Question

Calculate the mass in grams of each of the following samples. a. 3.09 mol of ammonium carbonate b. \(4.01 \times 10^{-6}\) mol of sodium hydrogen carbonate c. 88.02 mol of carbon dioxide d. 1.29 mmol of silver nitrate e. 0.0024 mol of chromium(III) chloride

Short answer

Mass in grams for each sample: a. 297.28 g b. \(3.37 \times 10^{-4}\) g c. 3873.24 g d. 0.2188 g e. 0.380 g

Step-by-step solution

a. 3.09 mol of ammonium carbonate

First, find the molar mass of ammonium carbonate (NH₄)₂CO₃. Molar mass of (NH₄)₂CO₃ = 2(N_mass + H_mass*4) + C_mass + O_mass*3 \(= 2(14.01 + 4 \times 1.01) + 12.01 + 3 \times 16.00 \) \(= 2(14.01 + 4.04) + 12.01 + 48.00 \) \(= 2 \times 18.05 + 60.01 \) \(= 96.11 \,g/mol\) Now, multiply the molar mass by the given moles to find the mass in grams: Mass = moles × molar mass Mass = 3.09 mol × 96.11 g/mol Mass = 297.28 g

b. \(4.01 \times 10^{-6}\) mol of sodium hydrogen carbonate

First, find the molar mass of sodium hydrogen carbonate (NaHCO₃). Molar mass of NaHCO₃ = Na_mass + H_mass + C_mass + O_mass*3 \(= 22.99 + 1.01 + 12.01 + 3 \times 16.00 \) \(= 22.99 + 1.01 + 12.01 + 48.00 \) \(= 84.01 \,g/mol\) Now, multiply the molar mass by the given moles to find the mass in grams: Mass = moles × molar mass Mass = \(4.01 \times 10^{-6}\, mol \times 84.01 \,g/mol\) Mass = \(3.37 \times 10^{-4}\, g\)

c. 88.02 mol of carbon dioxide

First, find the molar mass of carbon dioxide (CO₂). Molar mass of CO₂ = C_mass + O_mass*2 \(= 12.01 + 2 \times 16.00 \) \(= 12.01 + 32.00 \) \(= 44.01 \,g/mol\) Now, multiply the molar mass by the given moles to find the mass in grams: Mass = moles × molar mass Mass = 88.02 mol × 44.01 g/mol Mass = 3873.24 g

d. 1.29 mmol of silver nitrate

First, convert mmol to mol: \(1.29\, mmol = 1.29 \times 10^{-3}\, mol\) Next, find the molar mass of silver nitrate (AgNO₃). Molar mass of AgNO₃ = Ag_mass + N_mass + O_mass*3 \(= 107.87 + 14.01 + 3 \times 16.00 \) \(= 107.87 + 14.01 + 48.00 \) \(= 169.88 \,g/mol\) Now, multiply the molar mass by the given moles to find the mass in grams: Mass = moles × molar mass Mass = \(1.29 \times 10^{-3}\, mol \times 169.88 \,g/mol\) Mass = 0.2188 g

e. 0.0024 mol of chromium(III) chloride

First, find the molar mass of chromium(III) chloride (CrCl₃). Molar mass of CrCl₃ = Cr_mass + Cl_mass*3 \(= 51.99 + 3 \times 35.45 \) \(= 51.99 + 106.35 \) \(= 158.34 \,g/mol\) Now, multiply the molar mass by the given moles to find the mass in grams: Mass = moles × molar mass Mass = 0.0024 mol × 158.34 g/mol Mass = 0.380 g

Key concepts

Stoichiometry

Stoichiometry is the cornerstone of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. In essence, it tells us how much of a substance is needed or produced in a reaction. To solve stoichiometry problems, we use the mole concept, which allows us to count particles of substance using their weight.

One mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of carbon-12, which is approximately 6.022 x 10^23 entities, known as Avogadro's number. By understanding stoichiometry, students can convert between moles, mass, and the number of particles, enabling them to calculate the amounts of substances involved in chemical reactions.

Mole-to-Grams Conversion

Mole-to-grams conversion is a critical part of stoichiometry that involves changing the moles of a substance into its corresponding mass in grams. It hinges on the molar mass of a substance, which is the mass of one mole of that substance. The molar mass can be determined by adding up the atomic masses of all the atoms in the formula taken from the periodic table.

To convert from moles to grams, you simply multiply the number of moles by the molar mass of the substance. Such conversion allows chemists to measure out the amount of substance needed for a reaction in the laboratory. It's important for students to be comfortable with this conversion as it bridges the gap between the theoretical (moles) and practical (grams) aspects of chemistry.

Molecular Weight

Molecular weight, also referred to as molar mass, is the weight of one mole of a chemical compound. It's usually expressed in grams per mole (g/mol) and is calculated by adding up the atomic weights of all the atoms present in the molecule's formula. The atomic weights are again taken from the periodic table, where they represent the weights of an average atom of each element compared to 1/12th the weight of a carbon-12 atom.

Understanding molecular weight is crucial for students as it helps them perform molar mass calculations in stoichiometry. To calculate the molecular weight, each atom's weight must be multiplied by the number of times the atom is present in the molecule, then all of these weights are summed to get the total molecular weight. This plays a pivotal role when determining amounts in both chemical reactions and solution preparations.