Chapter 9: Problem 41
Lactose is a sugar found in milk. Calculate the percent composition of lactose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\).
Short Answer
Expert verified
The percent compositions are approximately 42.10% carbon, 6.49% hydrogen, and 51.41% oxygen in lactose.
Step by step solution
01
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}
02
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:\[= \left( \frac{144.12}{342.34} \right) \times 100 \approx 42.10\%\]
03
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:\[= \left( \frac{22.22}{342.34} \right) \times 100 \approx 6.49\%\]
04
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:\[= \left( \frac{176.00}{342.34} \right) \times 100 \approx 51.41\%\]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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:
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.
- 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 \( \times \, 16.00 \, \mathrm{g/mol} = 176.00 \, \mathrm{g/mol} \)
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:
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
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:
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.