About 50% of U.S. and most Canadian sulfur is produced by the Claus process, in which sulfur is obtained from the H2S(g) that occurs in natural gas deposits or is produced when sulfur is removed from petroleum. The reactions are described by the equations
1)2H2S(g)+3O2(g)=2OS2(g)+2H2O(g)
2)SO2(g)+2H2S(g)=3S(l)+2H2O(g)
How many metric tons of sulfur can be produced from 2.00 million liters of H2S(g) at 6.00 bar and 200.0 degrees C?
Use PV = nRT to convert 2 million liters H2S gas at the conditions listed to mols.
Use the coefficients in the balanced equations to convert mols H2S to mols S.
That will be
mols H2S x (2 mols SO2/2 mols H2S) x (3 mols S/1 mol SO2) = mols S
Convert mols S to grams. g = mols S x atomic mass S. Then convert to metric tons.
To solve this problem, we need to use the ideal gas law and stoichiometry to calculate the amount of sulfur produced.
Step 1: Convert the volume of H2S from liters to moles.
The ideal gas law equation is given by PV = nRT, where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given conditions to Kelvin and atm:
Pressure, P = 6.00 bar = 6.00 atm (since 1 bar = 1 atm)
Temperature, T = 200.0°C = 200.0 + 273.15 = 473.15 K
Next, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
Substituting the given values:
n = (6.00 atm * 2.00 million liters) / [(0.0821 L·atm/(mol·K)) * 473.15 K]
Step 2: Calculate the moles of sulfur produced.
From the balanced chemical equation:
2 H2S(g) + 3 O2(g) → 2 SO2(g) + 2 H2O(g)
2 moles of H2S produce 2 moles of sulfur (S)
Since we have the number of moles of H2S obtained in Step 1, we can directly convert it to moles of sulfur.
Step 3: Convert moles of sulfur to metric tons.
Since we're given the molar mass of sulfur, we can use it to convert moles of sulfur to grams and then to metric tons.
The molar mass of sulfur, S = 32.07 g/mol. (You can find this value on the periodic table.)
Finally, we can convert the grams of sulfur to metric tons.
Now, let's put all these steps together to calculate the amount of sulfur produced.
Step 1:
n = (6.00 atm * 2.00 million liters) / [(0.0821 L·atm/(mol·K)) * 473.15 K]
First, calculate the value inside the square brackets:
= (0.0821 L·atm/(mol·K)) * 473.15 K
= 38.80 L·atm/mol
Now, substitute the values into the equation for n:
n = (6.00 atm * 2.00 million liters) / 38.80 L·atm/mol
Calculate n:
n = 309,278.35 mol
Step 2:
Since 2 moles of H2S produce 2 moles of S, the moles of sulfur produced will also be 309,278.35 mol.
Step 3:
Now, let's calculate the mass of sulfur produced in grams:
mass of sulfur = moles of sulfur * molar mass of sulfur
mass of sulfur = 309,278.35 mol * 32.07 g/mol
Finally, let's convert the mass of sulfur to metric tons:
mass of sulfur in metric tons = (mass of sulfur in grams) / 1,000,000
Substituting the values:
mass of sulfur in metric tons = (309,278.35 mol * 32.07 g/mol) / 1,000,000
Calculate the value:
mass of sulfur in metric tons = 9.904 metric tons
Therefore, approximately 9.904 metric tons of sulfur can be produced from 2.00 million liters of H2S(g) at 6.00 bar and 200.0 degrees C.