Phosphorus burns in oxygen according to the equation P4 + 502 → P4O10. How many litres of oxygen will be required at S.T.P for complete oxidation of 12.4g of phosphorus? [P = 31,O = 16 and molar volume of a gas at S.T.P = 22.4 litres]
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Correct Answer: Option B
Explanation:
To solve this, we need to determine how many liters of oxygen are required to completely oxidize 12.4 g of phosphorus (P) to form phosphorus pentoxide (PāOāā).
Step-by-Step Solution:
1. Find the moles of phosphorus (P):
The molar mass of phosphorus (P) is 31 g/mol.
\[
\text{Moles of phosphorus} = \frac{\text{Mass of phosphorus}}{\text{Molar mass of phosphorus}} = \frac{12.4 \, \text{g}}{31 \, \text{g/mol}} = 0.4 \, \text{mol}
\]
2. Write the balanced equation:
The balanced equation is:
\[
P_4 + 5O_2 \rightarrow P_4O_{10}
\]
This shows that 1 mole of Pā requires 5 moles of Oā for complete oxidation.
3. Find the moles of oxygen (Oā) required:
Since 1 mole of Pā requires 5 moles of Oā, and we have 0.4 moles of P (which is 0.4/4 = 0.1 moles of Pā):
\[
\text{Moles of Oā} = 5 \times 0.1 = 0.5 \, \text{mol}
\]
4. Convert moles of oxygen to liters:
At Standard Temperature and Pressure (S.T.P.), the molar volume of a gas is 22.4 liters/mol.
\[
\text{Volume of Oā} = 0.5 \, \text{mol} \times 22.4 \, \text{L/mol} = 11.2 \, \text{L}
\]
Therefore, the volume of oxygen required is 11.20 liters, which is approximately 11.20 liters.
The closest answer choice is B: 11.20.
To solve this, we need to determine how many liters of oxygen are required to completely oxidize 12.4 g of phosphorus (P) to form phosphorus pentoxide (PāOāā).
Step-by-Step Solution:
1. Find the moles of phosphorus (P):
The molar mass of phosphorus (P) is 31 g/mol.
\[
\text{Moles of phosphorus} = \frac{\text{Mass of phosphorus}}{\text{Molar mass of phosphorus}} = \frac{12.4 \, \text{g}}{31 \, \text{g/mol}} = 0.4 \, \text{mol}
\]
2. Write the balanced equation:
The balanced equation is:
\[
P_4 + 5O_2 \rightarrow P_4O_{10}
\]
This shows that 1 mole of Pā requires 5 moles of Oā for complete oxidation.
3. Find the moles of oxygen (Oā) required:
Since 1 mole of Pā requires 5 moles of Oā, and we have 0.4 moles of P (which is 0.4/4 = 0.1 moles of Pā):
\[
\text{Moles of Oā} = 5 \times 0.1 = 0.5 \, \text{mol}
\]
4. Convert moles of oxygen to liters:
At Standard Temperature and Pressure (S.T.P.), the molar volume of a gas is 22.4 liters/mol.
\[
\text{Volume of Oā} = 0.5 \, \text{mol} \times 22.4 \, \text{L/mol} = 11.2 \, \text{L}
\]
Therefore, the volume of oxygen required is 11.20 liters, which is approximately 11.20 liters.
The closest answer choice is B: 11.20.