Question

A solution of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\right)\) in water is prepared by dissolving \(75.0 \mathrm{~mL}\) 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?

Short answer

The molarity of the ethanol solution is approximately 5.144 M.

Step-by-step solution

Calculate the mass of ethanol

Given the volume and density of ethanol, we can calculate the mass of ethanol by using the formula: mass = volume × density. Here, the volume of ethanol is 75.0 mL, and the density is 0.79 g/cm³. Since 1 mL is equivalent to 1 cm³, we can keep the same unit. mass_ethanol = volume_ethanol × density_ethanol mass_ethanol = 75.0 mL × 0.79 g/mL mass_ethanol = 59.25 g The mass of ethanol is 59.25 grams.

Calculate the number of moles of ethanol

To find the number of moles of ethanol, we will use the molar mass of ethanol, which is given by the formula: C₂H₅OH. The molar mass of ethanol is approximately 46.07 g/mol, considering the atomic masses of carbon (12.01), hydrogen (1.01) and oxygen (16.00). number_of_moles = mass_ethanol / molar_mass_ethanol number_of_moles = 59.25 g / 46.07 g/mol number_of_moles ≈ 1.286 mol The number of moles of ethanol in the solution is approximately 1.286 moles.

Calculate the molarity of the ethanol solution

Molarity is defined as the number of moles of solute per liter of solution. We are given the total volume of the solution, which is 250.0 mL or 0.250 L. We can now calculate the molarity of ethanol in the solution using the number of moles and the total volume: molarity_ethanol = number_of_moles / total_volume molarity_ethanol = 1.286 mol / 0.250 L molarity_ethanol ≈ 5.144 M The molarity of the ethanol solution is approximately 5.144 M.

Key concepts

Solution Concentration

When discussing the composition of a mixture, we often focus on the solution concentration. This is a measure of how much solute is dissolved within a given volume of solvent. In the world of chemistry, several types of concentrations are used, but one of the most common is molarity.

Molarity (\( M \)) is defined as the number of moles of solute per liter of solution, which tells us the strength of the solution. It's a straightforward way to communicate how concentrated a solution is and is crucial for predicting how substances will react with one another in a mixture. The formula is given as: \[\text{{Molarity}} = \frac{{\text{{moles of solute}}}}{{\text{{volume of solution in liters}}}}.\]
For instance, in the exercise about ethanol, molarity tells us how concentrated the ethanol is within the water solution. Calculating the molarity helps students understand and predict the behavior of substances in real-world scenarios, such as in medical solutions, industrial processes, or laboratory experiments.

Mole Concept

The mole concept is a fundamental bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we can observe. A mole is a unit that represents a quantity of material. Specifically, one mole is equal to Avogadro's number of particles (usually atoms or molecules), which is approximately \(6.022 \times 10^{23}\) particles.

This concept allows us to easily communicate and make calculations regarding the amount of substance involved in chemical reactions. When we discuss molarity, we're often dealing with moles. For example, we might say a solution contains 1.286 moles of ethanol, as was calculated in the given exercise. By using the mole concept, chemists can quantify and understand the relationships in chemical reactions.

Molar Mass

Understanding molar mass is crucial when performing calculations in chemistry, especially when working with solution concentrations and reactions. Molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). It's calculated by summing the atomic masses of all the atoms in a molecule.

Each element's atomic mass can be found on the periodic table and represents the average mass of a single atom of that element in atomic mass units (amu). For example, the molar mass of ethanol (\(C_2H_5OH\)) is calculated using the atomic masses of carbon, hydrogen, and oxygen. This value is critical when converting mass to moles as part of molarity calculations, just as we saw in the exercise with ethanol.

Stoichiometry

The term stoichiometry is derived from two Greek words meaning 'element' and 'measure,' and it involves the quantitative relationships of the elements in chemical reactions. It's very much like a recipe for chemistry where the required amounts of reactants to produce desired products are detailed.

In terms of the calculation process, stoichiometry allows us to predict how much of a substance will be needed or produced in a chemical reaction. It involves using balanced chemical equations to find the balance between reactants and products. The stoichiometry process involves understanding the mole concept and molar mass to ensure that atoms are conserved in the reactions and to calculate quantities such as molarity of solutions, another key point demonstrated in the ethanol solution exercise.