Question

A \(10.00 \%\) -by-mass solution of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in water has a density of \(0.9831 \mathrm{g} / \mathrm{mL}\) at \(15^{\circ} \mathrm{C}\) and \(0.9804 \mathrm{g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C} .\) Calculate the molality of the ethanol-water solution at these two temperatures. Does the molality differ at the two temperatures (that is, at 15 and \(25^{\circ} \mathrm{C}\) )? Would you expect the molarities to differ? Explain.

Short answer

The calculated molality of the ethanol-water solution is 2.41 moles/kg at both 15°C and 25°C. Despite the temperature change, the molality remains the same as it only depends on the mass of the solvent (water in this case) and the number of moles of solute (ethanol), and these do not change with temperature. On the other hand, the molarities would be expected to differ at the two temperatures, since molarity is dependent on the volume of the solution, and the volume can change with temperature.

Step-by-step solution

Understanding Molality

Molality \(m\) is a measure of the concentration of a solute in a solution, or a measure of the moles of solute per kilogram of solvent. Its unit is moles/kg.

Calculating the Mass of the Solution

In this case, using the mass percentage and density at 15°C, the mass of the solution can be calculated. The density given (0.9831 g/mL) is equivalent to 0.9831 kg/L. Since the solution is 10% ethanol by mass, the mass of ethanol in 1 L of solution is 0.10 * 0.9831 kg = 0.09831 kg.

Calculating Molality at 15°C

Once the mass of the ethanol is known, the molality can be calculated. The molar mass of ethanol \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) is approximately 46.07 g/mol or 0.04607 kg/mol. The number of moles of ethanol in the solution is therefore 0.09831 kg / 0.04607 kg/mol = 2.133 moles. The mass of the water in the solution is 0.9831 kg - 0.09831 kg = 0.88479 kg. Thus, the molality of the solution at 15°C is 2.133 moles / 0.88479 kg = 2.41 moles/kg.

Repeating Calculations for 25°C

The above calculations can be repeated for the solution at 25°C with a density of 0.9804 kg/L. The mass of ethanol in the solution would be 0.10 * 0.9804 kg = 0.09804 kg and the mass of the water would be 0.9804 kg - 0.09804 kg = 0.88236 kg. Thus, the molality at 25°C is 2.13 moles / 0.88236 kg = 2.41 moles/kg.

Comparing the Molalities

Observing the molality at both temperatures, it can be seen that they are equal - the molality does not change with temperature.

Discussing Molarity

However, molarity - moles of solute per litre of solution - would be expected to differ at different temperatures. This is because molarity depends on the volume of the solution, which can change with temperature due to thermal expansion or contraction.

Key concepts

Ethanol solution

Ethanol is a common solvent used in many chemical reactions and processes. It is an organic compound with the formula \( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} \). In this context, we are dealing with a solution where ethanol is mixed with water. A 10% by mass ethanol solution means that the mass of ethanol is 10% of the total mass of the solution. Ethanol solutions are often used for studying physical and chemical properties because they exhibit interesting behaviors with temperature changes.

Density

Density is a measure of mass per unit volume. When we say the density of the ethanol solution is 0.9831 g/mL at \(15^{\circ} \mathrm{C}\), this means that 1 mL of the solution has a mass of 0.9831 grams.
To convert this to a familiar unit for molality calculations, it is useful to express this in kg/L, which is equivalent to the values provided.
Density is crucial in converting between mass and volume, especially when dealing with solutions at varying temperatures.

Temperature effect on solutions

Temperature can affect both the physical and chemical properties of solutions, such as density, solubility, and reactivity. As temperature increases, most liquids expand, which affects their volume and thus their density.
A notable example is how the density of the ethanol solution decreases from 0.9831 g/mL at \(15^{\circ} \mathrm{C}\) to 0.9804 g/mL at \(25^{\circ} \mathrm{C}\). This decrease in density is typical because the solution expands slightly at higher temperatures.
Understanding these effects is important when considering changes in properties like molarity, which depends on volume.

Molarity

Molarity, unlike molality, is the concentration of a solution expressed as the number of moles of solute per liter of solution. While molality is unaffected by temperature, molarity can change because temperature affects the solution's volume.
As the solution heats up, its volume increases while the number of moles of solute remains constant, thus lowering the molarity.

• This distinction is crucial in experiments where precise concentration measurements are necessary.
• Molarity is more practical in reactions occurring at constant temperature but less reliable across different temperatures.

Concentration calculations

Calculations dealing with concentrations, such as molality and molarity, are vital in chemistry for preparing solutions and understanding chemical properties.

• Molality: Number of moles of solute per kilogram of solvent. It remains constant with temperature changes.
• Molarity: Number of moles of solute per liter of solution. It changes with temperature due to volume variations.

For chemists, selecting the appropriate expression for concentration in a given experiment is essential to ensure accuracy and relevance of results. Consequently, a deep understanding of both helps ensure robust outcomes in both lab and industrial settings.