Dilution And Concentration Calculations

To find the final concentration of the NaOH solution, we begin by calculating the moles of NaOH in each solution, using the formula: moles = concentration (M) × volume (L).

Step 1: Calculate moles in the 2 M NaOH solution.
Volume = 20 mL = 0.020 L
Concentration = 2 M
Moles = 2 × 0.020 = 0.040 moles

Step 2: Calculate moles in the 0.5 M NaOH solution.
Volume = 400 mL = 0.400 L
Concentration = 0.5 M
Moles = 0.5 × 0.400 = 0.200 moles

Step 3: Calculate total moles of NaOH in the mixture.
Total moles = 0.040 + 0.200 = 0.240 moles

Step 4: Find the total volume of the solution.
Total Volume = 20 mL + 400 mL = 420 mL = 0.420 L

Step 5: Calculate the final concentration of the NaOH solution.
Final Concentration = Total moles / Total volume = 0.240 / 0.420 = 0.571 M

Step 6: Express the concentration in the form required by the problem.
The final concentration is 0.571 M, which is equivalent to 57.1 × 10^-2 M. The nearest integer value is 57.

Verification: The calculated range falls within 6,6 as expected.