298K). If 3.45g of silver sulfate is added to 1.75L of water, will it l dissolve? Show your work/explain your reasoning.

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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**Question 4: Solubility of Silver Sulfate in Water**

Silver sulfate is slightly soluble in water, represented by the following equilibrium reaction:

\[ Ag_2SO_4(s) \leftrightarrow 2Ag^+(aq) + SO_4^{2-}(aq) \]

The equilibrium constant, \( K_c \), at 298 K is \( 1.1 \times 10^{-5} \).

**Problem Statement:**

If 3.45 grams of silver sulfate is added to 1.75 liters of water, will it all dissolve? Show your work and explain your reasoning.

**Solution Approach:**

1. **Calculate the Molar Mass of Silver Sulfate (Ag_2SO_4):**

   \[ \text{Molar mass of } Ag = 107.87 \, \text{g/mol} \]
   \[ \text{Molar mass of } S = 32.07 \, \text{g/mol} \]
   \[ \text{Molar mass of } O = 16.00 \, \text{g/mol} \]
   
   \[ Molar\,mass\,of\,Ag_2SO_4 = (2 \times 107.87) + 32.07 + (4 \times 16.00) \]
   \[ = 215.74 + 32.07 + 64.00 \]
   \[ = 311.81 \, \text{g/mol} \]

2. **Calculate the Number of Moles of Silver Sulfate (Ag_2SO_4):**

   \[ \text{Mass of Ag_2SO_4} = 3.45 \, \text{g} \]
   \[ \text{Moles of Ag_2SO_4} = \frac{3.45 \, \text{g}}{311.81 \, \text{g/mol}} \]
   \[ = 0.0111 \, \text{mol} \]

3. **Determine the Solubility Product (K_sp) Expression:**

   The equilibrium expression for the solubility of Ag_2SO_4 is:
   \[ K_c = [Ag^+]^2 [SO_4^{2-}] \]
   
   Let \( x \) be the mol
Transcribed Image Text:**Question 4: Solubility of Silver Sulfate in Water** Silver sulfate is slightly soluble in water, represented by the following equilibrium reaction: \[ Ag_2SO_4(s) \leftrightarrow 2Ag^+(aq) + SO_4^{2-}(aq) \] The equilibrium constant, \( K_c \), at 298 K is \( 1.1 \times 10^{-5} \). **Problem Statement:** If 3.45 grams of silver sulfate is added to 1.75 liters of water, will it all dissolve? Show your work and explain your reasoning. **Solution Approach:** 1. **Calculate the Molar Mass of Silver Sulfate (Ag_2SO_4):** \[ \text{Molar mass of } Ag = 107.87 \, \text{g/mol} \] \[ \text{Molar mass of } S = 32.07 \, \text{g/mol} \] \[ \text{Molar mass of } O = 16.00 \, \text{g/mol} \] \[ Molar\,mass\,of\,Ag_2SO_4 = (2 \times 107.87) + 32.07 + (4 \times 16.00) \] \[ = 215.74 + 32.07 + 64.00 \] \[ = 311.81 \, \text{g/mol} \] 2. **Calculate the Number of Moles of Silver Sulfate (Ag_2SO_4):** \[ \text{Mass of Ag_2SO_4} = 3.45 \, \text{g} \] \[ \text{Moles of Ag_2SO_4} = \frac{3.45 \, \text{g}}{311.81 \, \text{g/mol}} \] \[ = 0.0111 \, \text{mol} \] 3. **Determine the Solubility Product (K_sp) Expression:** The equilibrium expression for the solubility of Ag_2SO_4 is: \[ K_c = [Ag^+]^2 [SO_4^{2-}] \] Let \( x \) be the mol
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