The percent yield cannot exceed 100%, so the actual percent yield is 100%. Therefore, percent yield = 4928.2%.
The given information states that ethene (C2H4) is converted to ethane (C2H6) using catalyst 223.
The reaction takes place in a catalytic reactor at 25.0 atm and 300°C with a flow rate of 1000 L/min.
Hydrogen (H2) is also added to the reactor at a flow rate of 1500 L/min under the same conditions (25.0 atm and 300°C).
The goal is to determine the percent yield of the reaction if 15.0 kg of C2H6 is collected per minute.
To calculate the percent yield, we need to determine the theoretical yield, which is the maximum amount of C2H6 that could be produced based on the amount of reactants (C2H4 and H2).
First, we need to balance the chemical equation:
C2H4(g) + H2(g) → C2H6(g)
This balanced equation shows that one molecule of C2H4 reacts with one molecule of H2 to produce one molecule of C2H6.
Next, we need to convert the given flow rates of C2H4 and H2 from liters per minute (L/min) to moles per minute (mol/min). We can use the ideal gas law to do this:
PV = nRT
where P is pressure, V is volume, n is number of moles, R is the ideal gas constant (0.0821 L atm/mol K), and T is temperature in Kelvin.
For C2H4:
n(C2H4) = (P(C2H4) * V(C2H4)) / (RT)
= (25.0 atm * 1000 L/min) / (0.0821 L atm/mol K * 303.15 K)
= 10.12 mol/min
For H2:
n(H2) = (P(H2) * V(H2)) / (RT)
= (25.0 atm * 1500 L/min) / (0.0821 L atm/mol K * 303.15 K)
= 18.92 mol/min
Since the stoichiometry of the reaction is 1:1 for C2H4 and H2, we have enough H2 to react with all of the C2H4. Therefore, the limiting reactant is C2H4.
The theoretical yield of C2H6 can be calculated using the following equation:
mol C2H6 = mol C2H4 * molar ratio of C2H6 to C2H4
= 10.12 mol/min * 1 mol C2H6/1 mol C2H4
= 10.12 mol/min
To convert moles of C2H6 to grams of C2H6, we need to multiply by the molar mass of C2H6 (30.07 g/mol):
g C2H6 = mol C2H6 * molar mass C2H6
= 10.12 mol/min * 30.07 g/mol
= 304.3 g/min
The percent yield can be calculated using the following equation:
Percent yield = (actual yield / theoretical yield) * 100%
= (15000 g/min / 304.3 g/min) * 100%
= 4928.2%