Question

Calculate the mass in grams of each of the following samples. a. 0.251 mole of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) b. 1.26 moles of carbon dioxide c. \(9.31 \times 10^{-4}\) moles of gold(III) chloride d. 7.74 moles of sodium nitrate e. 0.000357 mole of iron

Short answer

a. 11.56 g of ethyl alcohol, \(C_2H_6O\) b. 55.45 g of carbon dioxide c. 0.282 g of gold(III) chloride d. 658.9 g of sodium nitrate e. 0.0199 g of iron

Step-by-step solution

a. Ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\)

Step 1: Calculate molar mass Molar mass of ethyl alcohol = 2 * molar mass of carbon + 6 * molar mass of hydrogen + molar mass of oxygen = 2(12.01 g/mol) + 6(1.01 g/mol) + 16.00 g/mol = 46.07 g/mol Step 2: Calculate mass Mass (in grams) = moles * molar mass = 0.251 mole * 46.07 g/mol = 11.56 g of ethyl alcohol

b. Carbon dioxide

Step 1: Calculate molar mass Molar mass of carbon dioxide = molar mass of carbon + 2 * molar mass of oxygen = 12.01 g/mol + 2(16.00 g/mol) = 44.01 g/mol Step 2: Calculate mass Mass (in grams) = moles * molar mass = 1.26 moles * 44.01 g/mol = 55.45 g of carbon dioxide

c. Gold(III) chloride

Step 1: Calculate molar mass Molar mass of gold(III) chloride = molar mass of gold + 3 * molar mass of chlorine = 197.0 g/mol + 3(35.45 g/mol) = 303.35 g/mol Step 2: Calculate mass Mass (in grams) = moles * molar mass = \(9.31 \times 10^{-4}\) moles * 303.35 g/mol = 0.282 g of gold(III) chloride

d. Sodium nitrate

Step 1: Calculate molar mass Molar mass of sodium nitrate = molar mass of sodium + molar mass of nitrogen + 3 * molar mass of oxygen = 22.99 g/mol + 14.01 g/mol + 3(16.00 g/mol) = 85.00 g/mol Step 2: Calculate mass Mass (in grams) = moles * molar mass = 7.74 moles * 85.00 g/mol = 658.9 g of sodium nitrate

e. Iron

Step 1: Molar mass Molar mass of iron (Fe) = 55.85 g/mol Step 2: Calculate mass Mass (in grams) = moles * molar mass = 0.000357 mole * 55.85 g/mol = 0.0199 g of Iron

Key concepts

Molar Mass

Understanding molar mass is fundamental to mastering stoichiometry calculations in chemistry. Molar mass is defined as the mass of one mole of a substance (the mass per mole of its molecules or atoms). This property is particularly important because it bridges the gap between the microscopic scale of atoms and molecules and the macroscopic world we can measure in the laboratory.

The unit for molar mass is grams per mole (g/mol). To calculate the molar mass of a chemical compound, sum up the atomic masses of all the atoms in the molecule. For example, to calculate the molar mass of water ( H_2O), you add the molar masses of two hydrogen atoms with one oxygen atom.

H_2O contains:

• 2 hydrogen atoms ( 2(1.01 g/mol))
• 1 oxygen atom (16.00 g/mol)

This sums up to approximately 18.02 g/mol. Calculating the molar mass is a crucial step in stoichiometry, as it allows for conversions between the number of moles and the mass of a substance.

Mole-to-Gram Conversion

After understanding the concept of molar mass, the next step in stoichiometry calculations is the mole-to-gram conversion. This process involves converting the number of moles of a substance to its mass in grams using the formula:

Mass (in grams) = Moles times Molar Mass

For instance, if you have 0.251 moles of ethyl alcohol ( C_2H_6O) and know the molar mass is 46.07 g/mol, you can find the mass of ethyl alcohol by multiplying the number of moles by the molar mass:

0.251 mole times 46.07 g/mol = 11.56 g

This conversion is essential for practical chemistry applications, allowing chemists to measure out amounts of substances accurately for reactions and experiments.

Chemical Compounds

Chemical compounds are substances composed of two or more different elements that are chemically bonded together. Each compound has a unique chemical formula that reflects its composition. For example, carbon dioxide's formula is CO_2, indicating it contains one carbon atom and two oxygen atoms. In stoichiometry, understanding chemical compounds is crucial because it helps identify the elements involved and their proportions when performing calculations.

Each chemical compound has its distinct properties, including a specific molar mass, which must be taken into account during stoichiometry calculations. The steps taken in the exercise to calculate the mass of different compounds, such as carbon dioxide ( CO_2) and sodium nitrate ( NaNO_3), showcase how knowledge of the chemical formula is applied to derive the molar mass and subsequently find the mass of a given number of moles.