Calculate the percent composition of gallium sulfite. 2) A compound contains 92.3% C and 7.7% H and has a molar mass of 78.0 g/mol. Determine the molecular formula. (3) Sorbitol, used as a sweetener in some sugar free foods, has a molecular formula of 182 g/mol and percent composition of 39.56% carbon, 7.74% hydrogen, and 52.70% of oxygen. What is the empirical formula and molecular formula of sorbitol.
The Correct Answer and Explanation is:
) Percent Composition of Gallium Sulfite (Ga2(SO3)3)
To find the percent composition of gallium sulfite, we need to calculate the molar mass of Ga2(SO3)3 and the contribution of each element.
Step 1: Calculate the Molar Mass of Ga2(SO3)3
- Gallium (Ga) has a molar mass of approximately 69.72 g/mol.
- Sulfur (S) has a molar mass of approximately 32.07 g/mol.
- Oxygen (O) has a molar mass of approximately 16.00 g/mol.
Molar mass of Ga2(SO3)3 = (2 × 69.72) + (3 × [32.07 + (3 × 16.00)])
= 139.44 + 3 × (32.07 + 48.00)
= 139.44 + 3 × 80.07
= 139.44 + 240.21
= 379.65 g/mol
Step 2: Calculate the Percent Composition of Each Element
- Percent composition of Ga = (139.44 / 379.65) × 100 = 36.74%
- Percent composition of S = (96.21 / 379.65) × 100 = 25.35%
- Percent composition of O = (240.21 / 379.65) × 100 = 63.26%
2) Molecular Formula of a Compound with 92.3% C and 7.7% H (Molar Mass = 78.0 g/mol)
Step 1: Find the Empirical Formula
Given:
- 92.3% C, 7.7% H
- Molar mass = 78.0 g/mol
Step 2: Convert Percentages to Grams (Assume 100 g of the compound)
- 92.3 g of carbon
- 7.7 g of hydrogen
Step 3: Convert Grams to Moles
- Moles of C = 92.3 g / 12.01 g/mol = 7.69 mol
- Moles of H = 7.7 g / 1.008 g/mol = 7.64 mol
Step 4: Determine the Ratio of Elements
- The ratio of moles of C to H is approximately 1:1.
- So, the empirical formula is CH.
Step 5: Determine the Molecular Formula
The empirical formula mass of CH is 12.01 + 1.008 = 13.018 g/mol.
- Molar mass of the compound is 78.0 g/mol.
- Ratio of molar mass to empirical formula mass = 78.0 / 13.018 = 6.
Thus, the molecular formula is C6H6 (benzene).
3) Empirical and Molecular Formulas of Sorbitol
Given:
- Molecular formula = 182 g/mol
- Percent composition:
- 39.56% C
- 7.74% H
- 52.70% O
Step 1: Convert Percentages to Grams (Assume 100 g of sorbitol)
- 39.56 g of carbon
- 7.74 g of hydrogen
- 52.70 g of oxygen
Step 2: Convert Grams to Moles
- Moles of C = 39.56 g / 12.01 g/mol = 3.296 mol
- Moles of H = 7.74 g / 1.008 g/mol = 7.67 mol
- Moles of O = 52.70 g / 16.00 g/mol = 3.294 mol
Step 3: Find the Empirical Formula
- The mole ratio of C:H:O is approximately 3:8:3.
- The empirical formula is C3H8O3.
Step 4: Determine the Molecular Formula
The empirical formula mass of C3H8O3 is:
(3 × 12.01) + (8 × 1.008) + (3 × 16.00) = 36.03 + 8.064 + 48.00 = 92.094 g/mol.
- The molar mass of sorbitol is 182 g/mol.
- Ratio of molar mass to empirical formula mass = 182 / 92.094 = 2.
Thus, the molecular formula is C6H14O6.
Summary:
- Gallium sulfite (Ga2(SO3)3) has a percent composition of 36.74% Ga, 25.35% S, and 63.26% O.
- The molecular formula of the compound with 92.3% C and 7.7% H and molar mass of 78.0 g/mol is C6H6 (benzene).
- The empirical formula of sorbitol is C3H8O3, and its molecular formula is C6H14O6.
