Dil. `HNO_(3)` , contains 20% acid and it dissolves 10 g `CaCO_(3)`. The quantity of acid is

Options

A. 315g
B. 63 g
C. 50 g
D. 12.6 g

Explanation

To solve the problem, we need to determine the quantity of acid in a dilute solution of HNO₃ that can dissolve 10 g of calcium carbonate (CaCO₃). Here’s a step-by-step solution:

### Step 1: Write the balanced chemical equation
The reaction between calcium carbonate and nitric acid can be represented as:
\[ \text{CaCO}_3 + 2 \text{HNO}_3 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

This equation tells us that 1 mole of calcium carbonate reacts with 2 moles of nitric acid.

### Step 2: Calculate the molar mass of CaCO₃
To find the molar mass of calcium carbonate (CaCO₃):
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (and there are 3 oxygen atoms)

Thus, the molar mass of CaCO₃ is:
\[ 40 + 12 + (16 \times 3) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 3: Calculate the moles of CaCO₃
Now, we can calculate the number of moles of CaCO₃ in 10 g:
\[ \text{Moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ mol} \]

### Step 4: Determine the moles of HNO₃ required
From the balanced equation, we know that 1 mole of CaCO₃ reacts with 2 moles of HNO₃. Therefore, for 0.1 moles of CaCO₃, the moles of HNO₃ required are:
\[ \text{Moles of HNO}_3 = 0.1 \text{ mol} \times 2 = 0.2 \text{ mol} \]

### Step 5: Calculate the mass of HNO₃ required
Next, we need to find the molar mass of HNO₃:
- Hydrogen (H) = 1 g/mol
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol (and there are 3 oxygen atoms)

Thus, the molar mass of HNO₃ is:
\[ 1 + 14 + (16 \times 3) = 1 + 14 + 48 = 63 \text{ g/mol} \]

Now, we can calculate the mass of HNO₃ required:
\[ \text{Mass of HNO}_3 = \text{moles} \times \text{molar mass} = 0.2 \text{ mol} \times 63 \text{ g/mol} = 12.6 \text{ g} \]

### Step 6: Calculate the quantity of acid in the solution
Since the dilute HNO₃ solution contains 20% acid by mass, we can find the total mass of the solution required to provide 12.6 g of HNO₃:
Let \( x \) be the total mass of the solution.
\[ 0.20x = 12.6 \]
\[ x = \frac{12.6}{0.20} = 63 \text{ g} \]

Thus, the quantity of acid in the solution is:
\[ 12.6 \text{ g} \]

### Final Answer
The quantity of acid in the dilute HNO₃ solution is **12.6 g**.

---