determine the mass of CO2 produced when 51.2 g of CaO is reacted with 50.0 g of C according to the unbalanced equation CaO + C --------CaC2 =CO2
2CaO + 5C ==> 2CaC2 + CO2
This is a limiting reagent problem. I know that because amounts are given for BOTH of the reactants.
a. Convert 51.2g CaO to mols. mols = grams/molar mass.
b. Convert 50.0 g C to mols.
c. Using the coefficients in the balanced equation, convert mols CaO to mols CO2. Do the same to convert mols C to mols CO2.
d. It is likely that mols CO2 from c will NOT be the same which means one of them is not right; the correct answer in limiting reagent problems is ALWAYS the smaller value and the reagent producing that value is the limiting reagent.
e. Now convert mols CO2 to grams. g = mols x molar mass
To determine the mass of CO2 produced, we need to balance the chemical equation first:
CaO + 3C → CaC2 + CO2
Now, we can calculate the amount of CO2 produced.
Step 1: Calculate the number of moles of CaO and C using their respective molar masses.
Molar mass of CaO = 40.08 g/mol
Molar mass of C = 12.01 g/mol
Number of moles of CaO = 51.2 g / 40.08 g/mol
Number of moles of CaO = 1.277 mol
Number of moles of C = 50.0 g / 12.01 g/mol
Number of moles of C = 4.165 mol
Step 2: Determine the limiting reactant.
The limiting reactant is the reactant that is completely consumed, limiting the amount of product that can be formed. To determine the limiting reactant, we need to compare the moles of CaO and C.
According to the balanced equation, 1 mole of CaO reacts with 3 moles of C to produce 1 mole of CO2.
From the balanced equation, we can see that for the reaction to be complete, it requires three times as many moles of C as moles of CaO. Since we have 4.165 moles of C, it is in excess. CaO is the limiting reactant.
Step 3: Calculate the number of moles of CO2 produced.
From the balanced equation, we can see that 1 mole of CaO produces 1 mole of CO2.
Number of moles of CO2 = Number of moles of CaO
Number of moles of CO2 = 1.277 mol
Step 4: Calculate the mass of CO2 produced.
Mass of CO2 = Number of moles of CO2 × Molar mass of CO2
Molar mass of CO2 = 44.01 g/mol
Mass of CO2 = 1.277 mol × 44.01 g/mol
Mass of CO2 = 56.22 g
Therefore, the mass of CO2 produced when 51.2 g of CaO is reacted with 50.0 g of C is approximately 56.22 g.
To determine the mass of CO2 produced, we follow a few steps:
Step 1: Write the balanced equation for the reaction:
CaO + C → CaC2 + CO2
Step 2: Calculate the molar masses of the substances involved:
- Molar mass of CaO (calcium oxide) = 40.08 g/mol
- Molar mass of C (carbon) = 12.01 g/mol
- Molar mass of CO2 (carbon dioxide) = 44.01 g/mol
Step 3: Convert the given masses of CaO and C into moles:
- Moles of CaO = mass of CaO / molar mass of CaO
= 51.2 g / 40.08 g/mol
= 1.277 mol (rounded to three decimal places)
- Moles of C = mass of C / molar mass of C
= 50.0 g / 12.01 g/mol
= 4.163 mol (rounded to three decimal places)
Step 4: Determine the limiting reactant:
To identify the limiting reactant, we compare the moles of CaO and C. The reactant that is present in a smaller amount compared to the balanced equation's stoichiometry is the limiting reactant.
The balanced equation shows that 1 mol of CaO reacts with 1 mol of C to produce 1 mol of CO2. Therefore, the stoichiometric ratio is 1:1.
In this case, both reactants have more than one mole, so we can use their stoichiometric ratios directly.
Looking at the moles, CaO has 1.277 mol, and C has 4.163 mol.
From the stoichiometry, we can see that 4.163 mol of C would require 4.163 mol of CaO to react fully. However, 1.277 mol of CaO is less than 4.163 mol of CaO, indicating that CaO is the limiting reactant.
Step 5: Calculate the moles of CO2 produced:
Since CaO is the limiting reactant, we can calculate the moles of CO2 produced using the stoichiometry of the balanced equation:
From the stoichiometry, 1 mol of CaO produces 1 mol of CO2.
Therefore, the moles of CO2 produced would be the same as the moles of CaO, which is 1.277 mol.
Step 6: Convert moles of CO2 produced to grams:
We multiply the moles of CO2 by the molar mass of CO2 to get the mass:
Mass of CO2 = moles of CO2 × molar mass of CO2
= 1.277 mol × 44.01 g/mol
= 56.21 g (rounded to two decimal places)
Therefore, the mass of CO2 produced when 51.2 g of CaO reacts with 50.0 g of C is approximately 56.21 g.