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. 45.0g conc . `HNO_(3)`
B. 90.0g conc.` HNO_(3)`
C. 70 .0 g conc .` HNO_(3)`
D. 54.0g 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 will follow these steps:

### Step 1: Calculate the number of moles of HNO₃ required
The formula for molarity (M) is given by:

\[ M = \frac{\text{number of moles}}{\text{volume in liters}} \]

Given that the molarity is 2.0 M and the volume is 250 mL (which is 0.250 L), we can rearrange the formula to find the number of moles (n):

\[ n = M \times \text{volume in liters} = 2.0 \, \text{mol/L} \times 0.250 \, \text{L} = 0.5 \, \text{moles} \]

### Step 2: Calculate the mass of HNO₃ needed
Next, we need to calculate the mass of HNO₃ required using the formula:

\[ \text{mass} = \text{number of moles} \times \text{molar mass} \]

The molar mass of HNO₃ (Hydrogen: 1 g/mol, Nitrogen: 14 g/mol, Oxygen: 16 g/mol × 3) is:

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

Now, substituting the values:

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

### Step 3: Calculate the mass of concentrated HNO₃ solution needed
The concentrated nitric acid solution is 70% HNO₃ by mass. This means that in 100 grams of the solution, there are 70 grams of HNO₃.

To find out how many grams of the concentrated solution we need to obtain 31.5 grams of HNO₃, we can set up the following proportion:

\[ \frac{70 \, \text{g HNO₃}}{100 \, \text{g solution}} = \frac{31.5 \, \text{g HNO₃}}{x \, \text{g solution}} \]

Cross-multiplying gives:

\[ 70x = 31.5 \times 100 \]

Solving for x:

\[ 70x = 3150 \implies x = \frac{3150}{70} = 45 \, \text{grams} \]

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

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