Question

f \(38.2 \mathrm{~mL}\) of \(0.248 M\) aluminum sulfate solution is diluted with deionized water to a total volume of \(0.639 \mathrm{~L}\), how many grams of aluminum ion are present in the diluted solution?

Short answer

0.5107 grams of aluminum ion are present.

Step-by-step solution

Calculate moles of aluminum sulfate before dilution

First, calculate the moles of aluminum sulfate present in the original 38.2 mL solution. The molarity (M) of the solution is given as 0.248 M. Thus, the moles of aluminum sulfate can be calculated using the formula: \[ \text{Moles} = \text{Molarity} \times \text{Volume in Liters} \]. Here, the volume is 38.2 mL, which is 0.0382 L. Therefore, moles = 0.248 M \times 0.0382 L = 0.0094736 \text{ moles}.

Determine moles of aluminum ions

Aluminum sulfate, with the formula \(\text{Al}_2(\text{SO}_4)_3\), dissociates in solution to produce 2 aluminum ions per formula unit. Therefore, the moles of aluminum ions are double the moles of aluminum sulfate. So, \(0.0094736 \times 2 = 0.0189472 \text{ moles of Al}^{3+} \).

Calculate grams of aluminum ions in the diluted solution

To find the grams of aluminum ions, multiply the moles of aluminum ions by the molar mass of aluminum (26.98 g/mol). Therefore, \(0.0189472 \text{ moles} \times 26.98 \text{ g/mol} = 0.5107 \text{ grams} \text{ of } \text{Al}^{3+} \).

Confirm moles of aluminum ions remain unchanged after dilution

Remember that dilution does not change the amount of solute present; it only changes the concentration. Hence, the moles of aluminum ions before and after dilution remain the same, ensuring that the calculation in Step 3 applies to the diluted solution.

Key concepts

Molarity

Molarity is a way to express the concentration of a solution. It tells us how many moles of a substance, called the solute, are present in a liter of solution. This unit helps us understand how strong or weak a solution is.

The formula to calculate molarity is:

• Molarity (M) = Moles of solute / Volume of solution in liters

For example, if you have a mixture with 0.248 moles of a solute in 1 liter, it is a 0.248 M (molar) solution. To find the molarity of smaller or larger volumes, you would adjust using the actual volume in liters. Using molarity helps us accurately express and manipulate solutions for various chemical reactions and analyses.

Moles of Solute

The concept of "moles of solute" is a fundamental part of chemistry calculations. A mole is a unit that measures the amount of a substance. It relates to the number of particles, like atoms or molecules, in a particular mass. For any chemical calculation, determining the number of moles helps to relate quantities of substances.

To find the moles of solute in a solution, you can use the formula:

• Moles = Molarity (M) × Volume in liters

For instance, if you have 38.2 mL (or 0.0382 L) of a 0.248 M solution of aluminum sulfate, you calculate: 0.248 mol/L × 0.0382 L = 0.0094736 moles.

This calculation shows how knowing the molarity and volume of a solution allows you to determine the exact amount of solute present.

Chemical Formulas

Chemical formulas use symbols from the periodic table to represent the composition of molecules. They provide crucial information about the elements in a compound and how they are bonded together. For aluminum sulfate, the chemical formula is \(\text{Al}_2(\text{SO}_4)_3\), indicating each unit consists of two aluminum atoms and three sulfate groups.

From formula \(\text{Al}_2(\text{SO}_4)_3\), we understand:

• Two aluminum (Al) atoms
• Three sulfate (SO₄) groups, each having a -2 charge

When dissolved, this compound provides 2 aluminum ions (Al³⁺) and 3 sulfate ions (SO₄²⁻) in the solution. Knowing the chemical formula helps us predict how substances will react and how they dissociate in solutions.

Ion Concentration

Ion concentration tells us how many ions are available in a solution and is essential for understanding reactions that occur in aqueous solutions. When a compound like aluminum sulfate dissolves, it breaks into its constituent ions.

If you start with 0.0094736 moles of aluminum sulfate, it dissociates to produce twice the number of moles of aluminum ions, due to its formula \(\text{Al}_2(\text{SO}_4)_3 \). That means:

• Moles of aluminum ions (Al³⁺) = 0.0094736 × 2 = 0.0189472 moles

This concentration calculation shows that despite dilution, the number of ions doesn't change; only their distribution in the final volume does. So, whether a solution is concentrated or diluted, understanding ion concentration helps us better plan out reactions and applications.