Calculate mass of phosphoric acid required to obtain 53.4 g pyrophosphoric acid.
`2H_(3)PO_(4) to H_(4)P_(2)O_(7) + H_(2)O`

Answer

To calculate the mass of phosphoric acid (H₃PO₄) required to obtain 53.4 g of pyrophosphoric acid (H₄P₂O₇), we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction is:
\[ 2 \text{H}_3\text{PO}_4 \rightarrow \text{H}_4\text{P}_2\text{O}_7 + \text{H}_2\text{O} \]

### Step 2: Determine the molar masses
- Molar mass of H₃PO₄:
- H: 1 g/mol × 3 = 3 g/mol
- P: 31 g/mol × 1 = 31 g/mol
- O: 16 g/mol × 4 = 64 g/mol
- Total = 3 + 31 + 64 = 98 g/mol

- Molar mass of H₄P₂O₇:
- H: 1 g/mol × 4 = 4 g/mol
- P: 31 g/mol × 2 = 62 g/mol
- O: 16 g/mol × 7 = 112 g/mol
- Total = 4 + 62 + 112 = 178 g/mol

### Step 3: Use stoichiometry to relate the masses
From the balanced equation, 2 moles of H₃PO₄ produce 1 mole of H₄P₂O₇. Therefore, the mass of H₃PO₄ required to produce 178 g of H₄P₂O₇ is:
- Mass of H₃PO₄ required = 2 × 98 g = 196 g

### Step 4: Set up a proportion to find the mass for 53.4 g of H₄P₂O₇
Using the ratio from the stoichiometry:
\[ \frac{196 \text{ g H}_3\text{PO}_4}{178 \text{ g H}_4\text{P}_2\text{O}_7} = \frac{x \text{ g H}_3\text{PO}_4}{53.4 \text{ g H}_4\text{P}_2\text{O}_7} \]

### Step 5: Solve for x
Cross-multiply to solve for x:
\[ x = \frac{196 \text{ g} \times 53.4 \text{ g}}{178 \text{ g}} \]
Calculating this gives:
\[ x = \frac{10478.4}{178} \approx 58.8 \text{ g} \]

### Conclusion
The mass of phosphoric acid required to obtain 53.4 g of pyrophosphoric acid is approximately **58.8 g**.

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