Question

Lactose is a sugar found in milk. Calculate the percent composition of lactose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\).

Short answer

The percent compositions are approximately 42.10% carbon, 6.49% hydrogen, and 51.41% oxygen in lactose.

Step-by-step solution

Determine Molar Mass of Lactose

First, find the molar mass of lactose, which is \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \) by adding the atomic masses of all the atoms in the molecule.- Carbon (C): 12 atoms \( \times \, 12.01 \, \mathrm{g/mol} = 144.12 \, \mathrm{g/mol} \)- Hydrogen (H): 22 atoms \( \times \, 1.01 \, \mathrm{g/mol} = 22.22 \, \mathrm{g/mol} \)- Oxygen (O): 11 atoms \( \times \, 16.00 \, \mathrm{g/mol} = 176.00 \, \mathrm{g/mol} \)**Total molar mass** = 144.12 + 22.22 + 176.00 = 342.34 \, \mathrm{g/mol}

Calculate Percent Composition of Carbon

To calculate the percent composition of carbon in lactose, use the formula:\[\text{Percent composition of } C = \left( \frac{\text{Mass of C in lactose}}{\text{Total molar mass of lactose}} \right) \times 100\]Substitute the values you found earlier:\[= \left( \frac{144.12}{342.34} \right) \times 100 \approx 42.10\%\]

Calculate Percent Composition of Hydrogen

To find the percent composition of hydrogen, use the formula:\[\text{Percent composition of } H = \left( \frac{\text{Mass of H in lactose}}{\text{Total molar mass of lactose}} \right) \times 100\]Substitute in the values:\[= \left( \frac{22.22}{342.34} \right) \times 100 \approx 6.49\%\]

Calculate Percent Composition of Oxygen

Now, determine the percent composition of oxygen using the formula:\[\text{Percent composition of } O = \left( \frac{\text{Mass of O in lactose}}{\text{Total molar mass of lactose}} \right) \times 100\]Replace the values:\[= \left( \frac{176.00}{342.34} \right) \times 100 \approx 51.41\%\]

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry. It refers to the mass of one mole of a substance, usually represented in grams per mole (g/mol). To find the molar mass of a compound, you sum the atomic masses of all atoms present in its structure.
For organic compounds like lactose, which has the formula \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), you would:

• Multiply the atomic mass of each element by the number of atoms of that element in the compound.
• Add these values together for all elements.

In the case of lactose, you calculate:

• Carbon (C): 12 atoms \( \times \, 12.01 \, \mathrm{g/mol} = 144.12 \, \mathrm{g/mol} \)
• Hydrogen (H): 22 atoms \( \times \, 1.01 \, \mathrm{g/mol} = 22.22 \, \mathrm{g/mol} \)
• Oxygen (O): 11 atoms \( \times \, 16.00 \, \mathrm{g/mol} = 176.00 \, \mathrm{g/mol} \)

Adding these gives you the total molar mass of lactose: \( 342.34 \, \mathrm{g/mol} \). This value is essential when calculating percent composition and converting between moles and grams.

Lactose

Lactose is a type of sugar that naturally occurs in milk. Chemically, it is known as a disaccharide, which means it is made up of two simple sugar molecules: glucose and galactose. When consumed, lactose needs to be broken down into these simpler sugars by the enzyme lactase in the digestive system.
Lactose's chemical formula is \( \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \). Each molecule consists of:

• 12 carbon atoms
• 22 hydrogen atoms
• 11 oxygen atoms

Understanding the composition of lactose is crucial, especially when calculating its percent composition. In nutritional sciences, knowing the content of substances like lactose in food products helps assess dietary energy supply. For those with lactose intolerance, recognizing its presence is important to avoid symptoms.

Chemical Formula

A chemical formula is more than just numbers and letters—it conveys essential information about the composition of molecules. The formula \( \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \), for example, tells you the number of each type of atom in a single molecule of a compound, in this case, lactose.
The chemical formula helps in:

• Identifying the type and number of atoms within the molecule.
• Determining the molecular and empirical formulas of compounds.
• Calculating the molar mass.

For students and professionals, reading chemical formulas accurately is vital. It serves as the foundation for further chemical analysis, enabling you to perform calculations like the percent composition, or predicting the behavior of the substance in chemical reactions. By knowing the formula, you can infer a lot about the properties and reactivity of a compound.