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 lb of ferric chloride e. \(1.0 \mathrm{~kg}\) of ferric chloride

Short answer

a. 0.311 mol of ammonium sulfide b. 0.270 mol of calcium nitrate c. 0.0501 mol of dichlorine monoxide d. 2.797 mol of ferric chloride in 1.0 lb e. 6.162 mol of ferric chloride in 1.0 kg

Step-by-step solution

Calculate the molar mass of each substance

a. Ammonium sulfide: (NH4)2S Molar mass = (2 x (1.01 (N) + 4.04 (H))) + 32.07 (S) = 68.17 g/mol b. Calcium nitrate: Ca(NO3)2 Molar mass = 40.08 (Ca) + 2 x (14.01 (N) + 3 x 16.00 (O)) = 164.10 g/mol c. Dichlorine monoxide: Cl2O Molar mass = (2 x 35.45 (Cl)) + 16.00 (O) = 86.90 g/mol d. Ferric chloride: FeCl3 Molar mass = 55.85 (Fe) + 3 x 35.45 (Cl) = 162.20 g/mol e. Ferric chloride: FeCl3 (same as d)

Convert the mass of each substance to the number of moles

a. \(21.2 \mathrm{~g} \)of ammonium sulfide Number of moles = \( \frac{21.2 \mathrm{~g}}{68.17 \mathrm{~g/mol}} = 0.311 \mathrm{~mol} \) b. \(44.3 \mathrm{~g} \)of calcium nitrate Number of moles = \( \frac{44.3 \mathrm{~g}}{164.10 \mathrm{~g/mol}} = 0.270 \mathrm{~mol} \) c. \(4.35 \mathrm{~g} \)of dichlorine monoxide Number of moles = \( \frac{4.35 \mathrm{~g}}{86.90 \mathrm{~g/mol}} = 0.0501 \mathrm{~mol} \) d. 1.0 lb of ferric chloride First, we need to convert the mass from pounds to grams: 1 lb = 453.592 g Number of moles = \( \frac{453.592 \mathrm{~g}}{162.20 \mathrm{~g/mol}} = 2.797 \mathrm{~mol} \) e. \(1.0 \mathrm{~kg} \)of ferric chloride First, we need to convert the mass from kilograms to grams: 1 kg = 1000 g Number of moles = \( \frac{1000 \mathrm{~g}}{162.20 \mathrm{~g/mol}} = 6.162 \mathrm{~mol} \)

Present the final answers

a. There are 0.311 moles of ammonium sulfide present. b. There are 0.270 moles of calcium nitrate present. c. There are 0.0501 moles of dichlorine monoxide present. d. There are 2.797 moles of ferric chloride present in 1.0 lb. e. There are 6.162 moles of ferric chloride present in 1.0 kg.

Key concepts

Molar Mass

The molar mass is a core concept in chemistry that represents the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol). To calculate the molar mass, you add up the atomic masses of all the atoms present in a molecule. For example, in ammonium sulfide \((\text{NH}_4)_2\text{S}\), you calculate the molar mass by considering both the nitrogen \((\text{N})\), hydrogen \((\text{H})\), and sulfur \((\text{S})\) atoms. The atomic mass of nitrogen is 14.01, for hydrogen it is about 1.01, and for sulfur, it is 32.07. By multiplying the number of each type of atom by their respective atomic masses and summing them up, you get the molar mass of ammonium sulfide, which is 68.17 g/mol.

• Atomic masses are values from the periodic table.
• Molar mass of compounds depends on their molecular formula.
• Understanding molar mass is crucial for converting between mass and moles in chemical calculations.

Chemical Calculations

In chemical calculations, finding the number of moles is a common operation. Moles enable chemists to quantify substances at the atomic level. When given a mass of substance, you use chemical calculations to convert this mass into moles. The formula used is:\[ \text{Number of moles} = \frac{\text{mass of the substance (g)}}{\text{molar mass (g/mol)}} \] This formula requires two pieces of information: the mass of the substance you have and its molar mass. Once you know these, simply divide the mass by the molar mass to find out how many moles of the substance you have.

• For ammonium sulfide, with a mass of 21.2 g and a molar mass of 68.17 g/mol, the calculation gives you roughly 0.311 moles.
• Such calculations are foundational in determining proportions in chemical reactions.
• Different substances require different molar masses, all based on their chemical formulas.

Unit Conversion

Unit conversion is a vital skill in chemistry for switching between different measurement units. You might need to convert mass measurements when they are not in convenient units for your calculation, like when converting pounds to grams. To do this, always use conversion factors. For example, when converting from pounds to grams:

• Recognize the conversion factor: 1 pound equals 453.592 grams.
• Apply this factor by multiplying the mass in pounds by 453.592 to get the equivalent mass in grams.
• In the exercise, 1.0 lb of ferric chloride translates to 453.592 grams, allowing you to then calculate the moles.
• Similarly, converting kilograms to grams uses the conversion: 1 kilogram equals 1000 grams.
• These conversions ensure you have a correct base measure for further calculations.

By understanding how to convert units, you can confidently tackle any chemical calculation that requires precise measurement conversions.