Question

Calculate the mass in grams of 3.839 moles of (a) hydrazine, a rocket propellant. (b) caffeine, \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\) (c) theobromine, \(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{~N}_{4} \mathrm{O}_{2},\) the alkaloid present in chocolate and cocoa.

Short answer

Question: Calculate the mass in grams of 3.839 moles of each of the following substances: (a) hydrazine (N₂H₄), (b) caffeine (C₈H₁₀N₄O₂), and (c) theobromine (C₇H₈N₄O₂). Answer: (a) 123.01 g of hydrazine (N₂H₄), (b) 745.79 g of caffeine (C₈H₁₀N₄O₂), and (c) 691.19 g of theobromine (C₇H₈N₄O₂).

Step-by-step solution

Determine the molar mass of hydrazine

The molecular formula of hydrazine is N₂H₄. Calculate the molar mass by adding the molar masses of all the atoms present in the formula as follows: Molar mass of hydrazine = 2(Molar mass of N) + 4(Molar mass of H) = 2(14.01 g/mol) + 4(1.01 g/mol) = 32.05 g/mol

Calculate mass in grams of 3.839 moles of hydrazine

Now, multiply the molar mass of hydrazine by the number of moles (3.839) to find the mass in grams: Mass of hydrazine = 3.839 moles × 32.05 g/mol = 123.01395 g (b) Caffeine (C₈H₁₀N₄O₂)

Determine the molar mass of caffeine

The molecular formula of caffeine is C₈H₁₀N₄O₂. Calculate the molar mass by adding the molar masses of all the atoms present in the formula as follows: Molar mass of caffeine = 8(Molar mass of C) + 10(Molar mass of H) + 4(Molar mass of N) + 2(Molar mass of O) = 8(12.01 g/mol) + 10(1.01 g/mol) + 4(14.01 g/mol) + 2(16.00 g/mol) = 194.19 g/mol

Calculate mass in grams of 3.839 moles of caffeine

Now, multiply the molar mass of caffeine by the number of moles (3.839) to find the mass in grams: Mass of caffeine = 3.839 moles × 194.19 g/mol = 745.79261 g (c) Theobromine (C₇H₈N₄O₂)

Determine the molar mass of theobromine

The molecular formula of theobromine is C₇H₈N₄O₂. Calculate the molar mass by adding the molar masses of all the atoms present in the formula as follows: Molar mass of theobromine = 7(Molar mass of C) + 8(Molar mass of H) + 4(Molar mass of N) + 2(Molar mass of O) = 7(12.01 g/mol) + 8(1.01 g/mol) + 4(14.01 g/mol) + 2(16.00 g/mol) = 180.16 g/mol

Calculate mass in grams of 3.839 moles of theobromine

Now, multiply the molar mass of theobromine by the number of moles (3.839) to find the mass in grams: Mass of theobromine = 3.839 moles × 180.16 g/mol = 691.18944 g

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is essential for a variety of calculations in chemistry, and it plays a crucial role in mole to mass conversions. The molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol).

To calculate molar mass, you must know the molecular formula of the substance, which provides the number of each type of atom in a molecule. You then use the periodic table to find the atomic mass of each element. The atomic mass tells us the mass of one mole of atoms for a given element, also in grams per mole. For instance, the atomic mass of hydrogen (H) is approximately 1.01 g/mol, while that of carbon (C) is about 12.01 g/mol.

• Identify the number of each type of atom in the molecular formula.
• Multiply the atomic mass of each element by the number of atoms of that element in the formula.
• Add these values together to get the total molar mass of the substance.

Stoichiometry

Stoichiometry is a section of chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. For conversions like mole to mass, stoichiometry is key in determining how much of a substance is required or produced in a reaction.

When performing stoichiometric calculations, it's important to follow these steps:

• Write down the balanced chemical equation for the reaction.
• Use the coefficients in the equation to determine the mole ratios between reactants and products.
• Based on the mole ratios and the known quantity (such as moles of one substance), calculate the required quantity (like grams of another substance).

In essence, stoichiometry acts as a bridge between moles and mass, allowing for precise calculations in chemical reactions, which is essential for laboratory work and industrial applications.

Molecular Formula

The molecular formula of a compound provides a clear depiction of the types and numbers of atoms in a single molecule of the compound. It presents this information using the chemical symbols for the elements and numerical subscripts indicating the number of atoms.

For example, the molecular formula for hydrazine is N₂H₄, indicating that each molecule consists of two nitrogen (N) atoms and four hydrogen (H) atoms. Knowing the molecular formula is vital as it is used to calculate the molar mass and to perform stoichiometric calculations.

To determine the molecular formula from empirical data, the following steps are typically taken:

• Determine the empirical formula that shows the simplest whole-number ratio of elements in the compound.
• Find the molar mass of the empirical formula.
• Divide the molar mass of the compound by the molar mass of the empirical formula to find the multiplication factor.
• Multiply the subscripts in the empirical formula by this factor to get the molecular formula.

Correctly determining the molecular formula is important for understanding the exact nature of the compound and how it will interact in chemical reactions.