Question

If the mole fraction of a solute in a binary solution is \(0.3\), what could be the mole fraction of the solvent in the solution?

Short answer

Answer: The mole fraction of the solvent in the binary solution is 0.7.

Step-by-step solution

Recall the relationship between mole fractions of components in a binary solution

A binary solution consists of just two components: the solute and the solvent. The mole fraction of each component must add up to 1, mathematically represented by: \( x_{solute} + x_{solvent} = 1 \) where \( x_{solute} \) is the mole fraction of the solute and \(x_{solvent}\) is the mole fraction of the solvent.

Plug in the given value for the mole fraction of the solute

The problem states that the mole fraction of the solute (\(x_{solute}\)) is 0.3. Substitute this value into the equation: \( 0.3 + x_{solvent} = 1 \)

Solve the equation for the mole fraction of the solvent

Subtract the mole fraction of the solute from both sides of the equation to isolate \(x_{solvent}\): \( x_{solvent} = 1 - 0.3 \) \( x_{solvent} = 0.7 \) So the mole fraction of the solvent in the binary solution is 0.7.