a. Biodiesel is an alternative to standard diesel fuel - VCE - SSCE Chemistry - Question 7 - 2010 - Paper 1

To calculate the volume of methanol required, we first need to find the number of moles of POP in 10.0 kg:

$n(\text{POP}) = \frac{\text{mass}}{\text{molar mass}} = \frac{10.0\, \text{kg}}{833\, \text{g mol}^{-1}} \times 1000\, \text{g/kg} = 12.0 \, \text{mol}$

Now, since the stoichiometric ratio is 3:1, we need 3 times the moles of methanol:

$n(\text{methanol}) = 3 \times n(\text{POP}) = 3 \times 12.0 \text{mol} = 36.0 \text{mol}$

Next, we can calculate the volume of methanol required using its density:

$\text{density} = 0.79 \, ext{g mL}^{-1}$

The mass of methanol will be:

$\text{mass} = n(\text{methanol}) \times M_r(\text{methanol}) = 36.0 \, \text{mol} \times 32.04 \, \text{g mol}^{-1} = 1153.44 \, \text{g}$

Finally, we convert mass to volume:

$\text{volume} = \frac{\text{mass}}{\text{density}} = \frac{1153.44 \, \text{g}}{0.79 \, \text{g mL}^{-1}} = 1456.2 \, \text{mL} = 1.456 \, \text{L}$

To find the number of double bonds in cervonic acid, we first calculate the number of moles of cervonic acid reacted:

$n(\text{cervonic acid}) = \frac{0.328 \, \text{g}}{328.0 \, \text{g mol}^{-1}} = 0.001 \, \text{mol}$

The number of moles of I_2 used is:

$n(\text{I}_2) = 0.300 \, \text{mol L}^{-1} \times 0.02000 \, \text{L} = 0.0060 \, \text{mol}$

Each double bond in cervonic acid reacts with one molecule of iodine, so the number of double bonds is equal to the number of moles of iodine reacted:

$n(\text{double bonds}) = 6$

Given that there are 22 carbon atoms in a molecule of cervonic acid, and knowing its structure, the formula can be written based on common fatty acid structures. The formula for cervonic acid is:

$C_{22}H_{34}O_2$

This represents the full molecular structure of the cervonic acid, including the carboxylic acid group.