Animated Solution for Chemistry - Basic Concepts in Chemistry: The mole fraction of a solute in a $100$ molal aqueous solution is ......... $\times 10^{-2}$ (Round off to the nearest integer). [Given, atomic masses $\text{H}:1.0\text{ u}$, $\text{O}:16.0\text{ u}$]

Unraveling Mole Fractions

Imagine you have a beaker filled with exactly $1\text{ kg}$ of pure water. Now, you start dumping in your solute—$100\text{ moles}$ of it, to be exact! This incredibly concentrated mixture is what we call a $100\text{ molal}$ solution.

Molality ($m$) is a fantastic concentration term because it doesn't care about temperature changes; it's strictly based on the mass of the solvent. By definition, a $100\text{ molal}$ aqueous solution means there are $100\text{ moles}$ of solute dissolved in $1\text{ kg}$ of water.

To find the mole fraction, we need to know the total number of players in our beaker. We know we have $100\text{ moles}$ of the solute team. But what about the water team?

We have $1000\text{ grams}$ of water. Since each mole of water (${\text{H}}_2\text{O}$) weighs $18\text{ grams}$, we can easily find the number of moles:

This number, $55.5$, is a classic 'frequent flyer' in physical chemistry. Memorize it! It will save you precious seconds in exams.

Now, we bring out the mole fraction formula. The mole fraction of the solute, denoted by ${\chi }_{\text{solute}}$, is simply its share of the total moles:

Substituting our known values into the equation:

When we calculate this fraction, we get:

The final boss of this problem is the formatting. The question specifically asks for the answer in the form of an integer multiplied by $10^{-2}$. We need to shift our decimal point to match this requirement.

Rounding $64.3$ to the nearest integer gives us $64$. And just like that, we've cracked the code! Always read the required format carefully to avoid losing marks on a question you've solved perfectly.