Certainly! Let's solve the problem step-by-step, ensuring clarity in each stage of the calculation.
Step 1: Understand the given data and the chemical reaction
We have the chemical reaction:
[tex]\[ P_2O_3 + 3H_2O \rightarrow 2H_3PO_3 \][/tex]
Given:
- We start with 92.3 grams of [tex]\( P_2O_3 \)[/tex].
Step 2: Calculate the molar masses
1. Calculate the molar mass of [tex]\( P_2O_3 \)[/tex]:
- Phosphorus (P) has an atomic mass of approximately 30.97 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
- [tex]\( P_2O_3 \)[/tex] contains 2 atoms of phosphorus and 3 atoms of oxygen.
So, the molar mass of [tex]\( P_2O_3 \)[/tex] is:
[tex]\[ 2 \times 30.97 + 3 \times 16.00 = 61.94 + 48.00 = 109.94 \, \text{g/mol} \][/tex]
2. Calculate the molar mass of [tex]\( H_3PO_3 \)[/tex]:
- Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.
- Phosphorus (P) has an atomic mass of approximately 30.97 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
- [tex]\( H_3PO_3 \)[/tex] contains 3 atoms of hydrogen, 1 atom of phosphorus, and 3 atoms of oxygen.
So, the molar mass of [tex]\( H_3PO_3 \)[/tex] is:
[tex]\[ 3 \times 1.01 + 30.97 + 3 \times 16.00 = 3.03 + 30.97 + 48.00 = 82.00 \, \text{g/mol} \][/tex]
Step 3: Convert given mass to moles
To find the moles of [tex]\( P_2O_3 \)[/tex], use the formula:
[tex]\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \][/tex]
For [tex]\( P_2O_3 \)[/tex]:
[tex]\[ \text{moles of } P_2O_3 = \frac{92.3 \, \text{g}}{109.94 \, \text{g/mol}} = 0.8395 \, \text{moles} \][/tex]
Step 4: Use stoichiometry to find moles of [tex]\( H_3PO_3 \)[/tex]
From the balanced chemical equation:
[tex]\[ P_2O_3 + 3H_2O \rightarrow 2H_3PO_3 \][/tex]
1 mole of [tex]\( P_2O_3 \)[/tex] produces 2 moles of [tex]\( H_3PO_3 \)[/tex].
So, the moles of [tex]\( H_3PO_3 \)[/tex] produced will be:
[tex]\[ \text{moles of } H_3PO_3 = 0.8395 \, \text{moles of } P_2O_3 \times 2 = 1.6791 \, \text{moles} \][/tex]
Step 5: Convert moles of [tex]\( H_3PO_3 \)[/tex] to mass
To find the mass of [tex]\( H_3PO_3 \)[/tex], use the formula:
[tex]\[ \text{mass} = \text{moles} \times \text{molar mass} \][/tex]
For [tex]\( H_3PO_3 \)[/tex]:
[tex]\[ \text{mass of } H_3PO_3 = 1.6791 \, \text{moles} \times 82.00 \, \text{g/mol} = 137.69 \, \text{g} \][/tex]
Final Result:
The mass of [tex]\( H_3PO_3 \)[/tex] formed from 92.3 grams of [tex]\( P_2O_3 \)[/tex] is 137.69 grams.
