Problem 30 - Chemistry An Atoms First Approach

Question

A solution of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in water is prepared by dissolving 75.0 mL of ethanol (density \(=0.79 \mathrm{g} / \mathrm{cm}^{3}\) ) in enough water to make \(250.0 \mathrm{mL}\) of solution. What is the molarity of the ethanol in this solution?

Step-by-Step Solution

Answer

First, we find the mass of ethanol: Mass = 75.0 cm³ × 0.79 g/cm³ = 59.25 g. Next, we find the moles of ethanol: Moles = 59.25 g / 46.07 g/mol ≈ 1.285 mol. Then, we convert the volume of the solution to liters: 250.0 mL × (1 L / 1000 mL) = 0.250 L. Finally, we calculate the molarity: Molarity = 1.285 mol / 0.250 L ≈ 5.14 M. So, the molarity of ethanol in the solution is \(5.14\,M\).

Step 1: Find the mass of ethanol

First, calculate the mass of ethanol using the given volume and density: Mass = Volume × Density The volume and density of ethanol is given as 75.0 mL and 0.79 g/cm³, respectively. Note that 1 mL = 1 cm³. So, the mass can be calculated as follows: Mass = 75.0 cm³ × 0.79 g/cm³

Step 2: Calculate the moles of ethanol

Next, use the molar mass of ethanol to find the number of moles of ethanol. The molar mass of ethanol (C₂H₅OH) is (2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 46.07 g/mol. Moles of ethanol = Mass / Molar mass Moles = (Mass from Step 1) / 46.07 g/mol

Step 3: Calculate the solution's volume in liters

We are given the total volume of the solution as 250.0 mL. Convert this volume to liters: Volume in Liters = Total Volume (mL) × (1 L / 1000 mL) Volume in Liters = 250.0 mL × (1 L / 1000 mL)

Step 4: Calculate the molarity

Finally, find the molarity of ethanol in the solution by dividing the moles of ethanol (from Step 2) by the solution's volume in liters (from Step 3). Molarity = Moles of ethanol / Volume of solution in Liters Now, let's calculate the molarity using the information gathered in the previous steps.

Key Concepts

Ethanol Solution Preparation

Preparing an ethanol solution correctly involves measuring accurately the volume of ethanol needed and mixing it with an appropriate amount of water to achieve the desired concentration.

The first step is to measure the ethanol volume. In our case, we have 75.0 mL of ethanol. It is crucial to measure this volume using precise tools like a graduated cylinder to maintain the accuracy of the experiment. Next, the ethanol is mixed into a sufficient quantity of water to reach the final solution volume, here specified as 250.0 mL.

To ensure the solution is homogenous, it should be stirred thoroughly. Homogeneity is vital because it guarantees that the concentration of ethanol will be uniform throughout the solution. This uniformity is essential when samples are taken for testing the molarity of the solution, thereby providing reliable results.

Mass, Volume, and Density Relationship

The relationship between mass, volume, and density is a foundational concept in chemistry, often encapsulated by the formula: Density = Mass/Volume.

This formula allows us to calculate one of the three variables if the other two are known. In the context of ethanol solution preparation, understanding this relationship is critical for determining the mass of ethanol given its density and the volume used.

Density of Ethanol

For instance, ethanol has a density of 0.79 g/cm³. When we know the volume of ethanol, like our 75.0 mL (or cm³ due to the equivalence of 1 mL = 1 cm³), we can find the mass by multiplying the volume by the density. It's important to ensure that units are consistent when performing these calculations to get accurate results.

Molar Mass of Ethanol

The molar mass, sometimes referred to as molecular weight, is the mass of one mole of a substance. It is a fundamental characteristic used to convert between mass and moles of a substance, which is essential in preparing solutions with precise molarity.

The molar mass of ethanol (\( \text{C}_2\text{H}_5\text{OH} \)) is calculated by summing up the atomic masses of each constituent atom in the compound. For ethanol, this means adding the molar masses of two carbon atoms, six hydrogen atoms, and one oxygen atom, giving us a molar mass of 46.07 g/mol.

This information allows us to determine the number of moles of ethanol present in the solution, given the mass calculated using the density and volume relations previously discussed.

Solution Concentration

Solution concentration, particularly molarity, is a measure of how much of a substance is dissolved in a specific amount of solvent. Molarity is defined as the number of moles of solute per liter of solution (mol/L).

To find the molarity, one must know the number of moles of the solute—the substance being dissolved—and the total volume of the solution in liters. Once you have these two pieces of information, calculating the molarity is straightforward: divide the moles of the solute by the volume of the solution in liters.

When preparing solutions, controlling concentration is crucial, as it impacts the reactivity and properties of the solution, making it essential for a wide range of scientific and industrial processes.