Question

Calculate the number of moles of hydrogen atoms present in each of the following samples. a. \(2.71 \mathrm{g}\) of ammonia b. 0.824 mol of water c. \(6.25 \mathrm{mg}\) of sulfuric acid d. \(451 \mathrm{g}\) of ammonium carbonate

Short answer

a. \(0.477 \,\text{mol}\) b. \(1.648 \,\text{mol}\) c. \(1.274 \times 10^{-4} \,\text{mol}\) d. \(37.528 \,\text{mol}\)

Step-by-step solution

Find molecular weight of compounds involved

We will find the molecular weight for ammonia (NH3), water (H2O), sulfuric acid (H2SO4), and ammonium carbonate ((NH4)2CO3). We look up the atomic weights of the elements involved: - Hydrogen: H = 1.008 g/mol - Nitrogen: N = 14.007 g/mol - Oxygen: O = 15.999 g/mol - Sulfur: S = 32.06 g/mol - Carbon: C = 12.01 g/mol Molecular weight of NH3: = (1.008 g/mol × 3) + 14.007 g/mol = 17.031 g/mol Molecular weight of H2O: = (1.008 g/mol × 2) + 15.999 g/mol = 18.015 g/mol Molecular weight of H2SO4: = (1.008 g/mol × 2) + 32.06 g/mol + (15.999 g/mol × 4) = 98.082 g/mol Molecular weight of (NH4)2CO3: = (1.008 g/mol × 8) + (14.007 g/mol × 2) + 12.01 g/mol + (15.999 g/mol × 3) = 96.063 g/mol

Calculate moles of compounds

Calculate the moles of ammonia, water, sulfuric acid, and ammonium carbonate in each sample: a. moles of NH3 = 2.71 g / 17.031 g/mol ≈ 0.159 mol b. moles of H2O = 0.824 mol (given) c. moles of H2SO4 = (6.25 mg × (1 g/1000 mg)) / 98.082 g/mol ≈ 6.37 x 10^(-5) mol d. moles of (NH4)2CO3 = 451 g / 96.063 g/mol ≈ 4.691 mol

Calculate moles of hydrogen atoms

Now, we can determine the moles of hydrogen atoms in each compound: a. In NH3, there are 3 moles of H atoms in 1 mole of NH3. Moles of hydrogen in ammonia = 0.159 mol × 3 = 0.477 mol b. In H2O, there are 2 moles of H atoms in 1 mole of H2O. Moles of hydrogen in water = 0.824 mol × 2 = 1.648 mol c. In H2SO4, there are 2 moles of H atoms in 1 mole of H2SO4. Moles of hydrogen in sulfuric acid = 6.37 x 10^(-5) mol × 2 = 1.274 x 10^(-4) mol d. In (NH4)2CO3, there are 8 moles of H atoms in 1 mole of (NH4)2CO3. Moles of hydrogen in ammonium carbonate = 4.691 mol × 8 = 37.528 mol Now we have calculated the number of moles of hydrogen atoms present in each of the following samples: a. 0.477 mol b. 1.648 mol c. 1.274 x 10^(-4) mol d. 37.528 mol

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the calculation of the quantities of reactants and products in chemical reactions. It is a fundamental principle used to understand the relationships between the amounts of substances involved in reactions. For example, to calculate the moles of hydrogen atoms in various compounds, as in the exercise provided, stoichiometry utilizes the balanced chemical equations and the concept of the mole. The calculation process involves using the molecular formula of each compound to determine how many hydrogen atoms are present and then applying the information about the mass or moles given in the problem to find the amount of hydrogen atoms.

Understanding stoichiometry is crucial for students, as it can apply to various scenarios within chemical reactions, from laboratory experiments to industrial processes. The concept ensures that students can predict the quantities of substances needed and created, making it a backbone of chemical analysis and application.

Molecular Weight

Molecular weight, also known as molecular mass, is a critical concept in the calculation of moles of hydrogen atoms. It is the sum of the atomic weights of all atoms in a molecule and is typically expressed in atomic mass units (amu) or grams per mole (g/mol). The atomic weights of individual elements, like hydrogen (H = 1.008 g/mol), are usually found on the periodic table, and they are factored into calculating the total molecular weight of a compound. For instance, ammonia (NH3) has a molecular weight calculated by summing the weight of nitrogen and three hydrogen atoms to arrive at 17.031 g/mol.

Having the correct molecular weight is essential to convert between grams and moles during stoichiometric calculations. Incorrect molecular weights lead to errors in subsequent steps, so accurate determination of molecular weight is vital in exercises concerning the stoichiometry of compounds.

Chemical Composition

The chemical composition of a substance describes the identity and ratio of the elements within that substance. In our exercise, the chemical composition is used to determine the number of hydrogen atoms present in each compound. By knowing the molecular formula, such as NH3 for ammonia or H2SO4 for sulfuric acid, we can identify and count the number of each type of atom in a molecule. This count directly informs us about the stoichiometry, allowing us to calculate quantities such as moles of atoms. For example, each molecule of sulfuric acid contains two hydrogen atoms, as indicated by the 'H2' in its chemical formula. This information is key when we apply stoichiometric ratios to convert between moles of a compound and moles of individual atoms like hydrogen.

Avogadro's Number

Avogadro's number is a constant that represents the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. Its value is approximately 6.022 x 10^23 particles per mole. While Avogadro's number was not directly used in this exercise, it is intrinsically linked to any discussion regarding moles, as it provides a way to relate the macroscopic quantities we measure (in grams or moles) to the actual number of atoms or molecules present in a sample.

For a deeper comprehension of stoichiometry and moles, it's necessary to appreciate that one mole of any substance, as computed from its molecular weight, contains the same number of entities as given by Avogadro's number. This enables chemists to work with manageable amounts of substances while maintaining knowledge of the scale at the atomic level.