Question

A chemist adds 160.0 mL of a 9.7 x 10⁻⁴ magnesium fluoride (MgF₂ ) solution to a reaction flask. calculate the mass in milligrams of magnesium fluoride the chemist has added to the flask. round your answer to two significant digits.

Answer 1

The mass of magnesium fluoride added to the flask is approximately 0.159 grams.

Step-by-step explanation:

To calculate the mass of magnesium fluoride, we can use the formula:

\[ \text{Mass} = \text{Volume} \times \text{Concentration} \times \text{Molar Mass} \]

Given that the volume is \(160.0 \, \text{mL}\), the concentration is \(9.7 \times
`10^(-4)`\), and the molar mass of magnesium fluoride (MgF₂) is approximately \(62.32 \, \text{g/mol}\), we can substitute these values into the formula:

\[ \text{Mass} = 160.0 \, \text{mL} \times 9.7 \times
`10^(-4)` \times 62.32 \, \text{g/mol} \]

Calculating this expression yields the mass in grams. To convert this to milligrams, we can multiply by \(1000\) since there are \(1000\) milligrams in a gram:

\[ \text{Mass (mg)} = \text{Mass (g)} \times 1000 \]

The final answer is rounded to two significant digits, providing a mass of approximately \(0.159 \, \text{g}\) or \(159 \, \text{mg}\). This represents the amount of magnesium fluoride added to the reaction flask. The rounded result ensures adherence to significant digit conventions in the final answer.

Answer 2

The mass of magnesium fluoride added to the flask is 9.67 mg, rounded to three significant digits. To find the mass of magnesium fluoride added to the flask, convert the volume from mL to liters, calculate the moles of MgF2 from the molarity, convert the moles to grams using the molar mass of MgF2, and then convert grams to milligrams.

Step-by-step explanation:

To calculate the mass of magnesium fluoride (MgF2) in milligrams that the chemist has added to the reaction flask,

we first need to determine the number of moles of MgF2 in the solution.

The given concentration of the MgF2 solution is 9.7 x 10−4 moles per liter (M).

• Step 1: Convert the volume from mL to L by dividing by 1000.
  160.0 mL = 0.160 L
• Step 2: Multiply the volume in liters by the molarity to find moles of MgF2.
  (0.160 L) x (9.7 x 10−4 mol/L) = 1.552 x 10−5 mol
• Step 3: Calculate the mass in grams by multiplying the number of moles by the molar mass of MgF2. The molar mass of MgF2 is (24.305 + (2 x 18.998)) g/mol = 62.301 g/mol.
  (1.552 x 10−5 mol) x (62.301 g/mol) = 0.00967 g
• Step 4: Convert the mass from grams to milligrams by multiplying by 1000.
  0.00967 g x 1000 mg/g = 9.67 mg

Therefore, the mass of magnesium fluoride added to the flask is 9.67 mg, rounded to three significant digits.