5g sample of brass was dissolved in one litre dil. `H_(2)SO_(4)` . 20 ml of this solution were mixed with KI, liberating `I_(2)` and `Cu^(+)` and the `I_(2)` required 20 ml of 0.0327 N hypo solution for complete titration. Calculate the percentage of Cu in the alloy.

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the amount of iodine (I2) produced.
When the brass sample is treated with KI, copper ions (Cu²⁺) react with iodide ions (I⁻) to produce iodine (I2). The balanced reaction is:
\[ 2 \text{Cu}^{2+} + 2 \text{I}^- \rightarrow 2 \text{Cu}^+ + \text{I}_2 \]

### Step 2: Calculate the equivalents of Na2S2O3 used in the titration.
The normality (N) of the hypo solution (Na2S2O3) is given as 0.0327 N, and the volume used is 20 mL. Convert the volume from mL to L:
\[ \text{Volume in L} = \frac{20 \text{ mL}}{1000} = 0.020 \text{ L} \]

Now, calculate the equivalents of Na2S2O3:
\[ \text{Equivalents of Na2S2O3} = \text{Normality} \times \text{Volume in L} \]
\[ = 0.0327 \, \text{N} \times 0.020 \, \text{L} = 0.000654 \, \text{equivalents} \]

### Step 3: Relate the equivalents of Na2S2O3 to the equivalents of Cu.
From the balanced reaction, 1 mole of I2 reacts with 2 moles of Na2S2O3, which means:
\[ \text{Equivalents of Cu} = \text{Equivalents of Na2S2O3} \]
Thus, the equivalents of Cu are also 0.000654.

### Step 4: Calculate the mass of copper in the sample.
The equivalent weight of copper (Cu) can be calculated as:
\[ \text{Equivalent weight of Cu} = \frac{\text{Molar mass of Cu}}{n} \]
Where \( n \) is the number of electrons transferred (1 for Cu²⁺ to Cu⁺), and the molar mass of Cu is 63.5 g/mol:
\[ \text{Equivalent weight of Cu} = \frac{63.5 \, \text{g/mol}}{1} = 63.5 \, \text{g/equiv} \]

Now, calculate the mass of copper:
\[ \text{Mass of Cu} = \text{Equivalents of Cu} \times \text{Equivalent weight of Cu} \]
\[ = 0.000654 \, \text{equiv} \times 63.5 \, \text{g/equiv} = 0.0415 \, \text{g} \]

### Step 5: Calculate the percentage of copper in the brass sample.
The total mass of the brass sample is 5 g. Therefore, the percentage of copper in the alloy is:
\[ \text{Percentage of Cu} = \left( \frac{\text{Mass of Cu}}{\text{Total mass of sample}} \right) \times 100 \]
\[ = \left( \frac{0.0415 \, \text{g}}{5 \, \text{g}} \right) \times 100 = 0.83\% \]

### Final Answer:
The percentage of copper in the brass alloy is approximately **0.83%**.

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