One litre of water was added to 500mL of `32% HNO_(3)` of density `1.20g//mL` . What is the percent concentration of `HNO_(3)` in the solution obtained ?

Answer

To find the percent concentration of HNO₃ in the solution obtained after adding 1 liter of water to 500 mL of 32% HNO₃, we can follow these steps:

### Step 1: Calculate the weight of the nitric acid solution
Given that the density of the 32% HNO₃ solution is 1.20 g/mL and the volume is 500 mL, we can calculate the weight of the solution.

\[ \text{Weight of HNO}_3 \text{ solution} = \text{Volume} \times \text{Density} = 500 \, \text{mL} \times 1.20 \, \text{g/mL} = 600 \, \text{g} \]

### Step 2: Calculate the weight of HNO₃ in the solution
Since the solution is 32% HNO₃ by weight, we can find the weight of HNO₃ in the solution.

\[ \text{Weight of HNO}_3 = 32\% \text{ of } 600 \, \text{g} = \frac{32}{100} \times 600 \, \text{g} = 192 \, \text{g} \]

### Step 3: Calculate the weight of water added
The weight of the water added can be calculated using its volume and density. The density of water is approximately 1 g/mL.

\[ \text{Weight of water} = \text{Volume} \times \text{Density} = 1000 \, \text{mL} \times 1 \, \text{g/mL} = 1000 \, \text{g} \]

### Step 4: Calculate the total weight of the solution
Now, we can find the total weight of the new solution after adding water.

\[ \text{Total weight of solution} = \text{Weight of HNO}_3 \text{ solution} + \text{Weight of water} = 600 \, \text{g} + 1000 \, \text{g} = 1600 \, \text{g} \]

### Step 5: Calculate the percent concentration of HNO₃ in the new solution
Finally, we can calculate the percent concentration of HNO₃ in the new solution.

\[ \text{Percent concentration of HNO}_3 = \left( \frac{\text{Weight of HNO}_3}{\text{Total weight of solution}} \right) \times 100 = \left( \frac{192 \, \text{g}}{1600 \, \text{g}} \right) \times 100 = 12\% \]

### Final Answer:
The percent concentration of HNO₃ in the solution obtained is **12%**.

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