Questions: Concentration Units and Molarity Calculations

Question 1

A student dissolves 0.50 mol of NaCl into 0.80 L of water. The resulting solution has a total volume of 1.00 L. What is the molarity of the solution?

• A. 0.625 M — calculated as 0.50 mol ÷ 0.80 L (liters of water used)
• B. 0.50 M — calculated as 0.50 mol ÷ 1.00 L (liters of solution)
• C. 0.40 M — calculated as the average of the solute moles and total volume
• D. 1.00 M — because 0.50 mol in 0.50 L of water gives 1.0 M before dilution

Answer: (B)

Molarity = moles of solute ÷ liters of solution. The denominator is the total volume of the final solution (1.00 L), not the volume of solvent added (0.80 L). Using 0.80 L gives 0.625 M — the most common error, and the misconception option A represents. The final solution volume is what matters because molarity is defined with respect to the container holding the complete mixture. In practice, you would add solute to a volumetric flask and fill to the calibration mark with solvent — the 1.00 L is the endpoint, not the starting water volume.

Question 2

You need exactly 0.25 moles of HCl for a reaction. You have a 0.50 M HCl stock solution. What volume of stock solution should you measure out?

• A. 0.125 L — because 0.25 mol × 0.50 M = 0.125
• B. 0.50 L — because 0.25 mol ÷ 0.50 M = 0.50 L
• C. 0.50 L — because 0.50 M solution contains 0.50 mol per 0.50 L
• D. 2.0 L — because 0.25 mol × (1 L / 0.50 mol) = 0.50... wait, you need more

Answer: (B)

Rearranging M = n/V gives V = n/M = 0.25 mol ÷ 0.50 mol/L = 0.50 L. You measure 500 mL of the stock solution, which contains exactly 0.50 mol/L × 0.50 L = 0.25 mol of HCl. Option A is a dimensional-analysis error that multiplies instead of divides. This calculation — converting a mole requirement into a volume measurement — is the core practical application of molarity, used in every titration, dilution, and solution-based synthesis.

Question 3

To prepare a 1.0 M solution of NaCl, you should dissolve 1.0 mol of NaCl in exactly 1.0 L of water (solvent).

• T. True
• F. False

Answer: False

This is the single most common error in solution preparation. Molarity is defined as moles per liter of *solution*, not moles per liter of *solvent*. Adding 1.0 mol of NaCl to 1.0 L of water typically produces a final solution volume greater than 1.0 L (the solute occupies space). To make exactly 1.0 M, you would dissolve the solute in a smaller amount of solvent, then add additional solvent until the total solution volume reaches exactly 1.0 L — which is what a volumetric flask's calibration mark indicates.

Question 4

Molality is preferred over molarity for colligative property calculations because molality does not change with temperature, while molarity does.

• T. True
• F. False

Answer: True

Molarity uses volume of solution in its denominator. As temperature changes, liquids expand or contract, changing the solution volume and therefore the molarity — even if the moles of solute and mass of solvent are unchanged. Molality uses mass of solvent (kg), which is temperature-independent. For colligative properties like boiling point elevation and freezing point depression, whose magnitude depends on the number of solute particles per unit solvent mass, molality gives a temperature-stable measure that does not drift as conditions change.

Question 5

Explain why molarity is defined using liters of solution rather than liters of solvent, and give an example of why this distinction matters in practice.

Model answer: Molarity measures how many moles of solute are present in a given volume of the final solution. Using solution volume (not solvent volume) ensures that when you measure out a given volume with a pipette or graduated cylinder, you know exactly how many moles you have obtained — because the solution is what you actually handle. If molarity used solvent volume, you would need to know how much the solute changed the total volume before calculating moles, which is impractical. In practice: to make 1.0 M NaCl, you dissolve NaCl in some water, then add water until the total solution volume reaches exactly 1.0 L in a volumetric flask. Adding 1.0 mol to 1.0 L of water gives slightly more than 1.0 L of solution and therefore slightly less than 1.0 M.

The distinction matters most in concentrated solutions, where the solute contribution to total volume is significant. For very dilute aqueous solutions, the difference between solution volume and solvent volume is negligible, which is why the error 'dissolve in X liters of water' is often close enough in practice but wrong in principle. In precision work — analytical chemistry, pharmaceutical preparation, primary standard solutions — the distinction is always maintained.