogen (H) atom: NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol.

Calculate the Molar Mass of \(\text{Ag}_{2}\text{CO}_{3}\)

Add the atomic masses of two silver (Ag) atoms, one carbon (C) atom, and three oxygen (O) atoms: Ag2CO3 = 2(107.87) + 12.01 + 3(16.00) = 275.75 g/mol.

Calculate the Molar Mass of \(\text{Cr}_{2}\text{O}_{3}\)

Add the atomic masses of two chromium (Cr) atoms and three oxygen (O) atoms: Cr2O3 = 2(52.00) + 3(16.00) = 152.00 g/mol.

Calculate the Molar Mass of \(\left(\text{NH}_{4}\right)_{2}\text{CO}_{3}\)

Add the atomic masses of two ammonium (NH4) groups and one carbon (C) atom with three oxygen (O) atoms: (NH4)2CO3 = 2(14.01 + 4(1.01)) + 12.01 + 3(16.00) = 96.11 g/mol.

Calculate the Molar Mass of \(\text{Mg(HCO}_{3}\text{)}_{2}\)

Add the atomic masses of one magnesium (Mg) atom, two hydrogen (H) atoms, two carbon (C) atoms, and six oxygen (O) atoms: Mg(HCO3)2 = 24.31 + 2(1.01 + 12.01 + 3(16.00)) = 146.34 g/mol.

Calculate the Molar Mass of \(\text{C}_{6}\text{H}_{5}\text{COOH}\)

Add the atomic masses of seven carbon (C) atoms, six hydrogen (H) atoms, and two oxygen (O) atoms: C6H5COOH = 7(12.01) + 6(1.01) + 2(16.00) = 122.13 g/mol.

Calculate the Molar Mass of \(\text{C}_{6}\text{H}_{12}\text{O}_{6}\)

Add the atomic masses of six carbon (C) atoms, twelve hydrogen (H) atoms, and six oxygen (O) atoms: C6H12O6 = 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol.

Calculate the Molar Mass of \(\text{K}_{4}\text{Fe(CN)}_{6}\)

Add the atomic masses of four potassium (K) atoms, one iron (Fe) atom, six carbon (C) atoms, and six nitrogen (N) atoms: K4Fe(CN)6 = 4(39.10) + 55.85 + 6(12.01 + 14.01) = 368.41 g/mol.

Calculate the Molar Mass of \(\text{BaCl}_{2}\cdot 2\text{H}_{2}\text{O}\)

Add the atomic masses of one barium (Ba) atom, two chlorine (Cl) atoms, and four hydrogen (H) atoms with two oxygen (O) atoms from water molecules: BaCl2·2H2O = 137.34 + 2(35.45) + 2(2(1.01) + 16.00) = 244.26 g/mol.

Key concepts

atomic masses

When calculating molar masses, knowing the atomic masses of elements is crucial. Atomic masses are the weights of individual atoms measured in atomic mass units (amu). You can find these values in the periodic table.

For example, sodium (Na) has an atomic mass of 22.99 amu, while oxygen (O) is 16.00 amu. These values are essential to determine the total molar mass of any compound.

• Use atomic masses to find the weight of each element in a compound.
• Look these values up in the periodic table for accuracy.
• Sum the atomic masses for each constituent element to find the molar mass.

periodic table elements

The periodic table is your best friend when it comes to chemistry. It organizes all known elements in a way that allows you to predict many properties, including atomic masses.

Elements are listed in increasing order of their atomic number, which also helps in identifying their atomic masses. Each element’s block contains critical information: the atomic number, symbol, name, and atomic mass.

The periodic table helps you quickly reference the atomic masses needed for molar mass calculations.

compound formulas

Chemical compounds are made up of different elements in specific ratios. The formula of a compound tells you the types and numbers of atoms involved.

For instance, NaOH (sodium hydroxide) consists of one sodium (Na) atom, one oxygen (O) atom, and one hydrogen (H) atom. Understanding the formula is the first step to calculating molar mass.

• Identify each element in the compound.
• Note the number of atoms for each element as given in the formula.
• Use the atomic masses of these elements for your calculations.

step-by-step solution

Approaching molar mass calculations systematically ensures accuracy. Here's a detailed step-by-step method:

• **Step 1:** Identify the atomic mass of each element in the periodic table.
• **Step 2:** Write down the compound's formula to see the number of each type of atom.
• **Step 3:** Multiply the atomic mass by the number of atoms for each element.
• **Step 4:** Sum these values to get the total molar mass.

This structured approach makes complex calculations simpler and reduces errors.

chemistry education

Understanding how to calculate molar masses is a fundamental skill in chemistry education. It helps students grasp the concept of moles, which is critical for stoichiometry, chemical reactions, and understanding materials' properties.

Chem educators emphasize this topic early on because it's a building block for more advanced concepts. Mastering molar mass calculations leads to better comprehension of chemical quantities and reactions, enabling students to solve real-world chemistry problems effectively.