Question

Challenge What volume of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\right)\) is in 100.0 \(\mathrm{mL}\) of 0.15 \(\mathrm{M}\) solution? The density of ethanol is 0.7893 \(\mathrm{g} / \mathrm{mL}\) .

Short answer

The volume of ethanol in 100.0 mL of 0.15 M solution can be calculated as follows: 1. Calculate the number of moles of ethanol: Moles of ethanol = 0.15 × (100 / 1000) = 0.015 moles 2. Calculate the grams of ethanol present in the solution: Molar mass of ethanol (C2H5OH) = 46.08 g/mol Grams of ethanol = 0.015 moles × 46.08 g/mol = 0.6912 g 3. Calculate the volume of ethanol in the solution using density: Density of ethanol = 0.7893 g/mL Volume of ethanol = 0.6912 g / 0.7893 g/mL = 0.8755 mL Therefore, the volume of ethanol in the 100.0 mL of 0.15 M solution is approximately \(0.8755 \: \mathrm{mL}\).

Step-by-step solution

1. Calculate the number of moles of ethanol in the solution

To find the number of moles of ethanol in the solution, we will use the formula: Moles of solute = Molarity × volume of solution (in Liters) Given, Molarity (M) = 0.15 M and volume of solution = 100 mL. To convert mL to L, divide the volume by 1000. Moles of ethanol = Molarity × volume of solution (in L) = 0.15 × (100 / 1000)

2. Calculate the grams of ethanol present in the solution

Ethanol has a molecular formula of C2H5OH. Calculate the molar mass of ethanol: Molar mass of ethanol (C2H5OH) = (2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 24.02 + 6.06 + 16.00 = 46.08 g/mol To find the grams of ethanol in the solution, use the formula: grams of solute = moles of solute × molar mass So, grams of ethanol = moles of ethanol × molar mass of ethanol = (0.15 × 100 / 1000) × 46.08

3. Calculate the volume of ethanol in the solution using density

Given, the density of ethanol is 0.7893 g/mL. To find the volume of ethanol, use the formula: Volume of solute = mass of solute / density of solute So, volume of ethanol in the solution = grams of ethanol / density of ethanol = ((0.15 × 100 / 1000) × 46.08) / 0.7893 Now, calculate the final answer for the given exercise.

Key concepts

Molarity

Molarity (M) is an important concept in chemistry. It tells us how many moles of a solute are present in a given volume of solution. Molarity is defined as the number of moles of solute per liter of solution, and its formula is:\[\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}\]This measure is essential when mixing substances, as it helps to ensure the correct proportions are achieved. For example, in the original exercise, 0.15 M indicates there are 0.15 moles of ethanol in each liter of the solution. To find moles from molarity, multiply the molarity by the volume (in liters) of the solution you're working with. Always remember to convert volumes into liters by dividing milliliters by 1000. This step is crucial for accurate calculations.

Molecular Mass

Molecular mass, or molar mass, is the mass of one mole of a substance. It gives you the weight of a molecule based on the individual atomic masses of each element present in the molecule. To calculate the molecular mass of a compound, add up the atomic masses of all the atoms in its chemical formula. This mass is expressed in grams per mole (g/mol).For ethanol, the molecular formula is \(\text{C}_2\text{H}_5\text{OH}\). Let's break it down:

• Carbon (C): 12.01 g/mol, with 2 carbon atoms, giving you \(2 \times 12.01 = 24.02\) g/mol.
• Hydrogen (H): 1.01 g/mol, with 6 hydrogen atoms, totaling \(6 \times 1.01 = 6.06\) g/mol.
• Oxygen (O): 16.00 g/mol, and there's one oxygen atom, so \(1 \times 16.00 = 16.00\) g/mol.

Add these together to get the molar mass of ethanol as 46.08 g/mol. Understanding molecular mass is fundamental for converting between moles and grams when working with chemical reactions.

Density

Density is a measure of how much mass is contained in a given volume. It is a characteristic of physical properties of a substance and is expressed in units such as grams per milliliter (g/mL) or kilograms per liter (kg/L). The formula for density is:\[\text{Density} = \frac{\text{mass}}{\text{volume}}\]In the context of the exercise, knowing the density of ethanol as 0.7893 g/mL allows us to determine how much space a certain mass of ethanol will occupy. This is particularly useful when calculating the volume from a known mass. For example, with the calculated mass of ethanol from the molarity, dividing by the density gives you the exact volume the ethanol will take up in the solution. Understanding density helps in converting between mass and volume in practical scenarios.

Concentration Units

Concentration units are methods to express how much solute is present in a solution. Each unit has its unique use case, making it easier to communicate concentration across different contexts. Common concentration units include:

• Molarity (M): Representing moles per liter, it's a standard in chemistry for expressing solution concentration. It's convenient when precise chemical reactions are involved.
• Mass percent: Indicates the mass of solute per 100 parts of solution, usually in grams. It's useful in industries where compositions are required in mass units.
• Volume percent: Represents the volume of solute per 100 parts of solution, typically in milliliters, frequently used in liquid-liquid mixtures.

In practice, choosing the right concentration unit depends on the context of the experiment or industrial process. For quantitative chemical reactions, molarity is invaluable, as it directly relates the amount of substance to the volume of the solution.