Final answer:
A 1 M solution has a concentration of 1 mole of solute per liter of solution (molarity), whereas a 1 m solution has 1 mole of solute per kilogram of solvent (molality). These are different because molarity depends on the volume of the solution, while molality depends on the mass of the solvent.
Step-by-step explanation:
The main difference between a 1 M solution and a 1 m solution lies in the units used for expressing concentration. Molarity (M) measures the number of moles of solute per liter of solution, whereas molality (m) measures the number of moles of solute per kilogram of solvent.
Therefore, a 1 M solution has 1 mole of solute per 1 liter of solution, while a 1 m solution has 1 mole of solute per 1 kilogram of solvent. For dilute aqueous solutions, molarity and molality can be almost the same because the volume of 1 kilogram of water is roughly equivalent to 1 liter, given water's density is close to 1.0 g/mL.
However, molarity and molality are distinctly different measurements, and their values can diverge significantly for solutions with solvents other than water or for concentrated solutions.