Question

Using the average atomic masses given inside the front cover of the text, calculate how many moles of each substance the following masses represent. a. 4.21 g of copper(II) sulfate b. \(7.94 \mathrm{~g}\) of barium nitrate c. \(1.24 \mathrm{mg}\) of water d. \(9.79 \mathrm{~g}\) of tungsten c. 1.45 lb of sulfur f. 4.65 g of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) g. 12.01 g of carbon

Short answer

In summary: a. There are \(0.026\) moles of copper(II) sulfate in \(4.21\) g. b. There are \(0.030\) moles of barium nitrate in \(7.94\) g. c. There are 0.0000689 moles of water in 1.24 mg. d. There are 0.0532 moles of tungsten in 9.79 g. e. There are 20.48 moles of sulfur in 1.45 lb. f. There are 0.1009 moles of ethyl alcohol in 4.65 g. g. There is 1 mole of carbon in 12.01 g.

Step-by-step solution

Calculate the molar mass of copper(II) sulfate

The molecular formula for copper(II) sulfate is \(CuSO_4\), and we can calculate its molar mass by adding up the atomic masses of each element in the formula: Molar mass of \(CuSO_4\) = Atomic mass of Cu + Atomic mass of S + (4 × Atomic mass of O) Using the atomic masses provided in the text Molar mass of \(CuSO_4\) = 63.5 + 32.1 + (4 × 16.0) = 63.5 + 32.1 + 64.0 = 159.6 g/mol

Calculate the moles of copper(II) sulfate

Now we can use the formula to find the moles of copper(II) sulfate: Moles = Mass / Molar Mass Moles = 4.21 g / 159.6 g/mol = 0.026 moles #a. Answer: There are \(0.026\) moles of copper(II) sulfate in \(4.21\) g. Repeat this process for the other substances. #b. 7.94 g of barium nitrate#

Calculate the molar mass of barium nitrate

The molecular formula for barium nitrate is \(Ba(NO_3)_2\), and we can calculate its molar mass by adding up the atomic masses of each element: Molar mass of \(Ba(NO_3)_2\) = Atomic mass of Ba + (2 × (Atomic mass of N + (3 × Atomic mass of O)) ) Using the atomic masses provided in the text Molar mass of \(Ba(NO_3)_2\) = 137.3 + 2 × (14.0 + 3 × 16.0) = 137.3 + 2 × 62.0 = 261.3 g/mol

Calculate the moles of barium nitrate

Moles = Mass / Molar Mass Moles = 7.94 g / 261.3 g/mol = 0.030 moles #b. Answer: There are \(0.030\) moles of barium nitrate in \(7.94\) g. Continue doing the same calculations for the remaining substances: - \(1.24\) mg of water: The molar mass of water \(\mathrm{H_2O}\) is 18.0 g/mol, and 1.24 mg is equal to 0.00124 g. Thus, there are 0.0000689 moles of water in 1.24 mg. - \(9.79\) g of tungsten: The molar mass of tungsten is 183.8 g/mol, and there are 0.0532 moles of tungsten in 9.79 g. - 1.45 lb of sulfur: Convert the mass into grams (1 lb = 453.6 g), so 1.45 lb is 657.7 g. The molar mass of sulfur is 32.1 g/mol, and there are 20.48 moles of sulfur in 1.45 lb. - 4.65 g of ethyl alcohol (\(\mathrm{C_2H_5OH}\)): The molar mass of ethyl alcohol is 46.1 g/mol, and there are 0.1009 moles of ethyl alcohol in 4.65 g. - 12.01 g of carbon: The molar mass of carbon is 12.01 g/mol, and there is 1 mole of carbon in 12.01 g.

Key concepts

Average Atomic Mass

Understanding the average atomic mass is crucial for many chemistry calculations. When you look at the periodic table, the atomic mass listed is actually an average, reflecting the mix of isotopes that exist in nature for each element. It's calculated by taking into account the masses of each isotope and their relative abundances. For instance, chlorine has two main isotopes with masses around 35 and 37 amu (atomic mass units). The average atomic mass is closer to 35.5 amu because the isotope with a mass of 35 amu is more abundant.

When dealing with mole calculations, it's this average atomic mass that we use to determine the molar mass of a substance, which leads directly to the quantity of substance - moles - when given a certain mass.

Molar Mass

The molar mass of an element or compound is the mass in grams that corresponds to one mole of that substance. It is numerically equivalent to the average atomic mass of the element (for elemental substances) but is expressed in grams per mole (g/mol). For compounds, like copper(II) sulfate in the exercise, the molar mass is found by summing the products of the average atomic mass of each element and the number of atoms of that element in the molecular formula.

In the copper(II) sulfate example, the molar mass calculation incorporated the molar masses of copper, sulfur, and oxygen. This step is foundational in stoichiometry since it relates mass, an easily measurable quantity, to moles, which connect to the number of particles and the balanced chemical equations in reactions.

Stoichiometry

Moving to the broad subject of stoichiometry, it refers to the calculations of the quantities in chemical reactions. It is founded on the law of conservation of mass and the concept of moles. Stoichiometry uses balanced chemical equations to predict the amount of a product that will form in a reaction, or the amount of reactants needed to produce a desired quantity of product.

Knowing the mole ratios of substances in a balanced chemical equation, students can calculate how many moles of a reactant are necessary to completely react with a given amount of another reactant. For our exercises, stoichiometry principles allow us to convert the mass of substances into moles, and vice versa, which is the first and critical step of many stoichiometric calculations.

Molecular Formula

Finally, the molecular formula gives the actual number and type of atoms in a molecule of a compound. It's an extension of the elemental symbols found on the periodic table, creating a unique identifier for each compound. For example, ethyl alcohol's molecular formula is \( \mathrm{C_2H_5OH} \), indicating that a molecule contains two carbon atoms, six hydrogen atoms, and one oxygen atom.

To perform molar mass calculations, as highlighted in the exercise, the molecular formula is essential. It allows us to calculate the molar mass by summing the average atomic masses of all the atoms present in the formula, helping us to eventually determine the number of moles in a given sample based on its mass.