(a) Define the following terms:
(i) Mole fraction (ii) Van't Hoff factor
(b) `100mg` of a protein is dissolved in enough water to make `10.0 mL` of a solution. If this solution has an osmotic pressure of `13.3 mm Hg` at `25^(@)C`, what is the molar mass of protein?
`(R=0.821 L "atom mol"^(-1)K^(-1) "and" 760mm Hg=1` atm.)

Explanation

### Step-by-Step Solution

#### (a) Definitions

**(i) Mole Fraction:**
Mole fraction (denoted as \(X\)) is defined as the ratio of the number of moles of a particular component in a solution to the total number of moles of all components in that solution. Mathematically, for a component A in a solution containing components A and B, the mole fraction of A can be expressed as:

\[
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