A 0.276 g impure sample of copper ore is dissolved and `Cu^(2+)` is titrated with KI solution. `I_(2)` liberated required 40 mL of 0.1 M `Na_(2)` `S_(2)` `O_(3)` solution for titration. What is the % of impurities in the ore ?

Answer

To solve the problem of finding the percentage of impurities in the copper ore sample, we can follow these steps:

### Step 1: Determine the number of equivalents of sodium thiosulfate (Na2S2O3)
Given:
- Volume of Na2S2O3 = 40 mL = 0.040 L
- Molarity of Na2S2O3 = 0.1 M

The number of equivalents of Na2S2O3 can be calculated using the formula:
\[ \text{Number of equivalents} = \text{Molarity} \times \text{Volume (L)} \times \text{n factor} \]
The n factor for Na2S2O3 in this reaction is 1 (as it reacts with I2 in a 1:1 ratio).

Calculating:
\[ \text{Number of equivalents of Na2S2O3} = 0.1 \, \text{mol/L} \times 0.040 \, \text{L} \times 1 = 0.004 \, \text{equivalents} \]

### Step 2: Relate the equivalents of Cu²⁺ to the equivalents of Na2S2O3
From the reaction, the number of equivalents of Cu²⁺ is equal to the number of equivalents of I2 produced, which is equal to the number of equivalents of Na2S2O3 used. Therefore:
\[ \text{Number of equivalents of Cu²⁺} = 0.004 \, \text{equivalents} \]

### Step 3: Calculate the number of moles of Cu²⁺
The n factor for Cu²⁺ is 1 (as it is reduced from Cu²⁺ to Cu⁺). Thus, the number of moles of Cu²⁺ can be calculated as:
\[ \text{Number of moles of Cu²⁺} = \text{Number of equivalents} = 0.004 \, \text{moles} \]

### Step 4: Calculate the weight of Cu²⁺
The molecular weight of copper (Cu) is approximately 63.5 g/mol. Therefore, the weight of Cu²⁺ can be calculated as:
\[ \text{Weight of Cu²⁺} = \text{Number of moles} \times \text{Molecular weight} = 0.004 \, \text{moles} \times 63.5 \, \text{g/mol} = 0.254 \, \text{g} \]

### Step 5: Calculate the weight of impurities
The total weight of the impure sample is given as 0.276 g. The weight of impurities can be calculated as:
\[ \text{Weight of impurities} = \text{Total weight} - \text{Weight of Cu²⁺} = 0.276 \, \text{g} - 0.254 \, \text{g} = 0.022 \, \text{g} \]

### Step 6: Calculate the percentage of impurities
The percentage of impurities in the ore can be calculated using the formula:
\[ \text{Percentage of impurities} = \left( \frac{\text{Weight of impurities}}{\text{Total weight}} \right) \times 100 \]
Calculating:
\[ \text{Percentage of impurities} = \left( \frac{0.022 \, \text{g}}{0.276 \, \text{g}} \right) \times 100 \approx 7.97\% \]

### Final Answer
The percentage of impurities in the copper ore is approximately **8%**.

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