To calculate the concentration of the chemist's working solution, we can use the dilution formula:
\[ C_1V_1 = C_2V_2 \]
where:
- \(C_1\) is the concentration of the stock solution,
- \(V_1\) is the volume of the stock solution,
- \(C_2\) is the concentration of the diluted solution (working solution),
- \(V_2\) is the volume of the diluted solution.
Given:
- \(C_1 = 0.000157 , \text{M}\)
- \(V_1 = 0.100 , \text{L}\)
- \(V_2 = 0.800 , \text{L}\)
Now we can rearrange the formula to find \(C_2\):
\[ C_2 = \frac{C_1V_1}{V_2} \]
Substituting in the values:
\[ C_2 = \frac{(0.000157 , \text{M}) \times (0.100 , \text{L})}{0.800 , \text{L}} \]
Calculating \(C_2\):
\[ C_2 = \frac{0.0000157 , \text{mol}}{0.800 , \text{L}} \]
\[ C_2 = 0.000019625 , \text{M} \]
Now rounding to three significant digits:
\[ C_2 \approx 0.0000196 , \text{M} \]
So, the concentration of the chemist's working solution is:
\[ \boxed{0.0000196 , \text{M}} \]