Can a 1.446 g sample of potassium reacts with 8.178 g of chlorine to produce potassium chloride as the only product?

Yes. The formula for potassium chloride is KCl, showing that equal numbers of atoms of potassium and chlorine are required to form the compound. The gram atomic masses of these two atoms are close enough that the given amounts of the two elements show far more than enough chlorine to complete the reaction. Therefore, the only product of the reaction will be potassium chloride, but there will be a considerable amount of unreacted chlorine remaining after the reaction is complete.