The same quantity of electricity that liberated 2.158 g silver was passed through a solution of a gold salt and 1.314 g of gold was deposited. The equivalent mass of silver is 107.9. Calculate the equivalent mass of gold. What is the oxidation state of gold salt ? (At. mass of gold =197)

Answer

To solve the problem, we need to calculate the equivalent mass of gold based on the information provided about the mass of silver and gold deposited when the same quantity of electricity is passed through their respective solutions.

### Step-by-Step Solution:

1. **Understanding the relationship**: According to Faraday's law of electrolysis, the mass of a substance deposited during electrolysis is directly proportional to the equivalent mass of the substance when the same quantity of electricity is passed. This can be expressed mathematically as:
\[ \frac{m_{\text{Ag}}}{m_{\text{Au}}} = \frac{E_{\text{Ag}}}{E_{\text{Au}}} \]
where \( m \) is the mass deposited and \( E \) is the equivalent mass.

2. **Given values**:
- Mass of silver deposited, \( m_{\text{Ag}} = 2.158 \, \text{g} \)
- Mass of gold deposited, \( m_{\text{Au}} = 1.314 \, \text{g} \)
- Equivalent mass of silver, \( E_{\text{Ag}} = 107.9 \, \text{g} \)

3. **Setting up the equation**: We can rearrange the equation to solve for the equivalent mass of gold \( E_{\text{Au}} \):
\[ E_{\text{Au}} = E_{\text{Ag}} \times \frac{m_{\text{Au}}}{m_{\text{Ag}}} \]

4. **Substituting the values**:
\[ E_{\text{Au}} = 107.9 \, \text{g} \times \frac{1.314 \, \text{g}}{2.158 \, \text{g}} \]

5. **Calculating the equivalent mass of gold**:
\[ E_{\text{Au}} = 107.9 \times 0.609 = 65.7 \, \text{g} \]

6. **Finding the oxidation state of gold**: The equivalent mass is related to the molar mass and the number of electrons transferred (n) in the reaction:
\[ E_{\text{Au}} = \frac{M_{\text{Au}}}{n} \]
where \( M_{\text{Au}} = 197 \, \text{g/mol} \). Rearranging gives:
\[ n = \frac{M_{\text{Au}}}{E_{\text{Au}}} = \frac{197}{65.7} \approx 3 \]

7. **Conclusion**: The equivalent mass of gold is \( 65.7 \, \text{g} \) and the oxidation state of gold in the salt is \( +3 \).

### Final Answer:
- Equivalent mass of gold: \( 65.7 \, \text{g} \)
- Oxidation state of gold salt: \( +3 \)