Calculate the hydrogen ion and hydroxyl ion concentrations of solution containing 0.063 g of pure nitrie acid per litre.

Explanation

To calculate the hydrogen ion (H⁺) and hydroxyl ion (OH⁻) concentrations in a solution containing 0.063 g of pure nitric acid (HNO₃) per liter, follow these steps:

### Step 1: Calculate the molecular weight of nitric acid (HNO₃)
- The molecular weight of HNO₃ can be calculated as follows:
- Hydrogen (H) = 1 g/mol
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol (and there are 3 oxygen atoms in HNO₃)

Therefore, the molecular weight of HNO₃:
\[ \text{Molecular weight of HNO₃} = 1 + 14 + (16 \times 3) = 1 + 14 + 48 = 63 \text{ g/mol} \]

### Step 2: Calculate the number of moles of HNO₃ in the solution
- Use the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molecular weight}} \]

Given weight = 0.063 g, and molecular weight = 63 g/mol:
\[ \text{Number of moles of HNO₃} = \frac{0.063 \text{ g}}{63 \text{ g/mol}} = 0.001 \text{ moles} \]

### Step 3: Calculate the concentration of HNO₃ in moles per liter
- Since the solution is 1 liter, the concentration of HNO₃ is:
\[ \text{Concentration of HNO₃} = \frac{0.001 \text{ moles}}{1 \text{ L}} = 10^{-3} \text{ moles/L} \]

### Step 4: Determine the concentration of hydrogen ions (H⁺)
- HNO₃ is a strong acid and completely dissociates in water:
\[ \text{HNO₃} \rightarrow \text{H}^+ + \text{NO}_3^- \]

Therefore, the concentration of H⁺ ions will be equal to the concentration of HNO₃:
\[ [\text{H}^+] = 10^{-3} \text{ moles/L} \]

### Step 5: Calculate the concentration of hydroxyl ions (OH⁻)
- Use the ion product of water (K_w):
\[ K_w = [\text{H}^+][\text{OH}^-] = 10^{-14} \text{ at 25°C} \]

Rearranging the equation to find [OH⁻]:
\[ [\text{OH}^-] = \frac{K_w}{[\text{H}^+]} = \frac{10^{-14}}{10^{-3}} = 10^{-11} \text{ moles/L} \]

### Final Results
- The concentration of hydrogen ions (H⁺) is:
\[ [\text{H}^+] = 10^{-3} \text{ moles/L} \]
- The concentration of hydroxyl ions (OH⁻) is:
\[ [\text{OH}^-] = 10^{-11} \text{ moles/L} \]