Analysis of a compound gave 39.50% C, 2.20% H, and 58.30% Cl. When 0.855 g of this solid was dissolved in 7.50 g of napthalene, the solution had a freezing point of 78.0° C. The pure solvent freezes at 80.0° C; its molal freezing point constant is 6.8° C/m. What is the molecular formula of the compound? Assume that i is one. Enter your answer with the elements in the following order: Carbon, Hydrogen, and Chlorine. What is the molecular mass of the compound
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To determine the molecular formula of the compound, we need to first find the moles of carbon, hydrogen, and chlorine in the compound using the given percentages.
1. Assume we have 100g of the compound (for simple calculations).
- 39.50% of 100g = 39.50g of carbon
- 2.20% of 100g = 2.20g of hydrogen
- 58.30% of 100g = 58.30g of chlorine
2. Next, convert the masses of each element to moles using their molar masses.
- The molar mass of carbon (C) is 12.01 g/mol, so 39.50g of C represents 39.50 / 12.01 = 3.289 moles of carbon.
- The molar mass of hydrogen (H) is 1.008 g/mol, so 2.20g of H represents 2.20 / 1.008 = 2.183 moles of hydrogen.
- The molar mass of chlorine (Cl) is 35.45 g/mol, so 58.30g of Cl represents 58.30 / 35.45 = 1.644 moles of chlorine.
3. Determine the empirical formula by dividing each mole value by the smallest number of moles found.
- In this case, the smallest number of moles is 1.644 (chlorine), so divide all moles by 1.644:
- Carbon: 3.289 / 1.644 = 2
- Hydrogen: 2.183 / 1.644 ≈ 1.33 (rounded to the nearest whole number, so approximately 1)
- Chlorine: 1.644 / 1.644 = 1
- The empirical formula of the compound is C2H1Cl1, which simplifies to CHCl.
4. To find the molecular formula, we need to determine the ratio between the empirical formula and the molecular formula.
- Calculate the empirical formula's mass by adding the molar masses of each element:
- Carbon: 2 * 12.01 g/mol = 24.02 g/mol
- Hydrogen: 1 * 1.008 g/mol = 1.008 g/mol
- Chlorine: 1 * 35.45 g/mol = 35.45 g/mol
- The empirical formula mass is 60.478 g/mol.
5. Divide the molecular mass of the compound (which we are trying to find) by the empirical formula mass. This gives us the ratio of the two molecular formulas.
- Molecular mass of the compound = (Mass of the compound) / (Mass of the empirical formula)
- Let's assume the molecular mass of the compound is x.
- x / 60.478 g/mol = (molecular formula mass) / (empirical formula mass)
- We need to find the molecular formula mass.
6. Now let's use the cryoscopic constant and freezing point depression to find the molecular formula mass.
- Given:
- Freezing point depression (ΔTf) = 80.0°C - 78.0°C = 2.0°C
- Molal freezing point constant (Kf) = 6.8°C/molal
- Mass of solute (compound) = 0.855g
- Mass of solvent (napthalene) = 7.50g
- We can find the molality (m) using the formula:
- ΔTf = Kf * m
- Rearranging the formula, m = ΔTf / Kf
- m = 2.0°C / 6.8°C/molal
- m = 0.294 molal
- Next, we need to calculate the number of moles of the compound:
- Moles of compound = mass of compound / molar mass of compound
- Moles of compound = 0.855g / mass of compound (let's assume it is y g/mol)
- Combining the two equations, we get:
- 0.855g / y g/mol = 0.294 molal
- y = (0.855g) / (0.294 molal)
- y = 2.91 g/mol
7. Finally, substitute the value of y into the ratio equation from step 5 to find the molecular formula mass:
- Mass of the compound (molecular formula) = x = y / (empirical formula mass) * (mass of the empirical formula)
- x = (2.91 g/mol) / 60.478 g/mol * 60.478 g/mol
- x = 2.91 g/mol
Therefore, the molecular formula of the compound is CHCl, and its molecular mass is approximately 2.91 g/mol.
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