Final answer:
To find the mole fraction of KCl in the solution, we need to calculate the moles of KCl and moles of water, and then use these values to calculate the mole fraction. The mole fraction is the ratio of the moles of KCl to the total moles of solute and solvent in the solution. In this case, we can calculate the moles of KCl by dividing the mass of KCl by its molar mass, and the moles of water by subtracting the mass of KCl from the total mass of the solution and dividing it by the molar mass of water.
Step-by-step explanation:
First, we need to calculate the mole fraction of KCl, which is the ratio of the moles of KCl to the total moles of solute and solvent in the solution. The weight/weight % of KCl in the solution is given as 26.3%. This means that 26.3 g of KCl is present in 100 g of the solution. We can convert this mass of KCl into moles by dividing it by the molar mass of KCl. The molar mass of KCl is 74.55 g/mol. Therefore, the moles of KCl in the solution is:
Moles of KCl = (Mass of KCl / Molar mass of KCl) = (26.3 g / 74.55 g/mol)
Next, we need to calculate the moles of water in the solution. We know that the total mass of the solution is 100 g, and the mass of KCl is 26.3 g. Therefore, the moles of water in the solution is:
Moles of water = (Total mass of solution - Mass of KCl) / Molar mass of water
Finally, we can calculate the mole fraction of KCl:
Mole fraction of KCl = Moles of KCl / (Moles of KCl + Moles of water)
By substituting the values into the equation, we get:
Mole fraction of KCl = (26.3 g / 74.55 g/mol) / ((26.3 g / 74.55 g/mol) + ((100 g - 26.3 g) / 18.015 g/mol))
Simplifying this expression will give us the mole fraction of KCl in the solution.