Problem 75 - A Complete Resource Book in Chemistry for JEE Main

Question

If \(0.1 \mathrm{~g}\) of an organic compound containing phosphorus gave \(0.222 \mathrm{~g}\) of \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\), then the percentage of phosphorus in the compound is (a) 31 (b) \(0.2\) (c) 66 (d) 62

Step-by-Step Solution

Answer

The percentage of phosphorus in the compound is 62% (option d).

Step 1: Determine the Molar Mass of Mg2P2O7

Calculate the molar mass of the compound \( \text{Mg}_2\text{P}_2\text{O}_7 \). Molar masses are: Mg: 24 g/mol, P: 31 g/mol, O: 16 g/mol. Therefore, \( \text{Mg}_2\text{P}_2\text{O}_7 = 2(24) + 2(31) + 7(16) = 24 \times 2 + 31 \times 2 + 16 \times 7 = 222 \text{ g/mol} \).

Step 2: Calculate Moles of Mg2P2O7 Produced

Using the given mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \) produced, calculate the moles: \[ \text{Moles of Mg}_2\text{P}_2\text{O}_7 = \frac{0.222 \text{ g}}{222 \text{ g/mol}} = 0.001 \text{ mol} \].

Step 3: Determine the Moles of Phosphorus in Mg2P2O7

Each mole of \( \text{Mg}_2\text{P}_2\text{O}_7 \) contains 2 moles of phosphorus since the formula is \( \text{Mg}_2\text{P}_2\text{O}_7 \). Thus, the moles of phosphorus are: \[ 0.001 \text{ mol Mg}_2\text{P}_2\text{O}_7 \times 2 = 0.002 \text{ mol P} \].

Step 4: Convert Moles of Phosphorus to Grams

The atomic mass of phosphorus is 31 g/mol. Convert the moles of phosphorus to grams: \[ 0.002 \text{ mol P} \times 31 \text{ g/mol} = 0.062 \text{ g P} \].

Step 5: Calculate the Percentage of Phosphorus in the Compound

Now, use the mass of phosphorus obtained in the previous step to find the percentage. \[ \text{Percentage of P} = \frac{\text{Mass of P}}{0.1 \text{ g of compound}} \times 100 = \frac{0.062}{0.1} \times 100 = 62\% \].

Key Concepts

Molar Mass Calculation

One essential skill in chemistry is the calculation of molar mass. Molar mass represents the weight of one mole of a substance and is expressed in grams per mole (g/mol). To calculate it, you need to sum the masses of all atoms present in the molecule. For instance, in the compound \(\text{Mg}_2\text{P}_2\text{O}_7\), you identify its constituent elements along with their respective atomic masses:

• Magnesium (Mg): 24 g/mol.
• Phosphorus (P): 31 g/mol.
• Oxygen (O): 16 g/mol.

By substituting these values into the formula, you derive:\[\text{Molar mass of } \text{Mg}_2\text{P}_2\text{O}_7 = 2(24) + 2(31) + 7(16) = 222 \text{ g/mol}\]This calculation aids in the subsequent steps that involve stoichiometry and further quantitative analysis.

Organic Compound Analysis

Organic compound analysis often involves determining the amount of a specific element within a compound. Here, in an organic compound with phosphorus, the task is to find how much phosphorus is present. By using the molar mass of a given product that contains phosphorus, such as \(\text{Mg}_2\text{P}_2\text{O}_7\), we can backtrack to find the amount of phosphorus in the original compound.

• First, calculate how many moles of \(\text{Mg}_2\text{P}_2\text{O}_7\) were formed from the organic compound. This is done using the mass of \(\text{Mg}_2\text{P}_2\text{O}_7\) and its molar mass.
• Given the formula \(\text{Mg}_2\text{P}_2\text{O}_7\), each mole contains two moles of phosphorus atoms.

From the example, \(0.001 \text{ mol of Mg}_2\text{P}_2\text{O}_7\) gives \(0.002 \text{ mol of P}\). This analytical method allows us to accurately determine the amount of an element in complex organic mixtures.

Percentage Composition

Determining the percentage composition of an element within a compound provides insight into the elemental makeup of substances. It reflects the proportion of that element relative to the entire compound. This is crucial for understanding the composition and purity of a material.

To compute the percentage composition:

• First, determine the mass of the element (e.g., phosphorus) within the compound. Convert moles of the element to grams using its atomic mass.
• Next, divide this mass by the total mass of the compound sample you started with.
• Finally, multiply the result by 100 to get a percentage.

In the problem, you found that \(0.062 \text{ g of P}\) was in the \(0.1 \text{ g}\) of the compound provided. Thus, the percentage of phosphorus is calculated as:\[\text{Percentage of P} = \frac{0.062}{0.1} \times 100 = 62\%\]These calculations are essential for fields ranging from chemistry to material science, where the precise composition influences the material's properties and applicability.