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The problem asks to calculate the mass of aluminum sulfate (\( \text{Al}_2(\text{SO}_4)_3 \)) in kilograms added to the reaction flask, given that:

- The volume of the solution is 1.15 L.
- The concentration is 0.40 mol/L.

Here's how to solve it step-by-step:

### Step 1: Calculate the number of moles of aluminum sulfate
We can use the formula:
\[
\text{moles} = \text{concentration} \times \text{volume}
\]
where:
- The concentration is 0.40 mol/L.
- The volume is 1.15 L.

So:
\[
\text{moles of aluminum sulfate} = 0.40 \, \text{mol/L} \times 1.15 \, \text{L} = 0.46 \, \text{mol}
\]

### Step 2: Calculate the molar mass of aluminum sulfate
The chemical formula for aluminum sulfate is \( \text{Al}_2(\text{SO}_4)_3 \). To calculate its molar mass, we sum the atomic masses of all atoms involved:

- Aluminum (Al): 26.98 g/mol, and there are 2 Al atoms.
- Sulfur (S): 32.07 g/mol, and there are 3 S atoms.
- Oxygen (O): 16.00 g/mol, and there are 12 O atoms (since each sulfate group \( \text{SO}_4 \) contains 4 oxygen atoms and there are 3 sulfate groups).

Thus, the molar mass of \( \text{Al}_2(\text{SO}_4)_3 \) is:
\[
2(26.98) + 3(32.07) + 12(16.00) = 53.96 + 96.21 + 192.00 = 342.17 \, \text{g/mol}
\]

### Step 3: Calculate the mass of aluminum sulfate
Now that we know the moles of aluminum sulfate (0.46 mol) and its molar mass (342.17 g/mol), we can calculate the mass in grams using:
\[
\text{mass} = \text{moles} \times \text{molar mass}
\]
\[
\text{mass} = 0.46 \, \text{mol} \times 342.17 \, \text{g/mol} = 157.40 \, \text{g}
\]

### Step 4: Convert the mass to kilograms
Finally, convert grams to kilograms:
\[
\text{mass in kg} = \frac{157.40 \, \text{g}}{1000} = 0.1574 \, \text{kg}
\]

Thus, the mass of aluminum sulfate added to the flask is **0.1574 kg**.

Would you like further details or have any questions?

### Follow-up questions:
1. How would the mass change if the concentration were doubled?
2. What is the mass of sulfate ions \( \text{SO}_4^{2-} \) present in this amount of aluminum sulfate?
3. How does the volume of the solution affect the mass of solute added?
4. What is the purpose of significant figures in this calculation?
5. How would the result change if the molar mass of aluminum sulfate was slightly different?

### Tip:
Always be mindful of significant figures when dealing with measurements to ensure precision in your results.

A chemist adds 1.15 L of a 0.40 mol/L aluminum sulfate (Al2(SO4)3) solution to a reaction flask. Calculate the mass in kilograms of aluminum sulfate the chemist has added to the flask. Be sure your answer has the correct number of significant digits.

Learn how to calculate the mass of aluminum sulfate in kilograms added to a flask when given the molarity (0.40 mol/L) and volume (1.15 L) of the solution. Follow a detailed step-by-step guide covering stoichiometry and unit conversion. Suitable for high school chemistry students (Grades 10-12).

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