Chapter 11: Problem 58

The combustion of \(3.795 \mathrm{mg}\) of liquid \(\mathrm{B}\), which contains only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O},\) with excess oxygen gave 9.708 \(\mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(3.969 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\). In a molar mass determination, \(0.205 \mathrm{~g}\) of \(\mathrm{B}\) vaporized at \(1.00 \mathrm{~atm}\) and \(200.0^{\circ} \mathrm{C}\) and occupied a volume of \(89.8 \mathrm{~mL}\). Derive the empirical formula, molar mass, and molecular formula of \(\mathrm{B}\) and draw three plausible structures.

Short Answer

Expert verified

The empirical formula is derived from the stoichiometry of the base elements in the compound (C, H, O). Then the molar mass is calculated by applying the ideal gas law, substituting the given values. The molecular formula is derived from the division of the molar mass by the mass of the empirical formula, and this result multiplies each of the atoms in the empirical formula. Finally, the plausible structures are drawn by considering the molecular formula and principles of chemical bonding.

Step by step solution

Calculate Moles of Carbon and Hydrogen

To find the number of moles of Carbon and Hydrogen, first identify the mass of CO2 and H2O produced in the reaction, then use the molar mass to convert to moles. The number of moles of Carbon and Hydrogen can be calculated as follows:\nFor carbon: 9.708 mg CO2 × (1 mol CO2 / 44.01 g CO2) × (1 mol C / 1 mol CO2) = 0.0002205 mol C\nFor hydrogen: 3.969 mg H2O × (1 mol H2O / 18.015 g H2O) × (2 mol H / 1 mol H2O) = 0.0004407 mol H

Calculate Moles of Oxygen

To calculate moles of Oxygen, subtract the mass of Carbon and Hydrogen from the total mass of the compound B. Thus, moles of Oxygen can be calculated as follows:\nOxygen mass = Total mass - Carbon mass - Hydrogen mass\nOxygen mass = 3.795 mg - (0.0002205 mol C × 12.01 g/mol C) - (0.0004407 mol H × 1.008 g/mol H)\nOxygen moles = Oxygen mass / Oxygen molar mass

Calculate Empirical Formula

Next, use these moles to calculate Empirical formula:\nDivide each mole by the smallest mole to get the atom ratio.

Calculate the Molar Mass

The molar mass of compound B can be found by using the Ideal Gas Law. Given the temperature, the pressure, and the volume, we can use the Ideal Gas law (PV=nRT) to solve for n (number of moles):\n0.205 g B × (1 mol B / Molar Mass) = (1.00 atm) × (89.8 mL × 1 L / 1000 mL) / (0.0821 L · atm / (K · mol) × (200.0°C + 273.15))\nMolar Mass is then calculated in g/mol.

Find the Molecular Formula

To find the molecular formula, divide the molar mass by the mass of the empirical formula. The result will be a whole number, which when multiplied by the empirical formula's atoms, gives the molecular formula.

Draw Plausible Structures

Finally, using the molecular formula of B and knowledge of chemical bonding principles, draw three plausible structures of molecule B.

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Short Answer

Step by step solution

Calculate Moles of Carbon and Hydrogen

Calculate Moles of Oxygen

Calculate Empirical Formula

Calculate the Molar Mass

Find the Molecular Formula

Draw Plausible Structures

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