Calculate mole frication, molarity and morality of ethanol solution which is 50% by weight of Ethanol in H2O and has a density of. 9144 gram per ec

To calculate the mole fraction, molarity, and molality of a 50% by weight ethanol solution in water with a density of 0.9144 g/cm³, we need to break down the problem into manageable steps. Let's tackle each part systematically.

Mole Fraction Calculation

The mole fraction is a way of expressing the concentration of a component in a mixture. It is calculated using the formula:

X_component = n_component / (n_component + n_solvent)

First, we need to determine the number of moles of ethanol and water in the solution. Let's assume we have 100 grams of the solution for simplicity.

• Mass of ethanol: 50 grams (since it's 50% by weight)
• Mass of water: 50 grams

Next, we convert these masses to moles:

• Moles of ethanol:

  Using the molar mass of ethanol (C₂H₅OH), which is approximately 46.07 g/mol:

  n_ethanol = 50 g / 46.07 g/mol ≈ 1.085 moles

• Moles of water:

  The molar mass of water (H₂O) is about 18.02 g/mol:

  n_water = 50 g / 18.02 g/mol ≈ 2.775 moles

Now we can calculate the mole fraction of ethanol:

X_ethanol = n_ethanol / (n_ethanol + n_water) = 1.085 / (1.085 + 2.775) ≈ 0.281

Molarity Calculation

Molarity (M) is defined as the number of moles of solute per liter of solution. We already have the moles of ethanol, but we need to find the volume of the solution.

Using the density to find the volume:

Density = mass/volume

Rearranging gives us:

Volume = mass / density = 100 g / 0.9144 g/cm³ ≈ 109.36 cm³ = 0.10936 L

Now we can calculate molarity:

M = n_ethanol / volume = 1.085 moles / 0.10936 L ≈ 9.90 M

Molality Calculation

Molality (m) is defined as the number of moles of solute per kilogram of solvent. We already have the moles of ethanol and the mass of water:

First, convert the mass of water to kilograms:

50 g = 0.050 kg

Now we can calculate molality:

m = n_ethanol / mass_water = 1.085 moles / 0.050 kg = 21.70 m

Summary of Results

• Mole Fraction of Ethanol: 0.281
• Molarity of Ethanol: 9.90 M
• Molality of Ethanol: 21.70 m

In summary, we have successfully calculated the mole fraction, molarity, and molality of the ethanol solution. Each of these measures provides a different perspective on the concentration of ethanol in the solution, which can be useful in various chemical applications.