To calculate the concentration of the silver(II) oxide (AgO) solution, we can follow these steps:

Step 1: Convert micromoles (μmol) to moles

The amount of silver(II) oxide (AgO) is given as 0.00089 μmol. Since 1 μmol = $1 \times 10^{-6}$ moles, we can convert this to moles:

$\text{Moles of AgO} = 0.00089 \, \mu mol \times 10^{-6} \, mol/\mu mol = 8.9 \times 10^{-10} \, mol$

Step 2: Convert the volume from milliliters to liters

The volume of the solution is 250 mL. Since 1 L = 1000 mL, we convert the volume to liters:

$\text{Volume of solution} = \frac{250}{1000} = 0.250 \, L$

Step 3: Calculate the concentration

The concentration of a solution is given by the formula:

$\text{Concentration (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}$

Substitute the values we found:

$\text{Concentration of AgO} = \frac{8.9 \times 10^{-10} \, mol}{0.250 \, L} = 3.56 \times 10^{-9} \, M$

Thus, the concentration of the chemist's silver(II) oxide solution is:

$\boxed{3.56 \times 10^{-9} \, M}$

Would you like more details or further clarification on any part of the process?

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Here are 5 related questions:

1. How do you convert between different units of concentration (e.g., molarity to molality)?
2. What is the significance of molarity in chemical reactions?
3. How would temperature affect the solubility of AgO in water?
4. What are the steps to prepare a solution with a specific molarity?
5. How can the accuracy of the concentration measurement be improved?

Tip: Always ensure that all units (moles, liters) are consistent when calculating concentration to avoid mistakes.