Question

Mole fraction of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in ethanolwater system is \(0.25 .\) Thus it has: a. \(46 \%\) ethanol by weight of solution b. \(54 \%\) water by weight of solution c. \(25 \%\) ethanol by weight of solution d. \(75 \%\) water by weight of solution

Short answer

The solution has 46% ethanol and 54% water by weight.

Step-by-step solution

Understanding Mole Fraction

The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution. Here, the mole fraction of ethanol is given as 0.25, meaning one mole of ethanol per four moles total (ethanol + water).

Calculate Moles of Each Component

Assuming we have a total of 4 moles in the system, given the mole fraction of ethanol is 0.25, there is 1 mole of ethanol and 3 moles of water (0.25 * 4 = 1 for ethanol and 0.75 * 4 = 3 for water).

Find Molar Mass of Each Substance

The molar mass of ethanol is calculated as follows: C (12 g/mol * 2) + H (1 g/mol * 6) + O (16 g/mol) = 46 g/mol. The molar mass of water (H2O) is H (1 g/mol * 2) + O (16 g/mol) = 18 g/mol.

Calculate Total Mass of Each Component

Determine the mass for each component: 1 mole of ethanol is 46 g (1 * 46 g/mol) and 3 moles of water are 54 g (3 * 18 g/mol).

Calculate Total Mass of Solution

The total mass of the solution is the sum of the mass of ethanol and the mass of water: 46 g (ethanol) + 54 g (water) = 100 g.

Determine Weight Percentage of Each Component

To find the percentage by weight of each component, calculate: \[(\frac{46 g}{100 g}) \times 100 = 46\%\] for ethanol and \[(\frac{54 g}{100 g}) \times 100 = 54\%\] for water.

Key concepts

Ethanol-Water System

An ethanol-water system is a common example of a binary mixture consisting of two components, ethanol (\( \text{C}_2 \text{H}_5 \text{OH} \)) and water (\( \text{H}_2\text{O} \)). Understanding the interaction between ethanol and water is essential in chemistry, especially when determining properties like mole fraction, weight percentage, and total mass of the solution.

The mole fraction in such systems is a useful measure that explains how much of one component is present relative to the total mixture. In this exercise, the mole fraction of ethanol is given as 0.25, indicating that for every 4 moles of the total mixture, 1 mole is ethanol.

Ethanol and water interact in unique ways due to their molecular structures. Ethanol, being an alcohol, forms hydrogen bonds with water, leading to interesting properties when the two are mixed. The knowledge of such interactions is crucial for calculations that predict the behavior or outcome of chemical processes involving these substances.

Molar Mass Calculation

Calculating the molar mass of a substance is fundamental to understanding how chemical equations and solutions function. The molar mass is the mass of one mole of a given substance. For ethanol (\( \text{C}_2 \text{H}_5 \text{OH} \)), we calculate it by adding the molar masses of all atoms in a molecule:

• Carbon (C) has an atomic mass of 12 g/mol.
• Hydrogen (H) has an atomic mass of 1 g/mol.
• Oxygen (O) has an atomic mass of 16 g/mol.

For ethanol, the calculation becomes:\[ 2 \times 12 \,\text{g/mol (C)} + 6 \times 1 \,\text{g/mol (H)} + 1 \times 16 \,\text{g/mol (O)} = 46 \,\text{g/mol} \]
Similarly, for water (\( \text{H}_2\text{O} \)), it is:\[ 2 \times 1 \,\text{g/mol (H)} + 1 \times 16 \,\text{g/mol (O)} = 18 \,\text{g/mol} \]
These values are critical for any further weight or mass-related calculations in chemistry. Understanding how to determine molar mass helps in calculating the masses of substances needed or produced in reactions.

Weight Percentage Calculation

Weight percentage is a way of expressing concentration by indicating the percentage of the total weight of the solution that one component makes up. In the context of an ethanol-water system, finding the weight percentage allows us to describe the composition of the mixture in weight terms, which can be quite practical, especially in industrial applications.

To calculate weight percentage, you divide the mass of the component by the total mass of the solution and multiply by 100:
For ethanol:\[ \left( \frac{46 \,\text{g (mass of ethanol)}}{100 \,\text{g (total mass of solution)}} \right) \times 100 = 46\% \]
For water:\[ \left( \frac{54 \,\text{g (mass of water)}}{100 \,\text{g (total mass of solution)}} \right) \times 100 = 54\% \]
Weight percentages are an efficient way to communicate the concentration of each component in a mixture, especially when dealing with large-scale production or laboratory procedures where precise measurements can impact the results significantly. It gives a tangible sense of how each substance contributes to the overall mixture.