To determine which conversion is not correct for the molecule [tex]\( C_{12}H_{22}O_{11} \)[/tex], let's analyze each one carefully based on the molecular composition of [tex]\( C_{12}H_{22}O_{11} \)[/tex]:
1. First Conversion:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{12 \text{ mole C }}
\][/tex]
The molecule [tex]\( C_{12}H_{22}O_{11} \)[/tex] contains 12 carbon (C) atoms. The issue here is that we're comparing a molecule (which refers to a discrete number of atoms) and a mole (which is a large quantity, Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex]). This should be referring to atoms, not moles. Correctly, it should be:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{12 \text{ atoms C }}
\][/tex]
2. Second Conversion:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{22 \text{ atom H}}
\][/tex]
The molecule [tex]\( C_{12}H_{22}O_{11} \)[/tex] contains 22 hydrogen (H) atoms. This conversion correctly states the number of hydrogen atoms per molecule of [tex]\( C_{12}H_{22}O_{11} \)[/tex]. Therefore, it is correct.
3. Third Conversion:
[tex]\[
\frac{11 \text{ atom O}}{22 \text{ atom H}}
\][/tex]
The molecule [tex]\( C_{12}H_{22}O_{11} \)[/tex] contains 11 oxygen (O) atoms and 22 hydrogen (H) atoms. This ratio simplifies to:
[tex]\[
\frac{11 \text{ atom O}}{22 \text{ atom H}} = \frac{1 \text{ atom O}}{2 \text{ atom H}}
\][/tex]
Proportionally, this conversion correctly reflects the internal ratio of oxygen to hydrogen atoms in the molecule.
By closely analyzing these conversions, the first conversion is incorrectly given as:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{12 \text{ mole C }}
\][/tex]
It should refer to individual atoms rather than moles for correct internal comparison:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{12 \text{ atom C }}
\][/tex]
Therefore, the incorrect internal conversion is:
[tex]\[
\frac{1 \text{ molecule } C_{12}H_{22}O_{11}}{12 \text{ mole C }}
\][/tex]
