Chapter 4: Problem 75

Determine the number of moles (of molecules or formula units) in each sample. a. 25.5 g NO2 b. 1.25 kg CO2 c. 38.2 g KNO3 d. 155.2 kg Na2SO4

Short Answer

Expert verified

a. 0.554 mol NO2, b. 28.405 mol CO2, c. 0.378 mol KNO3, d. 1093.32 mol Na2SO4

Step by step solution

Calculate Moles of NO2

First, determine the molar mass of NO2 by adding the atomic masses found on the periodic table. The molar mass of nitrogen (N) is approximately 14.01 g/mol and oxygen (O) is approximately 16.00 g/mol. NO2 has one nitrogen atom and two oxygen atoms, so its molar mass is \(14.01 + 2(16.00) = 46.01 \text{g/mol}\). Next, convert grams to moles using the formula \(\frac{\text{mass}}{\text{molar mass}}\) for NO2: \(\frac{25.5 \text{ g}}{46.01 \text{ g/mol}} \approx 0.554 \text{ moles of NO2}\).

Calculate Moles of CO2

Find the molar mass of CO2, which is \(12.01 \text{ g/mol for C} + 2(16.00 \text{ g/mol for O}) = 44.01 \text{ g/mol}\). Then, convert kilograms to grams (1.25 kg CO2 = 1250 g CO2), and use the formula to convert to moles: \(\frac{1250 \text{ g}}{44.01 \text{ g/mol}} \approx 28.405 \text{ moles of CO2}\).

Calculate Moles of KNO3

Determine the molar mass of KNO3 by adding the atomic masses: potassium (K) is approximately 39.10 g/mol, nitrogen is 14.01 g/mol, and oxygen is 16.00 g/mol. The molar mass of KNO3 is \(39.10 + 14.01 + 3(16.00) = 101.11 \text{g/mol}\). Convert grams to moles: \(\frac{38.2 \text{ g}}{101.11 \text{ g/mol}} \approx 0.378 \text{ moles of KNO3}\).

Calculate Moles of Na2SO4

Find the molar mass of Na2SO4: sodium (Na) is approximately 22.99 g/mol, sulfur (S) is 32.07 g/mol, and oxygen is 16.00 g/mol. The molar mass is \(2(22.99) + 32.07 + 4(16.00) = 142.05 \text{g/mol}\). Convert kilograms to grams (155.2 kg Na2SO4 = 155200 g Na2SO4), and convert to moles: \(\frac{155200 \text{ g}}{142.05 \text{ g/mol}} \approx 1093.32 \text{ moles of Na2SO4}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass

Understanding molar mass is essential when it comes to converting grams into moles. The molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule.

For instance, in our sample problem, the molar mass of NO2 (nitrogen dioxide) has been calculated by adding the atomic mass of nitrogen (N) with the atomic mass of two oxygen (O) atoms. Each substance has its unique molar mass which acts as a conversion factor allowing you to translate between the mass of a substance and the amount of substance in moles.

Conversion to Moles

When dealing with chemical reactions and formulas, it's crucial to be able to convert between mass and moles. Conversion to moles can be done using the formula
\[\frac{\text{mass}}{\text{molar mass}} = \text{moles}\]
This conversion is pivotal in chemistry because it allows chemists to quantify atoms, ions, or molecules in a given sample, considering that we can directly weigh masses but cannot count out individual molecules. For example, converting 38.2 g of potassium nitrate (KNO3) to moles involves dividing the mass of the sample by its molar mass, as demonstrated in the step-by-step solution.

Atomic Masses

Atomic masses represent the mass of individual atoms and are the foundational blocks for calculating molar masses. These are usually described in atomic mass units (amu) but within the context of moles, they are expressed in grams per mole (g/mol).

Atomic masses are average masses, accounting for the various isotopes of an element that occur naturally and their relative abundances. As seen in the exercise, individual atomic masses are obtained from the periodic table, such as 14.01 g/mol for nitrogen (N), which is used to calculate the molar mass of compounds.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles. By understanding the stoichiometry of a reaction, you can predict the amounts of products formed from given reactants.

It involves calculations that are founded on the mole ratio between the reactants and products, which stems from the balanced chemical equation. For instance, if you know the number of moles of a reactant, you can use stoichiometry to find out how many moles of each product are produced, following the mole-to-mole conversion factors from the balanced equation.

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Determine the number of moles (of molecules or formula units) in each sample. a. 25.5 g NO2 b. 1.25 kg CO2 c. 38.2 g KNO3 d. 155.2 kg Na2SO4

Short Answer

Step by step solution

Calculate Moles of NO2

Calculate Moles of CO2

Calculate Moles of KNO3

Calculate Moles of Na2SO4

Key Concepts

Molar Mass

Conversion to Moles

Atomic Masses

Stoichiometry

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