To calculate the molar masses of the given compounds, we will use the atomic masses of the constituent elements: Carbon (C) has an atomic mass of 12.01 g/mol, Hydrogen (H) has an atomic mass of 1.01 g/mol, and Oxygen (O) has an atomic mass of 16.00 g/mol. Let's go through each compound step by step.
Wax: [tex]\( C_{25}H_{52} \)[/tex]
1. Count the number of each type of atom in the formula.
[tex]\[
\text{Carbon (C)}: 25 \quad \text{Hydrogen (H)}: 52
\][/tex]
2. Calculate the molar mass by multiplying the number of each atom by its atomic mass and then summing the results.
[tex]\[
\text{Molar mass of } C_{25}H_{52} = (25 \times 12.01) + (52 \times 1.01)
\][/tex]
[tex]\[
= 300.25 + 52.52
\][/tex]
[tex]\[
= 352.77 \text{ g/mol}
\][/tex]
Ethanol: [tex]\( C_2H_5OH \)[/tex]
1. Count the number of each type of atom in the formula.
[tex]\[
\text{Carbon (C)}: 2 \quad \text{Hydrogen (H)}: 6 \quad \text{Oxygen (O)}: 1
\][/tex]
2. Calculate the molar mass by multiplying the number of each atom by its atomic mass and then summing the results.
[tex]\[
\text{Molar mass of } C_2H_5OH = (2 \times 12.01) + (6 \times 1.01) + (16.00)
\][/tex]
[tex]\[
= 24.02 + 6.06 + 16.00
\][/tex]
[tex]\[
= 46.08 \text{ g/mol}
\][/tex]
Coconut oil: [tex]\( C_3H_5\left( C_{18}H_{30}O_2 \right)_3 \)[/tex]
Coconut oil's formula involves a more complex structure with a base molecule and a repeating unit. We calculate the molar mass in two parts, then combine them.
1. Base part [tex]\( C_3H_5 \)[/tex]:
[tex]\[
\text{Carbon (C)}: 3 \quad \text{Hydrogen (H)}: 5
\][/tex]
[tex]\[
\text{Molar mass of base part } C_3H_5 = (3 \times 12.01) + (5 \times 1.01)
\][/tex]
[tex]\[
= 36.03 + 5.05
\][/tex]
[tex]\[
= 41.08 \text{ g/mol}
\][/tex]
2. Fatty acid part [tex]\( C_{18}H_{30}O_2 \)[/tex]:
[tex]\[
\text{Carbon (C)}: 18 \quad \text{Hydrogen (H)}: 30 \quad \text{Oxygen (O)}: 2
\][/tex]
[tex]\[
\text{Molar mass of fatty acid part } C_{18}H_{30}O_2 = (18 \times 12.01) + (30 \times 1.01) + (2 \times 16.00)
\][/tex]
[tex]\[
= 216.18 + 30.30 + 32.00
\][/tex]
[tex]\[
= 278.48 \text{ g/mol}
\][/tex]
3. Since there are three fatty acid parts per molecule of coconut oil:
[tex]\[
\text{Total molar mass of fatty acid parts} = 3 \times 278.48
\][/tex]
[tex]\[
= 835.44 \text{ g/mol}
\][/tex]
4. Combine the base part and the fatty acid parts:
[tex]\[
\text{Molar mass of coconut oil } C_3H_5\left( C_{18}H_{30}O_2 \right)_3 = 41.08 + 835.44
\][/tex]
[tex]\[
= 876.52 \text{ g/mol}
\][/tex]
Summary of molar masses:
- Wax ([tex]\(C_{25}H_{52}\)[/tex]): 352.77 g/mol
- Ethanol ([tex]\(C_2H_5OH\)[/tex]): 46.08 g/mol
- Coconut oil ([tex]\(C_3H_5\left( C_{18}H_{30}O_2 \right)_3\)[/tex]): 876.52 g/mol
