If ratio of mole fraction of solute to solvent is unity, what would be % by weight? (concentration of solute) M solute = molecular mass of solute, M solvent = M molecular mass of solvent)

(M solute / (M solute + M solvent)) x 100

To find the percentage by weight (concentration of solute), let’s break it down step by step for clarity and simplicity, while keeping the key concept in mind: the mole fraction of solute is the ratio of moles of solute to the total moles in the solution.

Given:

• The ratio of mole fraction of solute to solvent is unity, i.e.,
• (mole fraction of solute) / (mole fraction of solvent) = 1.

This implies: mole fraction of solute = mole fraction of solvent = 1/2 (Since their sum must equal 1).

Step 1: Express mole fraction

Mole fraction is defined as:

mole fraction of solute = (n solute) / (n solute + n solvent) mole fraction of solvent = (n solvent) / (n solute + n solvent)

Here, mole fraction of solute = mole fraction of solvent = 1/2, so the ratio satisfies the condition of unity.

Step 2: Relate to masses and molecular masses

The number of moles is given by:

n = mass / molecular mass

Let:

• m solute = mass of solute
• m solvent = mass of solvent
• M solute = molecular mass of solute
• M solvent = molecular mass of solvent

Substitute the values into the mole fraction equations.

Step 3: Simplify mass ratio

The condition mole fraction of solute = mole fraction of solvent implies:

(m solute / M solute) / ((m solute / M solute) + (m solvent / M solvent)) = 1/2

Rearranging gives:

(m solute / M solute) = (m solvent / M solvent)

This means:

(m solute / m solvent) = (M solute / M solvent)

Step 4: Calculate percentage by weight

The percentage by weight (concentration of solute) is defined as:

Concentration of solute = (m solute / (m solute + m solvent)) x 100

Substitute the proportionality relation:

Concentration of solute = (M solute / (M solute + M solvent)) x 100

Final Answer:

The percentage by weight of solute is:

(M solute / (M solute + M solvent)) x 100