Final answer:
The concentration of the chemist's working solution of sodium carbonate is approximately 0.0364 M.
Step-by-step explanation:
The student asked how to calculate the concentration of a chemist's working solution made by diluting a stock solution of sodium carbonate. To determine the concentration of the working solution, we use the dilution formula M1V1 = M2V2, where M1 is the molarity of the stock solution, V1 is the volume of the stock solution, M2 is the molarity of the working solution, and V2 is the total volume of the working solution.
Using the information provided, we have:
M1 = 0.171 M (concentration of the stock solution)
V1 = 200 mL (volume of the stock solution)
M2 = unknown (concentration of the working solution we need to find)
V2 = 940 mL (final total volume of the working solution)
The next step is to convert all volumes to liters to ensure consistency in units. So, V1 = 0.200 L and V2 = 0.940 L.
Now plug in the values into the dilution formula:
M1V1 = M2V2
0.171 M × 0.200 L = M2 × 0.940 L
To solve for M2:
M2 = (0.171 M × 0.200 L) / 0.940 L
Calculate M2:
M2 = 0.0342 M ≈ 0.0364 M (after rounding to three significant digits)
Therefore, the concentration of the chemist's working solution is approximately 0.0364 M.