How many grams of concentrated nitric acid solution should be used to prepare `250 mL` of `2.0 M HNO_(3)`? The concentrated acid is `70% HNO_(3)`:

Options

A. (a)`90.0` g conc. `HNO_(3)`
B. (b)`70.0` g conc. `HNO_(3)`
C. (c )`54.0` g conc. `HNO_(3)`
D. (d)`45.0` g conc. `HNO_(3)`

Explanation

To solve the problem of how many grams of concentrated nitric acid solution should be used to prepare 250 mL of 2.0 M HNO₃, we can follow these steps:

### Step 1: Calculate the number of moles of HNO₃ needed
The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. We can use the formula:

\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in liters)} \]

Given:
- Molarity = 2.0 M
- Volume = 250 mL = 0.250 L

Calculating the number of moles:

\[ \text{Number of moles} = 2.0 \, \text{mol/L} \times 0.250 \, \text{L} = 0.5 \, \text{moles} \]

### Step 2: Calculate the mass of HNO₃ required
Next, we need to find the mass of HNO₃ required using its molar mass. The molar mass of HNO₃ can be calculated as follows:

- Atomic weight of H = 1 g/mol
- Atomic weight of N = 14 g/mol
- Atomic weight of O = 16 g/mol (and there are 3 oxygen atoms)

Calculating the molar mass:

\[ \text{Molar mass of HNO₃} = 1 + 14 + (3 \times 16) = 63 \, \text{g/mol} \]

Now, we can calculate the mass of HNO₃ required:

\[ \text{Mass of HNO₃} = \text{Number of moles} \times \text{Molar mass} = 0.5 \, \text{moles} \times 63 \, \text{g/mol} = 31.5 \, \text{grams} \]

### Step 3: Calculate the mass of concentrated nitric acid solution needed
Since the concentrated nitric acid solution is 70% HNO₃, we need to find out how much of the concentrated solution is required to obtain 31.5 grams of HNO₃.

Let \( x \) be the mass of the concentrated solution needed. Since 70% of this mass is HNO₃, we can set up the equation:

\[ 0.70x = 31.5 \, \text{grams} \]

Solving for \( x \):

\[ x = \frac{31.5}{0.70} = 45 \, \text{grams} \]

### Conclusion
To prepare 250 mL of 2.0 M HNO₃, you will need **45 grams** of concentrated nitric acid solution.

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