To solve this problem, we need to follow these steps:

1. **Write the balanced chemical equation for the Haber reaction:**
$$ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) $$

2. **Use the Ideal Gas Law to find the moles of dinitrogen consumed per second:**
The Ideal Gas Law is given by:
$$ PV = nRT $$
Where:
- $ P $ is the pressure (0.64 atm)
- $ V $ is the volume (349 L)
- $ n $ is the number of moles
- $ R $ is the ideal gas constant (0.0821 L·atm/(K·mol))
- $ T $ is the temperature in Kelvin (222°C + 273.15 = 495.15 K)

Rearrange the Ideal Gas Law to solve for $ n $:
$$ n = \frac{PV}{RT} $$

Substitute the given values:
$$ n = \frac{(0.64 \text{ atm})(349 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)})(495.15 \text{ K})} $$

Calculate $ n $:
$$ n \approx \frac{223.36}{40.64} \approx 5.50 \text{ moles/second} $$

3. **Determine the moles of ammonia produced per second:**
From the balanced equation, 1 mole of $ N_2 $ produces 2 moles of $ NH_3 $. Therefore, the moles of $ NH_3 $ produced per second is:
$$ 2 \times 5.50 \text{ moles/second} = 11.00 \text{ moles/second} $$

4. **Convert moles of ammonia to mass:**
The molar mass of $ NH_3 $ is:
$$ 14.01 \text{ (N)} + 3 \times 1.01 \text{ (H)} = 17.04 \text{ g/mol} $$

The mass of $ NH_3 $ produced per second is:
$$ 11.00 \text{ moles/second} \times 17.04 \text{ g/mol} = 187.44 \text{ g/second} $$

5. **Convert grams per second to kilograms per second:**
$$ 187.44 \text{ g/second} = 0.18744 \text{ kg/second} $$

6. **Round the answer to 2 significant digits:**
$$ 0.19 \text{ kg/second} $$

Therefore, the rate at which ammonia is being produced is $ 0.19 $ kilograms per second.

Question

To solve this problem, we need to follow these steps:

1. **Write the balanced chemical equation for the Haber reaction:**
   $$ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) $$

2. **Use the Ideal Gas Law to find the moles of dinitrogen consumed per second:**
   The Ideal Gas Law is given by:
   $$ PV = nRT $$
   Where:
   - $ P $ is the pressure (0.64 atm)
   - $ V $ is the volume (349 L)
   - $ n $ is the number of moles
   - $ R $ is the ideal gas constant (0.0821 L·atm/(K·mol))
   - $ T $ is the temperature in Kelvin (222°C + 273.15 = 495.15 K)

Rearrange the Ideal Gas Law to solve for $ n $:
   $$ n = \frac{PV}{RT} $$

Substitute the given values:
   $$ n = \frac{(0.64 \text{ atm})(349 \text{ L})}{(0.0821 \text{ L·atm/(K·mol)})(495.15 \text{ K})} $$

Calculate $ n $:
   $$ n \approx \frac{223.36}{40.64} \approx 5.50 \text{ moles/second} $$

3. **Determine the moles of ammonia produced per second:**
   From the balanced equation, 1 mole of $ N_2 $ produces 2 moles of $ NH_3 $. Therefore, the moles of $ NH_3 $ produced per second is:
   $$ 2 \times 5.50 \text{ moles/second} = 11.00 \text{ moles/second} $$

4. **Convert moles of ammonia to mass:**
   The molar mass of $ NH_3 $ is:
   $$ 14.01 \text{ (N)} + 3 \times 1.01 \text{ (H)} = 17.04 \text{ g/mol} $$

The mass of $ NH_3 $ produced per second is:
   $$ 11.00 \text{ moles/second} \times 17.04 \text{ g/mol} = 187.44 \text{ g/second} $$

5. **Convert grams per second to kilograms per second:**
   $$ 187.44 \text{ g/second} = 0.18744 \text{ kg/second} $$

6. **Round the answer to 2 significant digits:**
   $$ 0.19 \text{ kg/second} $$

Therefore, the rate at which ammonia is being produced is $ 0.19 $ kilograms per second.

Knowee AI · Accepted Answer