"solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.
Gd2(SO4)3, 3.98 g/100 mL"
To calculate the solubility product (Ksp) of Gd₂(SO₄)₃ from its solubility in grams per 100 mL, we will follow these steps:

### Step 1: **Convert Solubility to Moles per Liter**
The given solubility of Gd₂(SO₄)₃ is 3.98 g/100 mL, which is equivalent to 39.8 g/L.

Next, we convert grams to moles using the molar mass of Gd₂(SO₄)₃.

#### Molar Mass of Gd₂(SO₄)₃:
- Gd: 157.25 g/mol
- SO₄: (1 × 32.07) + (4 × 16.00) = 96.07 g/mol

Molar mass of Gd₂(SO₄)₃ = 2 × 157.25 + 3 × 96.07 = 314.5 + 288.21 = 602.71 g/mol

Now, convert the solubility to moles per liter (mol/L):

Molar solubility = 39.8 g/L ÷ 602.71 g/mol
Molar solubility ≈ 6.61 × 10⁻² mol/L

### Step 2: **Write the Dissolution Equation for Gd₂(SO₄)₃**
The dissolution equation for Gd₂(SO₄)₃ is:
Gd₂(SO₄)₃ (s) ⇌ 2Gd³⁺ (aq) + 3SO₄²⁻ (aq)

### Step 3: **Set Up the Ksp Expression**
The Ksp expression for Gd₂(SO₄)₃ is:
Ksp = [Gd³⁺]²[SO₄²⁻]³

Let the molar solubility of Gd₂(SO₄)₃ be 's'. At equilibrium:
- [Gd³⁺] = 2s
- [SO₄²⁻] = 3s

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