Nitric acid is manufactured by the Ostwald process, in which nitrogen dioxide reacts with water.
`3NO_(2)(g) + H_(2)O(l) to 2HNO_(3) (aq) + NO(g)`
How many grams of nitrogen dioxide are required in this reaction to produce 25.2 gm `HNO_(3)`?

Answer

To determine how many grams of nitrogen dioxide (NO₂) are required to produce 25.2 grams of nitric acid (HNO₃) in the Ostwald process, we can follow these steps:

### Step 1: Write the Balanced Chemical Equation
The balanced chemical equation for the reaction is:
\[ 3 \text{NO}_2(g) + \text{H}_2\text{O}(l) \rightarrow 2 \text{HNO}_3(aq) + \text{NO}(g) \]

### Step 2: Calculate the Molar Mass of HNO₃
To find the molar mass of nitric acid (HNO₃):
- Atomic mass of Hydrogen (H) = 1 g/mol
- Atomic mass of Nitrogen (N) = 14 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

Calculating the molar mass:
\[ \text{Molar mass of HNO}_3 = 1 \times 1 + 1 \times 14 + 3 \times 16 = 1 + 14 + 48 = 63 \text{ g/mol} \]

### Step 3: Convert Grams of HNO₃ to Moles
Now, we convert the mass of HNO₃ to moles:
\[ \text{Moles of HNO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{25.2 \text{ g}}{63 \text{ g/mol}} \approx 0.4 \text{ moles} \]

### Step 4: Use Stoichiometry to Find Moles of NO₂ Required
From the balanced equation, we see that 2 moles of HNO₃ are produced from 3 moles of NO₂. Therefore, the ratio of NO₂ to HNO₃ is:
\[ \frac{3 \text{ moles NO}_2}{2 \text{ moles HNO}_3} \]

Using this ratio, we can find the moles of NO₂ required:
\[ \text{Moles of NO}_2 = 0.4 \text{ moles HNO}_3 \times \frac{3 \text{ moles NO}_2}{2 \text{ moles HNO}_3} = 0.6 \text{ moles NO}_2 \]

### Step 5: Calculate the Molar Mass of NO₂
Next, we calculate the molar mass of nitrogen dioxide (NO₂):
- Atomic mass of Nitrogen (N) = 14 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

Calculating the molar mass:
\[ \text{Molar mass of NO}_2 = 1 \times 14 + 2 \times 16 = 14 + 32 = 46 \text{ g/mol} \]

### Step 6: Convert Moles of NO₂ to Grams
Finally, convert the moles of NO₂ to grams:
\[ \text{Mass of NO}_2 = \text{moles} \times \text{molar mass} = 0.6 \text{ moles} \times 46 \text{ g/mol} = 27.6 \text{ g} \]

### Final Answer
Therefore, the mass of nitrogen dioxide required to produce 25.2 grams of nitric acid is:
\[ \text{Mass of NO}_2 = 27.6 \text{ g} \]

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