Consider the following reaction.
SO3(g) + H2O(l) → H2SO4(aq)
A chemist allows 60.9 g of SO3 and 11.1 g of H2O to react. When the reaction is finished, the chemist collects 54.4 g of H2SO4. Determine the limiting reactant, theoretical yield, and percent yield for the reaction
mols SO3 = grams/molar mass = ?
mols H2O = grams/molar mass = ?
Using the coefficients in the balanced equation, convert mols SO3 to mols H2SO4.
Do the same and convert mols H2O to mols H2SO4.
In limiting reagent problems the SMALLER amount of product formed is ALWAYS the right correct answer and the reagent responsible for that is the limiting reagent.
Then grams H2SO4 = mols H2SO4 x molar mass H2SO4. The is the theoretical yield(TY). The actual yield (AY) in the problem is 54.4 g.
% yield = (AY/TY)*100 = ?
To determine the limiting reactant, we need to compare the number of moles of each reactant with the stoichiometric ratio in the balanced equation.
1. Calculate the number of moles of SO3:
Molar mass of SO3 = 32.07 g/mol + 3 * 16.00 g/mol = 80.07 g/mol
Number of moles of SO3 = mass of SO3 / molar mass of SO3 = 60.9 g / 80.07 g/mol
2. Calculate the number of moles of H2O:
Molar mass of H2O = 2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
Number of moles of H2O = mass of H2O / molar mass of H2O = 11.1 g / 18.02 g/mol
3. Use the stoichiometric ratio from the balanced equation:
From the balanced equation, 1 mole of SO3 reacts with 1 mole of H2O. Therefore, the ratio of moles of SO3 to H2O is 1:1.
Based on the calculations, both SO3 and H2O are present in a 1:1 ratio. Therefore, neither reactant limits the reaction. The reaction will proceed until one of the reactants is completely consumed.
Next, we need to calculate the theoretical yield of H2SO4. The theoretical yield is the maximum amount of product that can be obtained from the limiting reactant, based on the stoichiometry of the balanced equation.
4. Calculate the molar mass of H2SO4:
Molar mass of H2SO4 = 2 * 1.01 g/mol + 32.07 g/mol + 4 * 16.00 g/mol = 98.09 g/mol
5. Calculate the number of moles of H2SO4:
Number of moles of H2SO4 = mass of H2SO4 / molar mass of H2SO4 = 54.4 g / 98.09 g/mol
6. The theoretical yield is the number of moles of H2SO4 obtained from the limiting reactant. Since both reactants are in a 1:1 ratio, the moles of H2SO4 is equal to the moles of SO3 and H2O (which are both the same).
7. Calculate the mass of the theoretical yield of H2SO4:
Mass of H2SO4 = Number of moles of H2SO4 * molar mass of H2SO4
Finally, we can calculate the percent yield of the reaction:
8. Percent yield = (Actual yield / Theoretical yield) * 100
Note: The actual yield is given as 54.4 g.
I hope these steps help! Let me know if you need any further assistance.
To determine the limiting reactant, theoretical yield, and percent yield for the reaction, we need to follow these steps:
Step 1: Calculate the molar masses of both SO3 and H2O.
The molar mass of SO3 = 32.1 g/mol (1 S atom + 3 O atoms)
The molar mass of H2O = 18.0 g/mol (2 H atoms + 1 O atom)
Step 2: Convert the masses of SO3 and H2O to moles.
Moles of SO3 = 60.9 g / 32.1 g/mol ≈ 1.9 mol
Moles of H2O = 11.1 g / 18.0 g/mol ≈ 0.6 mol
Step 3: Determine the stoichiometric ratio between SO3 and H2O.
From the balanced equation, for every 1 mole of SO3, we need 1 mole of H2O to react. Therefore, the ratio of moles between SO3 and H2O is 1:1.
Step 4: Identify the limiting reactant.
The limiting reactant is the one that is completely consumed, limiting the amount of the product that can be formed. Looking at the stoichiometric ratio, we can see that the ratio of moles is the same as the ratio of masses. Since the ratio is 1:1, the limiting reactant is H2O because it has the smaller number of moles (0.6 mol).
Step 5: Calculate the theoretical yield of H2SO4.
The balanced equation tells us that 1 mole of H2O reacts to produce 1 mole of H2SO4. Therefore, the theoretical yield of H2SO4 is equal to the number of moles of the limiting reactant (0.6 mol).
Step 6: Convert the theoretical yield from moles to grams.
The molar mass of H2SO4 = 98.1 g/mol (2 H atoms + 1 S atom + 4 O atoms).
The theoretical yield of H2SO4 = 0.6 mol × 98.1 g/mol ≈ 58.9 g.
Step 7: Calculate the percent yield.
The percent yield is a measure of how much of the theoretical yield was actually obtained.
Percent yield = (Actual yield / Theoretical yield) × 100
In this case, the actual yield is given as 54.4 g.
Percent yield = (54.4 g / 58.9 g) × 100 ≈ 92.4%
Therefore, the limiting reactant is H2O, the theoretical yield of H2SO4 is approximately 58.9 g, and the percent yield is approximately 92.4%.