Problem 73 - Chemistry and Chemical Reactivity

Question

What mass is represented by 0.0255 mol of each of the following compounds? (a) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH},\) 2-propanol, rubbing alcohol (b) \(\mathrm{C}_{11} \mathrm{H}_{16} \mathrm{O}_{2},\) an antioxidant in foods, also known as BHA (butylated hydroxyanisole) (c) \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4},\) aspirin (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO},\) acetone, an important industrial solvent

Step-by-Step Solution

Answer

0.0255 moles represent masses of 1.53355 g (2-propanol), 4.5951 g (BHA), 4.59108 g (aspirin), and 1.48204 g (acetone).

Step 1: Calculate Molar Mass for C3H7OH (2-Propanol)

Firstly, we need to determine the molar mass of 2-propanol, \(\mathrm{C}_{3}\mathrm{H}_{7}\mathrm{OH}\). The atomic weights are: C = 12.01, H = 1.008, O = 16.00. The molar mass will be calculated as follows: \(3 \times 12.01 + 8 \times 1.008 + 16.00 = 60.10\ \mathrm{g/mol}\) (note: \(8 \times 1.008\) accounts for the OH group in addition to the 7 hydrogens).

Step 2: Calculate Mass for 0.0255 mol of C3H7OH

To find the mass of 0.0255 moles of 2-propanol, use the formula: \(\text{mass} = \text{moles} \times \text{molar mass}\). So, we calculate: \(0.0255 \times 60.10 = 1.53355\ \mathrm{g}\).

Step 3: Calculate Molar Mass for C11H16O2 (BHA)

Next, calculate the molar mass for BHA, \(\mathrm{C}_{11}\mathrm{H}_{16}\mathrm{O}_{2}\). The atomic weights are: C = 12.01, H = 1.008, O = 16.00. Hence, \(11 \times 12.01 + 16 \times 1.008 + 2 \times 16.00 = 180.24\ \mathrm{g/mol}\).

Step 4: Calculate Mass for 0.0255 mol of C11H16O2

Use the formula \(\text{mass} = \text{moles} \times \text{molar mass}\) to find the mass: \(0.0255 \times 180.24 = 4.5951\ \mathrm{g}\).

Step 5: Calculate Molar Mass for C9H8O4 (Aspirin)

Determine the molar mass of aspirin, \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\). The atomic weights are: C = 12.01, H = 1.008, O = 16.00. Calculate: \(9 \times 12.01 + 8 \times 1.008 + 4 \times 16.00 = 180.16\ \mathrm{g/mol}\).

Step 6: Calculate Mass for 0.0255 mol of C9H8O4

Using the formula \(\text{mass} = \text{moles} \times \text{molar mass}\), we find the mass as: \(0.0255 \times 180.16 = 4.59108\ \mathrm{g}\).

Step 7: Calculate Molar Mass for (CH3)2CO (Acetone)

Determine the molar mass for acetone, \((\mathrm{CH}_{3})_{2}\mathrm{CO}\). Atomic weights are: C = 12.01, H = 1.008, O = 16.00. The calculation is \(3 \times 12.01 + 6 \times 1.008 + 16.00 = 58.08\ \mathrm{g/mol}\).

Step 8: Calculate Mass for 0.0255 mol of (CH3)2CO

Finally, use the formula \(\text{mass} = \text{moles} \times \text{molar mass}\) to calculate: \(0.0255 \times 58.08 = 1.48204\ \mathrm{g}\).

Key Concepts

2-propanol

2-Propanol, commonly known as isopropanol or rubbing alcohol, is a colorless compound with the formula \(\mathrm{C}_3\mathrm{H}_7\mathrm{OH}\). It is widely used as a disinfectant and a solvent. To calculate the molar mass of 2-propanol, we start by considering the atomic weights:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Oxygen (O): 16.00 g/mol

The compound contains 3 carbon atoms, 8 hydrogen atoms (including the OH group), and 1 oxygen atom. The molar mass is thus calculated as \[ 3 \times 12.01 + 8 \times 1.008 + 16.00 = 60.10 \ g/mol \] To find out the mass of 0.0255 moles of 2-propanol, use the formula: \[ \text{mass} = \text{moles} \times \text{molar mass} \] Substituting the values, we get \[ 0.0255 \times 60.10 = 1.53355 \ g \]. This shows that 0.0255 moles of 2-propanol has a mass of approximately 1.5336 grams.

butylated hydroxyanisole (BHA)

Butylated hydroxyanisole, or BHA, is a synthetic antioxidant with the chemical formula \(\mathrm{C}_{11}\mathrm{H}_{16}\mathrm{O}_2\). It is often used to prevent spoilage in food products due to its properties that inhibit oxidation. To determine its molar mass, we use:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Oxygen (O): 16.00 g/mol

The calculation involves 11 carbon atoms, 16 hydrogen atoms, and 2 oxygen atoms, which results in\[ 11 \times 12.01 + 16 \times 1.008 + 2 \times 16.00 = 180.24 \ g/mol \] The mass of 0.0255 moles of BHA can be calculated using: \[ \text{mass} = \text{moles} \times \text{molar mass} \]Thus, \[ 0.0255 \times 180.24 = 4.5951 \ g \]This means 0.0255 moles of BHA weighs approximately 4.595 grams.

aspirin

Aspirin, chemically known as acetylsalicylic acid, has the formula \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_4\). It is one of the most common medications used worldwide for pain relief, reducing fever, and as an anti-inflammatory. The molecular composition comprises the following atomic components:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Oxygen (O): 16.00 g/mol

For the molar mass calculation, aspirin contains 9 carbons, 8 hydrogens, and 4 oxygens, giving\[ 9 \times 12.01 + 8 \times 1.008 + 4 \times 16.00 = 180.16 \ g/mol \] The mass for 0.0255 moles of aspirin can be calculated as:\[ \text{mass} = \text{moles} \times \text{molar mass} \]So,\[ 0.0255 \times 180.16 = 4.59108 \ g \]Hence, 0.0255 moles of aspirin has a mass close to 4.591 grams.

acetone

Acetone is a simple organic compound with the formula \((\mathrm{CH}_3)_2\mathrm{CO}\). It is widely known as a solvent and is used in many industrial applications and also as the main ingredient in nail polish remover. The calculation of its molar mass involves:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Oxygen (O): 16.00 g/mol

Acetone consists of 3 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom, leading to\[ 3 \times 12.01 + 6 \times 1.008 + 16.00 = 58.08 \ g/mol \] To find the mass of 0.0255 moles of acetone:\[ \text{mass} = \text{moles} \times \text{molar mass} \] This gives\[ 0.0255 \times 58.08 = 1.48204 \ g \]Thus, 0.0255 moles of acetone weigh about 1.482 grams.