In the case of ideal solutions, the activity \( a_i \) of a component is defined as being directly proportional to its mole fraction \( x_i \).
For ideal behavior, the proportionality constant is 1, which means:
\[
a_i = x_i
\]
This definition simplifies many thermodynamic calculations and holds true only under the assumption of ideal mixing, where the interactions between unlike molecules are the same as those between like molecules.
Hence, for ideal solutions, the activity of a component is equal to its mole fraction.