To determine the percentage composition of the elements in the compound [tex]\( \text{H}_4\text{P}_2\text{O}_7 \)[/tex] (pyrophosphoric acid), follow these steps:
### Step 1: Determine Atomic Weights
Given:
- The atomic weight of Hydrogen (H) is 1.
- The atomic weight of Phosphorus (P) is 31.
- The atomic weight of Oxygen (O) is 16.
### Step 2: Count the Number of Atoms in the Compound
The molecular formula [tex]\( \text{H}_4\text{P}_2\text{O}_7 \)[/tex] indicates:
- 4 Hydrogen (H) atoms
- 2 Phosphorus (P) atoms
- 7 Oxygen (O) atoms
### Step 3: Calculate the Molar Mass of the Compound
To find the molar mass of [tex]\( \text{H}_4\text{P}_2\text{O}_7 \)[/tex], sum the contributions of each element.
[tex]\[
\begin{align*}
\text{Molar mass of H}_4\text{P}_2\text{O}_7 &= (4 \cdot \text{atomic weight of H}) + (2 \cdot \text{atomic weight of P}) + (7 \cdot \text{atomic weight of O}) \\
&= (4 \cdot 1) + (2 \cdot 31) + (7 \cdot 16) \\
&= 4 + 62 + 112 \\
&= 178 \, \text{g/mol}
\end{align*}
\][/tex]
### Step 4: Calculate the Mass Contribution of Each Element
Now, calculate the mass of each element in one mole of [tex]\( \text{H}_4\text{P}_2\text{O}_7 \)[/tex]:
- Hydrogen: [tex]\( 4 \cdot 1 = 4 \, \text{g} \)[/tex]
- Phosphorus: [tex]\( 2 \cdot 31 = 62 \, \text{g} \)[/tex]
- Oxygen: [tex]\( 7 \cdot 16 = 112 \, \text{g} \)[/tex]
### Step 5: Calculate the Percentage Composition of Each Element
The percentage composition of each element is calculated as follows:
[tex]\[
\text{Percentage of H} = \left( \frac{\text{Mass of H}}{\text{Molar Mass}} \right) \cdot 100 = \left( \frac{4}{178} \right) \cdot 100 \approx 2.25\%
\][/tex]
[tex]\[
\text{Percentage of P} = \left( \frac{\text{Mass of P}}{\text{Molar Mass}} \right) \cdot 100 = \left( \frac{62}{178} \right) \cdot 100 \approx 34.83\%
\][/tex]
[tex]\[
\text{Percentage of O} = \left( \frac{\text{Mass of O}}{\text{Molar Mass}} \right) \cdot 100 = \left( \frac{112}{178} \right) \cdot 100 \approx 62.92\%
\][/tex]
### Summary
Thus, the percentage composition of [tex]\( \text{H}_4\text{P}_2\text{O}_7 \)[/tex] (pyrophosphoric acid) is:
- Hydrogen (H): [tex]\( \approx 2.25\% \)[/tex]
- Phosphorus (P): [tex]\( \approx 34.83\% \)[/tex]
- Oxygen (O): [tex]\( \approx 62.92\% \)[/tex]
