Question

Calculate the number of moles of the indicated substance present in each of the following samples. a. \(21.2 \mathrm{g}\) of ammonium sulfide b. \(44.3 \mathrm{g}\) of calcium nitrate c. \(4.35 \mathrm{g}\) of dichlorine monoxide d. 1.0 Ib of ferric chloride e. \(1.0 \mathrm{kg}\) of ferric chloride

Short answer

The number of moles for each substance are as follows: a. 0.31 mol of ammonium sulfide b. 0.27 mol of calcium nitrate c. 0.05 mol of dichlorine monoxide d. 2.80 mol of ferric chloride (1.0 lb) e. 6.16 mol of ferric chloride (1.0 kg)

Step-by-step solution

Determine the molar mass of ammonium sulfide

We need to find the molar mass of ammonium sulfide - (NH4)2S - by adding the molar masses of its component elements. Molar mass of N = 14.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of S = 32.07 g/mol Molar mass of (NH4)2S = 2 × (1 × 14.01 + 4 × 1.01) + 1 × 32.07 = 68.14 g/mol

Calculate the number of moles

Now, we can calculate the number of moles using the given mass and the molar mass of ammonium sulfide: Number of moles = (21.2 g) / (68.14 g/mol) ≈ 0.31 mol b. 44.3 g of calcium nitrate

Determine the molar mass of calcium nitrate

We need to find the molar mass of calcium nitrate - Ca(NO3)2 - by adding the molar masses of its component elements. Molar mass of Ca = 40.08 g/mol Molar mass of N = 14.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of Ca(NO3)2 = 1 × 40.08 + 2 × (1 × 14.01 + 3 × 16.00) = 164.10 g/mol

Calculate the number of moles

Now, we can calculate the number of moles using the given mass and the molar mass of calcium nitrate: Number of moles = (44.3 g) / (164.10 g/mol) ≈ 0.27 mol c. 4.35 g of dichlorine monoxide

Determine the molar mass of dichlorine monoxide

We need to find the molar mass of dichlorine monoxide - Cl2O - by adding the molar masses of its component elements. Molar mass of Cl = 35.45 g/mol Molar mass of O = 16.00 g/mol Molar mass of Cl2O = 2 × 35.45 + 1 × 16.00 = 86.90 g/mol

Calculate the number of moles

Now, we can calculate the number of moles using the given mass and the molar mass of dichlorine monoxide: Number of moles = (4.35 g) / (86.90 g/mol) ≈ 0.05 mol d. 1.0 lb of ferric chloride

Convert lb to g and determine the molar mass of ferric chloride

First, we need to convert the weight from lb to g. There are 453.59 g in 1 lb. Therefore, 1.0 lb of ferric chloride is equivalent to 453.59 g. Now, we need to find the molar mass of ferric chloride - FeCl3 - by adding the molar masses of its component elements. Molar mass of Fe = 55.85 g/mol Molar mass of Cl = 35.45 g/mol Molar mass of FeCl3 = 1 × 55.85 + 3 × 35.45 = 162.20 g/mol

Calculate the number of moles

Now, we can calculate the number of moles using the converted mass and the molar mass of ferric chloride: Number of moles = (453.59 g) / (162.20 g/mol) ≈ 2.80 mol e. 1.0 kg of ferric chloride

Convert kg to g

First, we need to convert the weight from kg to g. There are 1,000 g in 1 kg. Therefore, 1.0 kg of ferric chloride is equivalent to 1,000 g.

Calculate the number of moles

Now, we can calculate the number of moles using the converted mass and the molar mass of ferric chloride (162.20 g/mol) that we determined in part 'd': Number of moles = (1,000 g) / (162.20 g/mol) ≈ 6.16 mol

Key concepts

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is a crucial concept in chemistry because it acts as a bridge between the atomic scale and the mass scale. To calculate the molar mass of a compound, you sum up the atomic masses of all the atoms in the molecule. To find these atomic masses, refer to the periodic table. Each element has an atomic mass, which tells you the mass of one mole of that element's atoms. Here's a simple process:

• Identify each element in the compound.
• Count the number of atoms of each element.
• Multiply the atomic mass of each element by the number of atoms present.
• Add up all these values to obtain the molar mass.

For example, the molar mass of ammonium sulfide \((NH_4)_2S\) is calculated by adding twice the molar mass of nitrogen, eight times the molar mass of hydrogen, and once the molar mass of sulfur. Notice, the benefit of finding the molar mass is that it enables you to convert between grams of a substance and moles, which is a standard unit in chemistry.

Chemical Compounds

Chemical compounds are made up of two or more different elements that are chemically bonded together. Each compound has a unique combination of elements in fixed proportions, which determines its chemical behavior and properties. Understanding chemical compounds is essential for mole calculations because the components of the compound influence both its molar mass and resulting reactions.Chemical formulas show the types and numbers of atoms in a compound. For instance, calcium nitrate is represented as \( Ca(NO_3)_2 \). This formula indicates that one molecule of calcium nitrate consists of one calcium (Ca) atom and two nitrate \((NO_3)\) groups. To understand how chemical compounds work in reactions, remember these points:

• Each compound's formula shows the ratio of atoms, which helps in understanding how much of each is needed to form or is formed in a chemical reaction.
• By knowing the formula, you can determine how masses of different compounds relate to each other through their molar masses.
• Stoichiometry, the calculations of reactants and products in chemical reactions, heavily relies on understanding these compounds and their mole relationships.

Unit Conversion

Unit conversion is critical when working with different units of measurement in chemistry problems. Conversions allow us to work seamlessly from one unit to another without losing accuracy. For mole calculations, such conversions are often necessary to ensure that the mass of a substance aligns with its molar mass. Common conversions in chemistry include:

• Mass: Converting kilograms to grams or pounds to grams (since 1 lb = 453.59 g and 1 kg = 1,000 g).
• Volume: Converting liters to milliliters or cubic centimeters.
• Moles: Using the molar mass to convert between moles and grams.

For example, when given a mass in pounds (like 1 lb of ferric chloride), first convert the mass to grams. Then, use the molar mass to find out how many moles exist in that mass. Proper unit conversions ensure your calculations deliver accurate results.

Mole Concept

The mole concept is a fundamental idea in chemistry that provides a bridge between the atomic world and our observable world. A mole is defined as exactly \(6.022 \times 10^{23}\) entities, which can be atoms, molecules, ions, or other particles. This number is called Avogadro's number.The mole serves as a convenient way to express amounts of a chemical substance. Here's how it fits into chemistry calculations:

• Moles allow us to convert between atoms or molecules and grams. Using the molar mass, we can understand how a sample's mass correlates to the number of atoms or molecules it contains.
• It simplifies comparing amounts of different substances, as equal moles of different chemicals contain the same number of entities.
• In chemical equations, moles ensure we are accounting for the balanced amounts of reactants and products.

For example, calculating the number of moles from a given mass involves dividing the mass of the sample by its molar mass. This is useful for determining how much of a substance is present in sample, which can then be used in further analysis or reactions.