Question

${10^{24}}$ molecules of solute are dissolved in \[{10^{25}}\] molecules of solvent, the mole fraction of solute in solution is:
A. \[0.09\]
B. \[0.08\]
C. \[0.07\]
D. \[0.9\]

Answer 1

Hint:Mole can be defined as the amount of substance that contains as many elementary entities as there are atoms in \[0.012{\text{kg}}\] of carbon-12. The entities may be atoms, molecules, ions or other particles. Mole fraction is the number of moles of solute divided by the total number of moles in the solution.

Complete step by step answer:
A mole is a certain amount of material corresponding to a specified number of molecules, atoms, electrons, or any other specified types of particles. The word has been introduced by William Ostwald. Later mole has been approved as an SI unit. In the SI system, a mole is composed of \[6.022 \times {10^{23}}\] molecules. This number is called Avogadro number.
Number of moles can be represented as mass divided by molecular weight.
Mole fraction is simply the number of moles of a particular compound in a mixture or solution divided by the total number of moles in the mixture of solution.
Let’s consider the solute is named as A and the solvent is named as B. Number of moles of solute A is denoted by ${{\text{n}}_{\text{A}}}$ and number of moles of solvent B is denoted by \[{{\text{n}}_{\text{B}}}\].
Therefore mole fraction of A can be expressed as:
\[{{\text{X}}_{\text{A}}} = \dfrac{{{{\text{n}}_{\text{A}}}}}{{{{\text{n}}_{\text{A}}} + {{\text{n}}_{\text{B}}}}}\]
It is given that \[{{\text{n}}_{\text{A}}} = {10^{24}}\]and \[{{\text{n}}_{\text{B}}} = {10^{25}}\].
Substituting these values in the above equation, we get
\[{{\text{X}}_{\text{A}}} = \dfrac{{{{10}^{24}}}}{{{{10}^{24}} + {{10}^{25}}}} = \dfrac{{{{10}^{24}}}}{{1.1 \times {{10}^{25}}}} = 0.09\]
Therefore option A is correct.


Additional information- Mole fraction is temperature independent. A mixture of known mole fractions can be prepared by weighing the masses of constituents. When ideal gases are mixed, mole fraction can be expressed as ratio of partial pressure to total pressure of mixture.

Note:
Concentration can also be derived from the number of moles. Concentration generally refers to the quantity of some substance per unit volume. Mass per unit volume, moles per unit volume, parts per million, parts per million by volume, molarity, molality and normality are some ways of expressing concentration.