A student decomposes water to produce hydrogen and oxygen. If the student begins with 34.7 g of water and collects 24.9 g of oxygen, what is her percent yield?
To find the percent yield, you need to compare the actual yield (24.9 g of oxygen) to the theoretical yield (the amount of oxygen that would be produced if all the water decomposed completely). In this case, the theoretical yield of oxygen can be determined using the molar ratio between water (H₂O) and oxygen (O₂).
1. Determine the molar masses:
The molar mass of water (H₂O) = (2 × molar mass of hydrogen) + molar mass of oxygen
The molar mass of hydrogen = 1.01 g/mol (approximately)
The molar mass of oxygen = 16.00 g/mol (approximately)
Calculating the molar mass of water:
Molar mass of water = (2 × 1.01 g/mol) + 16.00 g/mol = 18.02 g/mol (approximately)
2. Calculate the number of moles of water:
Moles of water = mass of water / molar mass of water
Moles of water = 34.7 g / 18.02 g/mol (approximately) = 1.92 mol (approximately)
3. Use the balanced chemical equation for the decomposition of water:
2H₂O -> 2H₂ + O₂
According to the equation, for every 2 moles of water decomposed, 1 mole of oxygen is produced.
4. Calculate the theoretical yield of oxygen:
Theoretical yield of oxygen = (moles of water) × (1 mole of O₂ / 2 moles of H₂O)
Theoretical yield of oxygen = 1.92 mol × (1 mol / 2 mol) = 0.96 mol (approximately)
5. Convert the theoretical yield of oxygen to grams:
Theoretical yield of oxygen = (moles of oxygen) × (molar mass of oxygen)
Theoretical yield of oxygen = 0.96 mol × 16.00 g/mol = 15.36 g (approximately)
6. Calculate the percent yield:
Percent yield = (actual yield / theoretical yield) × 100%
Percent yield = (24.9 g / 15.36 g) × 100% = 161.52%
Therefore, the student's percent yield of oxygen is approximately 161.52%.