Problem 144 - General Chemistry

Question

What volume of a solution of ethylene glycol, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\), that is \(56.0 \%\) ethylene glycol by mass contains \(0.350\) mol \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\) ? The density of the solution is \(1.072 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The volume of the solution needed is 36.2 mL.

Step 1: Calculate Mass from Moles

First, determine the mass of ethylene glycol required. Use the molar mass of ethylene glycol to find the total mass. The molar mass of ethylene glycol \(\text{C}_2\text{H}_6\text{O}_2\) is the sum of the atomic masses: \(2\times12.01\) (C) + \(6\times1.01\) (H) + \(2\times16.00\) (O) which equals \(62.08 \, \text{g/mol}\). Multiply the moles by the molar mass: \(0.350 \, \text{mol} \times 62.08 \, \text{g/mol} = 21.728 \, \text{g}\).

Step 2: Determine Total Solution Mass

The solution is \(56.0\%\) ethylene glycol by mass. Thus, the mass of the ethylene glycol is \(56.0\%\) of the total mass of the solution. Set up the equation: \(0.56 \times \text{total mass} = 21.728 \, \text{g}\). Solving for the total mass, we find: \(\text{total mass} = \frac{21.728}{0.56} = 38.8 \, \text{g}\).

Step 3: Convert Mass to Volume

Using the density of the solution, convert the total mass to volume. The density is given as \(1.072 \, \text{g/mL}\). Use the formula: \(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\). Calculate \(\frac{38.8 \, \text{g}}{1.072 \, \text{g/mL}} = 36.2 \, \text{mL}\).

Key Concepts

Ethylene Glycol

Ethylene glycol is a chemical compound with the formula \( ext{C}_2 ext{H}_6 ext{O}_2\). It is widely used for its antifreeze and de-icing properties. This compound can lower the freezing point of water, making it valuable in regions with colder climates. Additionally, ethylene glycol is used in the production of polyester fibers and as a component in some industrial applications.
Unlike water, ethylene glycol is not safe for consumption; it is toxic if ingested. It is essential to handle it with care, especially since it is often mistaken for sweet-tasting liquids due to its slightly sweet taste. Ensure storage in secure containers to avoid accidental ingestion.
In chemical solutions, ethylene glycol can act as a solvent. Its presence in a solution can affect the overall properties, such as freezing and boiling points, making it an important topic of study in fields such as chemistry and materials science.

Molar Mass Calculation

Calculating the molar mass of a compound involves adding the atomic masses of all the atoms in its chemical formula. For ethylene glycol \( ext{C}_2 ext{H}_6 ext{O}_2\), it consists of:

• 2 Carbon (C) atoms, each with a mass of \(12.01 \, \text{amu}\)
• 6 Hydrogen (H) atoms, each with a mass of \(1.01 \, \text{amu}\)
• 2 Oxygen (O) atoms, each with a mass of \(16.00 \, \text{amu}\)

To find the total molar mass, the calculation will be:

• Carbon: \(2 \times 12.01 = 24.02 \, \text{amu}\)
• Hydrogen: \(6 \times 1.01 = 6.06 \, \text{amu}\)
• Oxygen: \(2 \times 16.00 = 32.00 \, \text{amu}\)

The combined molar mass of ethylene glycol is \(62.08 \, \text{g/mol}\).
This result is crucial for various calculations, such as determining the number of moles in a given mass of ethylene glycol and understanding its role in chemical reactions and solutions.

Density and Volume Conversion

Density is a property that relates the mass of a substance to its volume. It is a common concept when dealing with solution concentrations. The formula to remember is:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]In this context, you might have to rearrange the formula to find volume if mass and density are known:\[\text{Volume} = \frac{\text{Mass}}{\text{Density}}\]
In our exercise, the density is given as \(1.072 \, \text{g/mL}\). This means each milliliter (mL) of solution weighs 1.072 grams. To find the volume of the solution with a known mass, plug the values into the equation:

• If the total mass of the solution is given as \(38.8 \, \text{g}\)
• Volume is calculated as \(\frac{38.8 \, \text{g}}{1.072 \, \text{g/mL}} = 36.2 \, \text{mL}\)

Understanding how to convert between mass and volume using density can aid in solving many chemistry problems involving solution concentrations, making it an essential skill for students and professionals alike.