An experiment that led to the formation of the new field of organic chemistry involved the synthesis of urea, CN2H4O, by the controlled reaction of ammonia and carbon dioxide.
2 NH3(g) + CO2(g)= CN2H4O(s) + H2O(l)
What is the theoretical yield of urea when 100. g of ammonia is reacted with 100. g of carbon dioxide?
This is a limiting reagent problem. I do those this way.
mols NH3 = grams/molar mass
mols C = grams/molar mass
Using the coefficients in the balanced equation convert mols NH3 to mols urea.
Do the same with mols C to urea.
It is quite likely these values will be different which means one of them is not right. The correct value for mols in limiting reagent problems is ALWAYS the smaller value and the reagent responsible for that is the limiting reagent.
Using the smaller value, convert mol urea to g. g = mols x molasr mass. This is the theoretical yield.
To find the theoretical yield of urea, we need to determine the limiting reactant in the reaction. The limiting reactant is the reactant that is completely consumed and determines the maximum amount of product that can be formed.
We can find the limiting reactant by comparing the number of moles for each reactant.
Step 1: Calculate the number of moles for each reactant
Given:
Mass of ammonia (NH3) = 100 g
Molar mass of NH3 = 17.03 g/mol
Number of moles of NH3 = Mass / Molar mass
Number of moles of NH3 = 100 g / 17.03 g/mol
Given:
Mass of carbon dioxide (CO2) = 100 g
Molar mass of CO2 = 44.01 g/mol
Number of moles of CO2 = Mass / Molar mass
Number of moles of CO2 = 100 g / 44.01 g/mol
Step 2: Calculate the mole ratio of NH3 to CO2 in the balanced equation
The balanced equation is: 2 NH3(g) + CO2(g) = CN2H4O(s) + H2O(l)
From the equation, we can see that the mole ratio of NH3 to CO2 is 2:1.
Step 3: Determine the limiting reactant
To determine the limiting reactant, we compare the moles of each reactant using the mole ratio from the balanced equation.
From step 1:
Number of moles of NH3 = 100 g / 17.03 g/mol
Number of moles of CO2 = 100 g / 44.01 g/mol
Using the mole ratio of 2:1, we can see that CO2 is the limiting reactant because it has fewer moles compared to NH3.
Step 4: Calculate the theoretical yield of urea
Since CO2 is the limiting reactant, we need to find the number of moles of CO2 reacted, and then use the balanced equation to determine the number of moles of CN2H4O formed.
From step 1:
Number of moles of CO2 = 100 g / 44.01 g/mol
Using the balanced equation, the mole ratio of CO2 to CN2H4O is 1:1. Therefore, the number of moles of CN2H4O formed is also equal to the number of moles of CO2 reacted.
Step 5: Convert moles of CN2H4O to grams
Finally, we can calculate the mass of CN2H4O formed by multiplying the number of moles of CN2H4O by its molar mass.
Given:
Molar mass of CN2H4O = 60.06 g/mol
Mass of CN2H4O formed = Number of moles of CN2H4O * Molar mass of CN2H4O
Now, we can substitute the values into the equation:
Mass of CN2H4O formed = (100 g / 44.01 g/mol) * 60.06 g/mol
Simplifying the equation:
Mass of CN2H4O formed = 136.33 g
Therefore, the theoretical yield of urea when 100 g of ammonia is reacted with 100 g of carbon dioxide is 136.33 g.
To determine the theoretical yield of urea, you need to calculate the amount of the limiting reagent. The limiting reagent is the reactant that will be completely consumed and will determine the maximum amount of product that can be formed.
Step 1: Calculate the number of moles of ammonia (NH3) and carbon dioxide (CO2) using their respective molar masses.
Molar mass of NH3:
N = 14.01 g/mol × 1 = 14.01 g/mol
H = 1.01 g/mol × 3 = 3.03 g/mol
Total = 14.01 + 3.03 = 17.04 g/mol
Molar mass of CO2:
C = 12.01 g/mol × 1 = 12.01 g/mol
O = 16.00 g/mol × 2 = 32.00 g/mol
Total = 12.01 + 32.00 = 44.01 g/mol
Moles of NH3 = mass / molar mass
Moles of NH3 = 100. g / 17.04 g/mol = 5.86 mol
Moles of CO2 = mass / molar mass
Moles of CO2 = 100. g / 44.01 g/mol = 2.27 mol
Step 2: Determine the stoichiometric ratio between NH3 and urea (CN2H4O) from the balanced chemical equation.
From the balanced equation:
2 NH3 + CO2 = CN2H4O + H2O
The stoichiometric ratio between NH3 and CN2H4O is 2:1.
Step 3: Identify the limiting reagent.
To find the limiting reagent, compare the moles of each reactant with the stoichiometric ratio. The reactant with the smaller number of moles compared to the stoichiometric ratio is the limiting reagent.
Since the stoichiometric ratio between NH3 and CN2H4O is 2:1, you need twice as many moles of NH3 as CN2H4O to react fully.
Moles of CN2H4O = (5.86 mol NH3) / (2 mol NH3 / 1 mol CN2H4O) = 2.93 mol CN2H4O
Since the moles of CO2 (2.27 mol) are less than the moles of CN2H4O (2.93 mol), CO2 is the limiting reagent.
Step 4: Calculate the theoretical yield of CN2H4O (urea) using the moles of the limiting reagent (CO2) and the stoichiometric ratio from the balanced equation.
The stoichiometric ratio between CO2 and CN2H4O is 1:1.
Moles of CN2H4O = Moles of CO2 = 2.27 mol
Mass of CN2H4O = Moles of CN2H4O × Molar mass of CN2H4O
Mass of CN2H4O = 2.27 mol × (12.01 g/mol + 14.01 g/mol + 4 × 1.01 g/mol + 16.00 g/mol)
Mass of CN2H4O = 2.27 mol × 60.05 g/mol = 136.4 g
Therefore, the theoretical yield of urea (CN2H4O) when 100 g of ammonia and 100 g of carbon dioxide react is 136.4 g.