Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff65fb7b2-ba85-4e67-8fe1-01f97a564d1e%2F41e48be4-839f-46ef-9db8-3478e8f858e0%2F05yxce9_processed.png&w=3840&q=75)
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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