\begin{tabular}{l} Calculate the volume in liters of a $$ 7.74 imes 10^{-4} \mu \mathrm{~mol} / \mathrm{L} $$ magnesium fluoride \ solution that contains 300 . mmol of magnesium fluoride $$ \left(\mathrm{MgF}_{2} ight) $$. Round your \ answer to 3 significant digits. \ \hline $$ \mathrm{U}_{\mathrm{L}} $$\end{tabular}

Question

\begin{tabular}{l} Calculate the volume in liters of a $$ 7.74 	imes 10^{-4} \mu \mathrm{~mol} / \mathrm{L} $$ magnesium fluoride \ solution that contains 300 . mmol of magnesium fluoride $$ \left(\mathrm{MgF}_{2}ight) $$. Round your \ answer to 3 significant digits. \ \hline $$ \mathrm{U}_{\mathrm{L}} $$\end{tabular}

UpStudy AI · Accepted Answer

We are given a very dilute solution of magnesium fluoride (MgF₂) with a concentration of

7.74 × 10⁻⁴ µmol/L

and we need to know how many liters of this solution contain 300 mmol of MgF₂.

Step 1. Convert the amount of MgF₂ from mmol to µmol.

• 1 mmol = 1,000 µmol  
• 300 mmol = 300 × 1,000 µmol = 300,000 µmol

Step 2. Write the relationship for concentration:

Concentration = (number of µmol)/(Volume in L)

Since we know the concentration and the total number of µmol needed, we can solve for the volume:

Volume = (number of µmol) / (concentration in µmol/L)
  Volume = (300,000 µmol) / (7.74 × 10⁻⁴ µmol/L)

Step 3. Calculate the volume:

Volume = 300,000 / (7.74 × 10⁻⁴)
      = 300,000 / 0.000774

Divide 300,000 by 0.000774:

Volume ≈ 387,597, so approximately 3.88 × 10⁸ liters

Step 4. Rounding to three significant digits:

Volume ≈ 3.88 × 10⁸ L

Thus, the volume of the magnesium fluoride solution required to have 300 mmol of MgF₂ is approximately 3.88 × 10⁸ liters.
The volume of the magnesium fluoride solution needed is approximately 3.88 × 10⁸ liters.

Calculate the volume in liters of a magnesium fluoride

solution that contains 300 . mmol of magnesium fluoride . Round your

answer to 3 significant digits.

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Calculate the volume in liters of a magnesium fluoride solution that contains 300 . mmol of magnesium fluoride . Round your answer to 3 significant digits.