The Haber process for the synthesis of ammonia is one of the most significant industrial processes for the well being of humanity. It is used extensively in the production of fertilizers as well as polymers and other products.
N2 (g) + 3H2 (g) _ 2NH3 (g)
what volume of hydrogen at 15atm and at 350c must be supplied to produce 1.0 tons of NH3?
1 mole occupies 22.4L, so you want
PV = kT, so you want V such that
15V/(350+273) = 1*22.4/273
That's for each mole of H2 used.
How many moles of NH3 in 1 ton?
The equation tells you that you will need 3/2 that many moles of H2.
Well, if you're trying to produce 1.0 tons of NH3 using the Haber process, you'll need to do some calculations. Let's break it down step by step.
First, we need to convert the 1.0 tons of NH3 to grams. Since 1 ton is equal to 1000 kilograms, and 1 kilogram is equal to 1000 grams, we have:
1 ton = 1000 kg = 1000 * 1000 g = 1,000,000 g
Next, we need to convert the grams of NH3 to moles. The molar mass of NH3 is 17 g/mol, so we have:
1,000,000 g NH3 * (1 mol NH3 / 17 g NH3) = 58,823.53 mol NH3
According to the balanced equation, we need 3 moles of H2 for every 2 moles of NH3. So, to find the moles of H2 required, we can use a simple ratio:
58,823.53 mol NH3 * (3 mol H2 / 2 mol NH3) = 88,235.29 mol H2
Now, let's move on to determining the volume of hydrogen at 15 atm and 350°C. We can use the ideal gas law:
PV = nRT
where P is the pressure (15 atm), V is the volume in liters (which we need to find), n is the number of moles of the gas (88,235.29 mol H2), R is the ideal gas constant (0.08206 L·atm/(mol·K)), and T is the temperature in Kelvin (which we need to convert).
First, let's convert the temperature from Celsius to Kelvin:
350°C + 273.15 = 623.15 K
Now we can plug the values into the ideal gas law and solve for V:
(15 atm) * V = (88,235.29 mol H2) * (0.08206 L·atm/(mol·K)) * (623.15 K)
V = (88,235.29 mol H2) * (0.08206 L·atm/(mol·K)) * (623.15 K) / (15 atm)
V ≈ 233,187.06 liters of H2
So, to produce 1.0 ton of NH3, you would need to supply approximately 233,187.06 liters of hydrogen at 15 atm and 350°C. Just make sure you don't fill any balloons with hydrogen and start floating around like a real-life clown! Safety first!
To solve this problem, we need to use the ideal gas law equation and stoichiometry. Here are the steps to calculate the volume of hydrogen required:
Step 1: Convert the mass of ammonia to moles.
Given that 1.0 ton of NH3 is to be produced, we need to convert it to grams:
1.0 ton = 1000 kg = 1000000 g
Now, use the molar mass of ammonia (17.03 g/mol) to convert grams to moles:
Moles of NH3 = Mass of NH3 / Molar mass of NH3
Moles of NH3 = 1000000 g / 17.03 g/mol
Step 2: Use the balanced equation to find the moles of hydrogen needed.
From the balanced equation, we see that the stoichiometric ratio between ammonia and hydrogen is 2:3. Therefore, for every 2 moles of ammonia, we need 3 moles of hydrogen.
Moles of H2 = (Moles of NH3) × (3/2)
Moles of H2 = [(1000000 g / 17.03 g/mol)] × (3/2)
Step 3: Use the ideal gas law to calculate the volume of hydrogen.
The ideal gas law equation is: PV = nRT.
We are given:
Pressure (P) = 15 atm
Temperature (T) = 350°C = 350 + 273 = 623 K
We need to find the volume (V) at these conditions.
R is the ideal gas constant, which is 0.0821 L·atm/(K·mol).
Rearranging the ideal gas law equation, we get:
V = (nRT) / P
Substituting the values, we have:
V = [(Moles of H2) × (R) × (T)] / P
V = {[(1000000 g / 17.03 g/mol) × (3/2) × (0.0821 L·atm/(K·mol)) × (623 K)] / 15 atm
By performing the calculation, you will find the volume of hydrogen required to produce 1.0 ton of NH3 at the given conditions.
To find the volume of hydrogen gas needed to produce 1.0 ton of ammonia (NH3), we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L * atm / mol * K)
T = temperature (in Kelvin)
First, let's convert the weight of ammonia from tons to grams. Since 1 ton is equal to 1000 kilograms and 1 kilogram is equal to 1000 grams, 1.0 ton is equal to 1000 * 1000 grams = 1,000,000 grams.
Next, we need to find the number of moles of ammonia (NH3) produced. The molar mass of NH3 is calculated as follows:
(1 * atomic mass of N) + (3 * atomic mass of H) = (1 * 14.01 g/mol) + (3 * 1.01 g/mol) = 17.03 g/mol.
Moles of NH3 = (mass of NH3 / molar mass of NH3)
Moles of NH3 = (1,000,000 g / 17.03 g/mol)
Now, let's use the balanced equation to determine the mole ratio between hydrogen (H2) and ammonia (NH3). According to the equation, 3 moles of H2 produce 2 moles of NH3.
Moles of H2 needed = (moles of NH3 * ratio of H2 in the balanced equation)
Moles of H2 needed = [(1,000,000 g / 17.03 g/mol) * (3/2) ]
Now, let's apply the ideal gas law to find the volume of hydrogen gas at the given conditions.
P = 15 atm (given pressure)
T = 350°C + 273.15 = 623.15 K (convert Celsius to Kelvin)
Now, we can rearrange the ideal gas law equation to solve for volume (V):
V = (nRT) / P
V = [(moles of H2 needed) * (0.0821 L * atm / mol * K) * (623.15 K)] / 15 atm
By substituting the calculated values into the equation, you can find the volume of hydrogen gas required in liters.