Problem 27 - Chemistry: Principles and Reactions

Question

Convert the following to moles. (a) \(4.00 \times 10^{3} \mathrm{~g}\) of hydrazine, a rocket propellant (b) \(12.5 \mathrm{~g}\) of tin(II) fluoride, the active ingredient in fluoride toothpaste (c) \(13 \mathrm{~g}\) of caffeine, \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

Question: Calculate the number of moles for the given masses of the following compounds: (a) 4.00 x 10^3 g of hydrazine, (b) 12.5 g of tin(II) fluoride, and (c) 13 g of caffeine. Answer: (a) 124.84 moles of hydrazine, (b) 0.0797 moles of tin(II) fluoride, and (c) 0.0669 moles of caffeine.

Step 1: Determine the molar mass of each compound

To find the molar mass of a compound, we must first identify the molecular formula of that compound and then add the molar masses of all the atoms present in the compound. (a) Hydrazine: \(\mathrm{N}_{2}\mathrm{H}_{4}\) Molar mass: \(2 \cdot \mathrm{(N) +} 4 \cdot \mathrm{(H)} = 2\cdot(14.01 \mathrm{g/mol}) + 4\cdot(1.008 \mathrm{g/mol}) = 32.04 \mathrm{g/mol}\) (b) Tin(II) fluoride: \(\mathrm{SnF}_{2}\) Molar mass: \(1 \cdot \mathrm{(Sn)} + 2 \cdot \mathrm{(F)} = 1\cdot(118.71 \mathrm{g/mol}) + 2\cdot(19.00 \mathrm{g/mol}) = 156.71 \mathrm{g/mol}\) (c) Caffeine: \(\mathrm{C}_{8}\mathrm{H}_{10}\mathrm{N}_{4}\mathrm{O}_{2}\) Molar mass: \(8 \cdot \mathrm{(C)} + 10 \cdot \mathrm{(H)} + 4 \cdot \mathrm{(N)} + 2 \cdot \mathrm{(O)} = 8\cdot(12.01 \mathrm{g/mol}) + 10\cdot(1.008 \mathrm{g/mol}) + 4\cdot(14.01 \mathrm{g/mol}) + 2\cdot(16.00 \mathrm{g/mol}) = 194.19 \mathrm{g/mol}\)

Step 2: Calculate the moles of each compound using given mass and molar mass

To find the number of moles, divide the mass of the substance by its molar mass. (a) Moles of hydrazine: \(\dfrac{4.00 \times 10^{3} \mathrm{~g \; of \; hydrazine}}{32.04 \mathrm{g/mol}} = 124.84 \ \mathrm{moles}\) (b) Moles of tin(II) fluoride: \(\dfrac{12.5 \mathrm{~g \; of \; tin(II) \, fluoride}}{156.71 \mathrm{g/mol}} = 0.0797 \ \mathrm{moles}\) (c) Moles of caffeine: \(\dfrac{13 \mathrm{~g \; of \; caffeine}}{194.19 \mathrm{g/mol}} = 0.0669 \ \mathrm{moles}\) In conclusion: a) There are \(124.84 \, \mathrm{moles}\) of hydrazine b) There are \(0.0797 \, \mathrm{moles}\) of tin(II) fluoride c) There are \(0.0669 \, \mathrm{moles}\) of caffeine

Key Concepts

Molar Mass Calculation

To calculate the molar mass of a compound, you need to know the elements that compose it and their respective quantities. The molar mass is the sum of the atomic masses of all atoms in the molecule. For example, if a molecule is composed of two hydrogen atoms and one oxygen atom, its molar mass is the sum of the atomic masses of these atoms.
\[\text{Molar mass} = (\text{Number of } \text{H}) \times (\text{Atomic mass of } \text{H}) + (\text{Number of } \text{O}) \times (\text{Atomic mass of } \text{O})\]
Using periodic table values, you can find the atomic mass for each element and use it in calculations. This is essential for mole conversions in chemistry as it allows you to find how many moles are present in any given mass of a compound.

Hydrazine

Hydrazine, with the chemical formula \(\text{N}_2\text{H}_4\), is a compound that contains nitrogen and hydrogen. It is often used as a rocket propellant due to its ability to release a large amount of energy upon decomposition.
To find the molar mass of hydrazine, calculate:

• Two nitrogen atoms: \(2 \times 14.01 \text{ g/mol}\)
• Four hydrogen atoms: \(4 \times 1.008 \text{ g/mol}\)

Adding them gives you a molar mass of \(32.04 \text{ g/mol}\). This value is crucial when determining how many moles are present in a specific mass of hydrazine.

Tin(II) Fluoride

Tin(II) fluoride, represented as \(\text{SnF}_2\), is a compound used in toothpaste for its beneficial effects on dental health. In this molecule, tin (Sn) is combined with two fluorine atoms.
To calculate the molar mass of tin(II) fluoride, consider:

• One tin atom: \(1 \times 118.71 \text{ g/mol}\)
• Two fluorine atoms: \(2 \times 19.00 \text{ g/mol}\)

This results in a molar mass of \(156.71 \text{ g/mol}\). Knowing this helps to calculate the number of moles in a given mass, which is useful in chemical reactions and formulations.

Caffeine Chemistry

Caffeine, with the formula \(\text{C}_8\text{H}_{10}\text{N}_4\text{O}_2\), is a stimulant found in coffee and other beverages. The structure of caffeine includes carbon, hydrogen, nitrogen, and oxygen atoms.
To find its molar mass, calculate:

• Eight carbon atoms: \(8 \times 12.01 \text{ g/mol}\)
• Ten hydrogen atoms: \(10 \times 1.008 \text{ g/mol}\)
• Four nitrogen atoms: \(4 \times 14.01 \text{ g/mol}\)
• Two oxygen atoms: \(2 \times 16.00 \text{ g/mol}\)

These come together to form a molar mass of \(194.19 \text{ g/mol}\). This molar mass is essential for calculating dosages and understanding caffeine's effect in biochemical pathways.