Question

On combustion of 0.21 g of an organic compound containing C, H, and O, it gave 0.127 g of H$_2$O and 0.307 g of CO$_2$. The percentage of H and O in the given organic compound respectively are:

• A. 7.55 and 43.85
• B. 6.72 and 53.41
• C. 6.72 and 39.87
• D. 53.41 and 39.60

Hint:

When performing combustion analysis, ensure to account for the masses of carbon, hydrogen, and oxygen in the compound. Use stoichiometry to find the moles of each element and calculate the percentages.

Answer 1

The Correct Option is B

Step 1: Determine the moles of carbon in CO$_2$.
Given the molar mass of CO$_2$ is 44 g/mol and 0.307 g of CO$_2$ was produced during combustion.
The calculation for moles of carbon in CO$_2$ is as follows:
\[\text{Moles of C} = \frac{\text{Mass of CO}_2}{\text{Molar mass of CO}_2} = \frac{0.307 \, \text{g}}{44 \, \text{g/mol}} = 0.006977 \, \text{mol}\]As one mole of CO$_2$ contains one mole of carbon, the moles of carbon in the compound equate to 0.006977 mol.

Step 2: Compute the mass of carbon.
Using the molar mass of carbon as 12 g/mol, the mass of carbon is calculated as:
\[\text{Mass of C} = \text{Moles of C} \times \text{Molar mass of C} = 0.006977 \, \text{mol} \times 12 \, \text{g/mol} = 0.0837 \, \text{g}\]
Step 3: Ascertain the moles of hydrogen in H$_2$O.
The molar mass of H$_2$O is 18 g/mol, and 0.127 g of H$_2$O was yielded from combustion.
The number of moles of hydrogen in H$_2$O is determined by:
\[\text{Moles of H} = \frac{\text{Mass of H}_2\text{O}}{\text{Molar mass of H}_2\text{O}} = \frac{0.127 \, \text{g}}{18 \, \text{g/mol}} = 0.007056 \, \text{mol}\]Since each mole of H$_2$O contains two moles of hydrogen, the moles of hydrogen in the compound are 0.007056 mol × 2 = 0.014112 mol.

Step 4: Quantify the mass of hydrogen.
With the molar mass of hydrogen at 1 g/mol, the mass of hydrogen is determined as:
\[\text{Mass of H} = \text{Moles of H} \times \text{Molar mass of H} = 0.014112 \, \text{mol} \times 1 \, \text{g/mol} = 0.014112 \, \text{g}\]
Step 5: Compute the mass of oxygen.
Given the total mass of the compound is 0.21 g, the mass of oxygen is calculated as:
\[\text{Mass of O} = \text{Total mass of compound} - (\text{Mass of C} + \text{Mass of H}) = 0.21 \, \text{g} - (0.0837 \, \text{g} + 0.014112 \, \text{g}) = 0.21 \, \text{g} - 0.097812 \, \text{g} = 0.112188 \, \text{g}\]
Step 6: Calculate the percentage composition of hydrogen and oxygen.
The percentage of hydrogen is computed as:
\[\text{Percentage of H} = \frac{\text{Mass of H}}{\text{Mass of compound}} \times 100 = \frac{0.014112 \, \text{g}}{0.21 \, \text{g}} \times 100 = 6.72%\]The percentage of oxygen is calculated as:
\[\text{Percentage of O} = \frac{\text{Mass of O}}{\text{Mass of compound}} \times 100 = \frac{0.112188 \, \text{g}}{0.21 \, \text{g}} \times 100 = 53.41%\]