A chemist reacted 57.50 grams of sodium metal with an excess amount of chlorine gas. The chemical reaction that occurred is shown.
2Na + Cl2 → 2NaCl
If the percentage yield of the reaction is 86%, what is the actual yield? Show your work, including the use of stoichiometric calculations and conversion factors.
To find the actual yield, we need to first calculate the theoretical yield using stoichiometric calculations.
From the balanced chemical equation, we can see that 2 moles of sodium react with 1 mole of chlorine gas to produce 2 moles of sodium chloride.
1 mole of sodium has a molar mass of 22.99 g.
Therefore, 57.50 g of sodium is equal to 57.50 g / 22.99 g/mole = 2.50 moles of sodium.
Since the reaction is 2 moles of sodium to 2 moles of sodium chloride, we can deduce that 2.50 moles of sodium will produce 2.50 moles of sodium chloride.
The molar mass of sodium chloride is 58.44 g/mole.
Therefore, the theoretical yield of sodium chloride is 2.50 moles x 58.44 g/mole = 146.10 g.
Now, to find the actual yield, we can use the formula for percentage yield:
percentage yield = (actual yield / theoretical yield) x 100
Rearranging the formula to solve for the actual yield:
actual yield = (percentage yield / 100) x theoretical yield
actual yield = (86 / 100) x 146.10 g
actual yield = 0.86 x 146.10 g
actual yield = 125.67 g
Therefore, the actual yield of sodium chloride is 125.67 grams.
To determine the actual yield, we need to first calculate the theoretical yield using stoichiometric calculations.
Step 1: Find the molar mass of sodium (Na) and chlorine (Cl2).
- Molar mass of Na: 22.99 g/mol
- Molar mass of Cl2: 70.90 g/mol
Step 2: Convert grams of Na to moles.
- Moles of Na = Mass of Na / Molar mass of Na
- Moles of Na = 57.50 g / 22.99 g/mol
- Moles of Na ≈ 2.50 mol
Step 3: Use the stoichiometry of the balanced equation to determine the mole ratio.
- 2 moles of Na reacts with 1 mole of Cl2 to form 2 moles of NaCl.
Step 4: Calculate the moles of Cl2 needed for the reaction.
- Moles of Cl2 = Moles of Na * (1 mole Cl2 / 2 moles of Na)
- Moles of Cl2 = 2.50 mol * (1 mol Cl2 / 2 mol Na)
- Moles of Cl2 = 1.25 mol
Step 5: Convert moles of Cl2 to grams.
- Mass of Cl2 = Moles of Cl2 * Molar mass of Cl2
- Mass of Cl2 = 1.25 mol * 70.90 g/mol
- Mass of Cl2 ≈ 88.63 g
Step 6: Calculate the theoretical yield of NaCl (based on the balanced equation).
- The balanced equation shows that 2 moles of NaCl are produced from 1 mole of Cl2.
- Theoretical yield of NaCl = Moles of Cl2 * (2 moles of NaCl / 1 mole of Cl2)
- Theoretical yield of NaCl = 1.25 mol * (2 mol NaCl / 1 mol Cl2)
- Theoretical yield of NaCl = 2.50 mol
Step 7: Calculate the actual yield using the percentage yield.
- Percentage yield = (Actual yield / Theoretical yield) * 100
- Rearranging the formula to solve for actual yield: Actual yield = (Percentage yield / 100) * Theoretical yield
- Actual yield = (86 / 100) * 2.50 mol
- Actual yield ≈ 2.15 mol
Step 8: Convert the actual yield from moles to grams.
- Mass of NaCl(actual yield) = Moles of NaCl(actual yield) * Molar mass of NaCl
- Mass of NaCl(actual yield) = 2.15 mol * 58.44 g/mol
- Mass of NaCl(actual yield) ≈ 125.61 g
Therefore, the actual yield of NaCl is approximately 125.61 grams.