nitrogen gas reacts with hydrogen gas to form ammonia. The nitrogen gas is in a closed 500.0 mL flask at 751 mm HG connected to a 1.25 L flask containing the hydrogen gas at 1.21 atm pressure. Both flasks are kept at 37C. if the stopcock is opened and the gases are allowed to react with completion, how many moles of ammonia are formed?

To determine the number of moles of ammonia formed, we need to use the ideal gas law equation, PV = nRT, where P represents the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, let's convert the volume of the flask containing nitrogen gas to liters:
V1 = 500.0 mL = 500.0 / 1000 = 0.500 L

Next, we'll convert the pressure of the nitrogen gas to atm:
P1 = 751 mmHg = 751 / 760 atm

Similarly, we need to convert the volume of the flask containing hydrogen gas to liters:
V2 = 1.25 L

Finally, we'll convert the pressure of the hydrogen gas to atm:
P2 = 1.21 atm

The temperature, T, is given as 37°C, but we need to convert it to Kelvin:
T = 37°C + 273.15 = 310.15 K

Now, let's calculate the number of moles of ammonia formed using the ideal gas law equation.

For nitrogen gas:
n1 = (P1 * V1) / (R * T)

For hydrogen gas:
n2 = (P2 * V2) / (R * T)

Since the reaction between nitrogen and hydrogen is 1:3 (1 mole of nitrogen reacts with 3 moles of hydrogen to form 2 moles of ammonia), we need to use the ratio to find the limiting reactant.

Assuming nitrogen is the limiting reactant, we can calculate the moles of ammonia formed:
n_ammonia = (2/3) * n1

If hydrogen is the limiting reactant, we need to calculate the moles of ammonia accordingly:
n_ammonia = 2 * n2

To find the actual number of moles of ammonia formed, we compare the moles of ammonia from both scenarios (nitrogen and hydrogen being the limiting reactant) and choose the lower value.

Therefore, the number of moles of ammonia formed is the smaller of the two calculated values.

To solve this problem, we need to use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Step 1: Convert the given temperatures to Kelvin.
We need to convert the temperature of 37°C to Kelvin by adding 273.15. Thus, 37°C + 273.15 = 310.15 K.

Step 2: Calculate the number of moles for nitrogen gas.
Using the given information, the nitrogen gas is in a closed 500.0 mL flask at 751 mmHg pressure. To convert the volume to liters, divide by 1000: 500.0 mL ÷ 1000 = 0.5 L.
Now we can use the ideal gas law to find the moles of nitrogen gas:
PV = nRT
(751 mmHg)(0.5 L) = n(0.0821 L.atm/mol.K)(310.15 K)
37.55 = n(25.5248)
n ≈ 1.47 moles (rounded to two decimal places)

Step 3: Calculate the number of moles for hydrogen gas.
Using the given information, the hydrogen gas is in a 1.25 L flask at 1.21 atm pressure.
Using the ideal gas law again:
PV = nRT
(1.21 atm)(1.25 L) = n(0.0821 L.atm/mol.K)(310.15 K)
1.5125 = n(25.5248)
n ≈ 0.059 moles (rounded to three decimal places)

Step 4: Determine the limiting reactant.
To determine the limiting reactant, we compare the number of moles of nitrogen gas and hydrogen gas. The reactant that produces fewer moles of product is the limiting reactant.
Since nitrogen gas has 1.47 moles and hydrogen gas has 0.059 moles, hydrogen gas is the limiting reactant.

Step 5: Write the balanced chemical equation.
The balanced chemical equation for the reaction is:
N2 + 3H2 → 2NH3

Step 6: Determine the number of moles of ammonia formed.
From the balanced chemical equation, we can see that every two moles of NH3 is formed from three moles of H2. Therefore, the moles of NH3 formed would be:
(0.059 moles H2) x (2 moles NH3 / 3 moles H2) = 0.039 moles NH3

Therefore, approximately 0.039 moles of ammonia are formed when the gases react with completion.