Question

Margarine is produced from the hydrogenation of vegetable oils, which contain unsaturated fatty acids. How many grams of hydrogen are required to completely saturate \(75.0 \mathrm{~g}\) of oleic acid, \(\mathrm{C}_{18} \mathrm{H}_{34} \mathrm{O}_{2}\), which has one double bond?

Short answer

0.5361 grams of hydrogen are required.

Step-by-step solution

Determine the Molar Mass of Oleic Acid

Calculate the molar mass of oleic acid, \(\text{C}_{18}\text{H}_{34}\text{O}_{2}\). The calculation is as follows: \[ 18(12.01 \text{ g/mol}) + 34(1.01 \text{ g/mol}) + 2(16.00 \text{ g/mol}) = 282.46 \text{ g/mol} \]

Calculate the Number of Moles of Oleic Acid

Use the mass given (75.0 g) and the molar mass of oleic acid to find the number of moles. \(\text{Number of moles} = \frac{75.0 \text{ g}}{282.46 \text{ g/mol}} = 0.2656 \text{ moles}\)

Determine the Moles of Hydrogen Required

Each mole of oleic acid requires one mole of hydrogen to saturate the double bond. Therefore, 0.2656 moles of oleic acid will require 0.2656 moles of hydrogen.

Calculate the Mass of Hydrogen Required

Use the molar mass of hydrogen (H\textsubscript{2}) which is \(2.02 \text{ g/mol}\). \[ \text{Mass of hydrogen} = 0.2656 \text{ moles} \times 2.02 \text{ g/mol} = 0.5361 \text{ g} \]

Key concepts

Unsaturated Fatty Acids

Unsaturated fatty acids are a type of fat found in foods like vegetable oils, nuts, and seeds. They are called 'unsaturated' because they contain at least one double bond between carbon atoms.
This double bond causes a kink in the fatty acid chain, preventing the molecules from packing closely together. This makes unsaturated fats liquid at room temperature.

• Types: There are two main types: monounsaturated (one double bond) and polyunsaturated (multiple double bonds).
• Importance: These fats are considered healthier than saturated fats, which have no double bonds and can contribute to heart disease.
• Examples: Olive oil (high in monounsaturated fats) and fish oil (high in polyunsaturated fats like omega-3 fatty acids).

Understanding unsaturated fatty acids helps us see why hydrogenation is used to convert these healthier oils into semi-solid forms like margarine.

Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a key concept in chemistry for calculating the amount of a substance in a given sample.
To find the molar mass, you sum the atomic masses of all the atoms in a molecule:

• Example: For oleic acid (C₁₈H₃₄O₂):
• Calculate the atomic masses:
• Carbon (C): 12.01 g/mol, Hydrogen (H): 1.01 g/mol, Oxygen (O): 16.00 g/mol
• Sum them up: 18(C) * 12.01 g/mol + 34(H) * 1.01 g/mol + 2(O) * 16.00 g/mol = 282.46 g/mol

This molar mass allows us to convert between the mass of a substance and the number of moles, essential for chemical reaction calculations.

Oleic Acid

Oleic acid is a common unsaturated fatty acid found in olive oil and other plant sources. It has the chemical formula C₁₈H₃₄O₂ and contains one double bond.
Its structure includes a long carbon chain with various hydrogen atoms and a carboxyl group (-COOH):

• Properties: Here are some important properties:
• Monounsaturated: Contains a single double bond, making it more beneficial for cardiovascular health.
• Appearance: Generally, it is a pale yellow liquid.
• Common Uses: Often used in the production of soaps, cosmetics, and foods like margarine through hydrogenation.
Understanding oleic acid helps us see how hydrogenation can change its properties and applications.

Chemical Reactions

Chemical reactions involve the transformation of substances through breaking and forming chemical bonds. In the context of our topic, hydrogenation is a key chemical reaction.
Hydrogenation involves adding hydrogen (H₂) to unsaturated fats to convert them into saturated fats:

• Mechanism: The double bonds in unsaturated fats like oleic acid are broken, and hydrogen atoms are added.
• Catalyst: Often a metal catalyst like nickel is used to speed up the reaction.
• Outcome: The result is a more solid form of fat at room temperature, making it suitable for products like margarine and shortening.

This reaction highlights how molecular structure changes can alter the physical properties and uses of fatty acids.