Mole fraction is expressed as the number of moles of solute over the total number of moles of solute and the number of moles of solvent. When expressed in molal, this is equal to number of moles of solute per liter solvent. If the mole fraction is 1.00, this means, all that is in the solution is solute. Hence the molal equivalent is 1.00 too
Since the name of the acid (and the equation) is not given, you must assume that it is a 1:1 ratio. Use equation: volume of acid x molarity of acid = volume of base x molarity of base (when the ratio is 1:1).