. Determine the molecular formula of a compound that has a molar mass of 122.11 g/mol and an empirical formula of C2H5O2.

122.11 g/mol and an empirical formula of C2H5O2. Determine the molecular formula of a compound that has a molar mass of 122.11 g/mol and an empirical formula of C2H5O2. C2H5O2 C8H20O8 C6H15O6 C4H10O4 C3H7O3

The Correct Answer and Explanation is:

To determine the molecular formula of a compound, we need to use the empirical formula and the molar mass of the compound.

1. Step 1: Find the molar mass of the empirical formula.

The empirical formula is C2H5O2C_2H_5O_2C2​H5​O2​. We will calculate the molar mass of this empirical formula by adding the atomic masses of each element:

• Carbon (C): 12.01 g/mol12.01 \, \text{g/mol}12.01g/mol
• Hydrogen (H): 1.008 g/mol1.008 \, \text{g/mol}1.008g/mol
• Oxygen (O): 16.00 g/mol16.00 \, \text{g/mol}16.00g/mol

So, the molar mass of the empirical formula C2H5O2C_2H_5O_2C2​H5​O2​ is: Molar mass of empirical formula=(2×12.01)+(5×1.008)+(2×16.00)\text{Molar mass of empirical formula} = (2 \times 12.01) + (5 \times 1.008) + (2 \times 16.00)Molar mass of empirical formula=(2×12.01)+(5×1.008)+(2×16.00) =24.02+5.04+32.00=61.06 g/mol= 24.02 + 5.04 + 32.00 = 61.06 \, \text{g/mol}=24.02+5.04+32.00=61.06g/mol

2. Step 2: Compare the molar mass of the empirical formula to the given molar mass.

The molar mass of the compound is given as 122.11 g/mol122.11 \, \text{g/mol}122.11g/mol.

Now, divide the molar mass of the compound by the molar mass of the empirical formula to find how many times the empirical formula is repeated in the molecular formula: Molar mass of the compoundMolar mass of empirical formula=122.1161.06≈2\frac{\text{Molar mass of the compound}}{\text{Molar mass of empirical formula}} = \frac{122.11}{61.06} \approx 2Molar mass of empirical formulaMolar mass of the compound​=61.06122.11​≈2

3. Step 3: Multiply the empirical formula by this factor.

Since the ratio is approximately 2, we multiply the empirical formula C2H5O2C_2H_5O_2C2​H5​O2​ by 2: Molecular formula=(C2H5O2)×2=C4H10O4\text{Molecular formula} = (C_2H_5O_2) \times 2 = C_4H_{10}O_4Molecular formula=(C2​H5​O2​)×2=C4​H10​O4​

4. Step 4: Identify the correct molecular formula.

From the options provided:

• C2H5O2C_2H_5O_2C2​H5​O2​ is the empirical formula, not the molecular formula.
• C8H20O8C_8H_{20}O_8C8​H20​O8​, C6H15O6C_6H_{15}O_6C6​H15​O6​, and C3H7O3C_3H_7O_3C3​H7​O3​ are not correct since they do not match the factor of 2.
• The correct molecular formula is C4H10O4C_4H_{10}O_4C4​H10​O4​.

Conclusion:

The molecular formula of the compound is C4H10O4.