Problem 193 - Chemistry Matter and Change

Question

How many moles are present in 1.00 \(\mathrm{g}\) of each compound? \begin{equation} \begin{array}{l}{\text { a. L-tryptophan }\left(\mathrm{C}_{11} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{2}\right), \text { an essential amino acid }} \\ {\text { b. magnesium sulfate heptahydrate, also known as }} \\\ {\text { Epsom salts }} \\ {\text { c. propane }\left(\mathrm{C}_{5} \mathrm{H}_{8}\right), \text { a fuel }}\end{array} \end{equation}

Step-by-Step Solution

Answer

L-tryptophan: 0.00490 mol; Magnesium sulfate heptahydrate: 0.00406 mol; Propane: 0.0147 mol.

Step 1: Calculate Molar Mass of Each Compound

For each compound, calculate the molar mass (molecular weight) by adding the atomic masses of the elements, multiplied by their respective quantities in the formula. - **L-tryptophan**: - Carbon (C): 11 atoms × 12.01 g/mol = 132.11 g/mol - Hydrogen (H): 12 atoms × 1.01 g/mol = 12.12 g/mol - Nitrogen (N): 2 atoms × 14.01 g/mol = 28.02 g/mol - Oxygen (O): 2 atoms × 16.00 g/mol = 32.00 g/mol - **Total Molar Mass** = 204.25 g/mol - **Magnesium sulfate heptahydrate (MgSO₄·7H₂O)**: - Magnesium (Mg): 24.31 g/mol - Sulfur (S): 32.07 g/mol - Oxygen (O) in sulfate (SO₄): 4 atoms × 16.00 g/mol = 64.00 g/mol - Water (H₂O): 7 molecules × 18.02 g/mol = 126.14 g/mol - **Total Molar Mass** = 246.47 g/mol - **Propane**: - Carbon (C): 5 atoms × 12.01 g/mol = 60.05 g/mol - Hydrogen (H): 8 atoms × 1.01 g/mol = 8.08 g/mol - **Total Molar Mass** = 68.13 g/mol

Step 2: Calculate Moles of L-tryptophan

Use the formula to calculate the number of moles:\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]For L-tryptophan:\[ \text{Moles of L-tryptophan} = \frac{1.00 \, \text{g}}{204.25 \, \text{g/mol}} \approx 0.00490 \, \text{mol} \]

Step 3: Calculate Moles of Magnesium Sulfate Heptahydrate

Apply the same formula to find moles of magnesium sulfate heptahydrate:\[ \text{Moles of magnesium sulfate heptahydrate} = \frac{1.00 \, \text{g}}{246.47 \, \text{g/mol}} \approx 0.00406 \, \text{mol} \]

Step 4: Calculate Moles of Propane

Calculate the moles of propane using the formula:\[ \text{Moles of propane} = \frac{1.00 \, \text{g}}{68.13 \, \text{g/mol}} \approx 0.0147 \, \text{mol} \]

Key Concepts

Molar Mass

Understanding the concept of molar mass is crucial when dealing with chemical compounds in chemistry. The molar mass is the weight of one mole (or 6.022 × 10²³ particles) of a substance, usually expressed in grams per mole (g/mol). To find the molar mass of a compound, add up the atomic masses of all the elements present in the compound according to their quantities.
For example, to find the molar mass of L-tryptophan

• Identify the elements and their counts: Carbon (11), Hydrogen (12), Nitrogen (2), Oxygen (2).
• Multiply each element's atomic mass by its count.
• Add the results together: 204.25 g/mol.

This method applies to any compound to determine how much one mole weighs, making it an integral step in stoichiometry for calculating moles from a given mass.

L-tryptophan

L-tryptophan is an essential amino acid, which means it is vital for human health but cannot be synthesized by the body. It must be obtained from dietary sources. Consequently, knowing its molar mass is essential for nutrition science, as it helps in calculating the exact amount needed from food or supplements.
The chemical formula of L-tryptophan is (C₁₁H₁₂N₂O₂). This formula signifies it contains 11 carbon atoms, 12 hydrogen atoms, 2 nitrogen atoms, and 2 oxygen atoms. Using the atomic masses, its total molar mass is calculated as 204.25 g/mol. To find out how many moles are in a certain mass of L-tryptophan, divide the mass in grams by its molar mass. This technique provides a foundational understanding necessary for applying L-tryptophan in dietary calculations and research.

Magnesium Sulfate Heptahydrate

Magnesium sulfate heptahydrate, commonly known as Epsom salts, has the formula MgSO₄·7H₂O. It is a compound widely used in medicine and agriculture thanks to its role in providing vital nutrients and therapeutic properties.
When calculating its molar mass, consider both the main compound and the water molecules:

• Magnesium: 24.31 g/mol
• Sulfur: 32.07 g/mol
• Oxygen in sulfate: 64.00 g/mol
• Water (7 H₂O): 126.14 g/mol

This results in a total molar mass of 246.47 g/mol, crucial for precise dosing in medical applications or fertilizer formulation based on the number of moles needed.

Propane

Propane is a simple hydrocarbon, widely used as a fuel in heating appliances, cooking equipment, and vehicles. It is a member of the alkane family with the chemical formula C₃H₈.
To calculate its molar mass:

• Carbon (3 atoms): 36.03 g/mol
• Hydrogen (8 atoms): 8.08 g/mol

This sums up to 44.09 g/mol. Knowing the molar mass of propane is essential for determining the amount of energy yields and efficiency calculations. By dividing a given mass by the molar mass, you can discover the number of moles present, which is crucial for precise and efficient use in energy production and supply.