Question

1 g of an organic compound produces 1.49 g of \( \text{Mg}_2\text{P}_2\text{O}_7 \). Determine the percentage of phosphorus (P).

Hint:

When calculating the percentage composition of an element in a compound, first find the molar mass of the compound, then calculate the mass of the element of interest, and finally calculate the percentage.

Answer 1

Correct Answer: 42

Step 1: Molar Mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \).
To calculate the percentage of phosphorus, we first need to find the molar mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \). The molar masses of the elements are as follows: - \( \text{Mg} = 24.3 \, \text{g/mol} \), - \( \text{P} = 30.97 \, \text{g/mol} \), - \( \text{O} = 16.00 \, \text{g/mol} \). The molar mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \) is: \[ M = 2 \times 24.3 + 2 \times 30.97 + 7 \times 16.00 = 48.6 + 61.94 + 112.00 = 222.54 \, \text{g/mol} \]
Step 2: Calculate the mass of P in \( \text{Mg}_2\text{P}_2\text{O}_7 \).
The mass of phosphorus in \( \text{Mg}_2\text{P}_2\text{O}_7 \) is given by: \[ \text{Mass of P} = 2 \times 30.97 = 61.94 \, \text{g/mol} \]
Step 3: Determine the amount of phosphorus in 1.49 g of \( \text{Mg}_2\text{P}_2\text{O}_7 \).
We are given that 1 g of the organic compound produces 1.49 g of \( \text{Mg}_2\text{P}_2\text{O}_7 \). The amount of phosphorus in 1.49 g of \( \text{Mg}_2\text{P}_2\text{O}_7 \) is: \[ \text{Mass of P} = \frac{61.94}{222.54} \times 1.49 = 0.4187 \, \text{g} \]
Step 4: Calculate the percentage of phosphorus.
The percentage of phosphorus in the organic compound is: \[ \text{Percentage of P} = \frac{0.4187}{1} \times 100 = 42% \] Thus, the percentage of phosphorus in the organic compound is 42%.