A 5.2 molal aqueous solution of methyl alcohol, CH₃OH is supplied. What is the mole fraction of methyl alcohol in the solution?

We are given a 5.2 molal aqueous solution of methyl alcohol (CH₃OH) and need to calculate the mole fraction of methyl alcohol in the solution. Here’s a step-by-step explanation to find the answer:

Step 1: Understand what molality means

Molality is defined as the number of moles of solute (methyl alcohol) per kilogram of solvent (water). A 5.2 molal aqueous solution of methyl alcohol means there are 5.2 moles of CH₃OH in 1 kg of water.

Step 2: Calculate moles of water

The molar mass of water (H₂O) is approximately 18 g/mol. Since 1 kg of water is 1000 g:

Moles of water = 1000 / 18 ≈ 55.56 moles.

Step 3: Calculate the total moles in the solution

The total number of moles in the solution is the sum of the moles of methyl alcohol and the moles of water:

Total moles = Moles of CH₃OH + Moles of H₂O Total moles = 5.2 + 55.56 ≈ 60.76 moles.

Step 4: Calculate the mole fraction of methyl alcohol

The mole fraction of a substance is calculated as:

Mole fraction of CH₃OH = Moles of CH₃OH / Total moles Mole fraction of CH₃OH = 5.2 / 60.76 ≈ 0.086

Final Answer:

The mole fraction of methyl alcohol in a 5.2 molal aqueous solution of methyl alcohol is approximately 0.086.