https://file.aiquickdraw.com/mathbot/file/1727328371162hozd7bin.jpg

The problem in the image describes a reaction based on the Haber process for synthesizing ammonia (NH₃) from nitrogen (N₂) and hydrogen (H₂) gases:

**Balanced reaction:**
\[
N_2 (g) + 3H_2 (g) \rightarrow 2NH_3 (g)
\]

You are provided with:
1. A flask containing **8.65 L** of nitrogen gas.
2. A flask containing **15.7 L** of hydrogen gas.
3. The gases are at **294 K** and a pressure of **0.94 bar**.

The question asks for the **mass of ammonia (NH₃)** produced under these conditions.

### Step-by-Step Solution

1. **Use the Ideal Gas Law** to determine the number of moles of each reactant (nitrogen and hydrogen).

   The ideal gas law is:
   \[
   PV = nRT
   \]
   Where:
   - \( P \) = pressure (0.94 bar, convert to atm),
   - \( V \) = volume of gas,
   - \( n \) = number of moles,
   - \( R \) = ideal gas constant (0.08206 L·atm/mol·K),
   - \( T \) = temperature (294 K).

2. **Calculate moles of nitrogen and hydrogen** available.

   After that, use the stoichiometry of the balanced equation to determine the limiting reagent (the one that gets completely used up). The ratio of nitrogen to hydrogen in the balanced equation is 1:3.

3. **Determine moles of ammonia produced** based on the limiting reagent.

4. **Convert moles of ammonia** into grams using its molar mass (17.03 g/mol).

I'll calculate each of these steps for you.The moles of nitrogen (\(N_2\)) and hydrogen (\(H_2\)) available are:

- Moles of \(N_2\): **0.333 moles**
- Moles of \(H_2\): **0.604 moles**

### Step 2: Identify the limiting reagent
From the balanced equation:
\[
N_2 (g) + 3H_2 (g) \rightarrow 2NH_3 (g)
\]
- 1 mole of \(N_2\) reacts with 3 moles of \(H_2\).

To find the limiting reagent:
- For 0.333 moles of \(N_2\), we would need \(0.333 \times 3 = 0.999\) moles of \(H_2\), but we only have 0.604 moles of \(H_2\). 

Thus, **\(H_2\) is the limiting reagent**.

### Step 3: Calculate the amount of ammonia (\(NH_3\)) produced
According to the stoichiometric ratio, 3 moles of \(H_2\) produce 2 moles of \(NH_3\). We can calculate the moles of \(NH_3\) from the moles of \(H_2\) available.

\[
\text{Moles of } NH_3 = \frac{2}{3} \times \text{moles of } H_2
\]

Let's calculate that next.The moles of ammonia (\(NH_3\)) produced are approximately **0.402 moles**.

### Step 4: Convert moles of ammonia to grams
The molar mass of \(NH_3\) is 17.03 g/mol. To find the mass of ammonia:

\[
\text{Mass of } NH_3 = \text{moles of } NH_3 \times \text{molar mass of } NH_3
\]

I'll calculate the mass now.The mass of ammonia (\(NH_3\)) produced is approximately **6.85 grams**.

### Summary of the process:
- Limiting reagent: \(H_2\)
- Moles of ammonia produced: 0.402 moles
- Mass of ammonia: 6.85 grams

Would you like further details or have any additional questions?

Here are 5 related questions for further exploration:
1. How would changing the temperature affect the yield of ammonia?
2. What role does pressure play in the Haber process?
3. How is the ideal gas law modified at very high pressures or low temperatures?
4. What industrial catalysts are used to speed up the Haber process?
5. How does the stoichiometry change if there is a different ratio of reactants?

**Tip:** In chemical reactions, identifying the limiting reagent helps predict how much product can be formed, making it crucial for efficiency and cost calculations.

Consider a reaction between a 8.65 L flask containing nitrogen gas and a 15.7 L flask of hydrogen gas. Both gases have a temperature of 294 K and the pressures inside both flasks is 0.94 bar. What mass of ammonia (in g) would you expect to be produced at a temperature of 294 K and a pressure of 0.94 bar?

Learn how to calculate the mass of ammonia produced in the Haber process from a reaction between nitrogen and hydrogen gas at 294 K and 0.94 bar using stoichiometry and the ideal gas law. Step-by-step guide on limiting reagent determination and gas laws.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation