Final answer:
The saponification value of olive oil is 190 mg KOH/1g fat. To calculate the average molecular weight of the fatty acids in the oil, the saponification value needs to be converted to moles of KOH and then divided by the number of moles of fat. The resulting value is 294.98 g/mol.
Step-by-step explanation:
The saponification value of olive oil is given as 190 mg KOH/1g fat. The saponification value is the amount of milligrams of KOH required to saponify 1 gram of fat. It is an indication of the molecular weight of the fatty acids in the oil. A high saponification value indicates low molecular weight fatty acids, while a low saponification value indicates high molecular weight fatty acids.
To calculate the average molecular weight of the fatty acids in the oil, we need to convert the saponification value to moles of KOH and then divide by the number of moles of fat. The formula weight of KOH is 56.11 g/mol.
First, convert the saponification value from mg KOH/1g fat to g KOH/1g fat:
saponification value = 190 mg KOH/1g fat = 0.190 g KOH/1g fat
Next, convert g KOH to moles KOH:
moles KOH = 0.190 g KOH / 56.11 g/mol = 0.00339 mol KOH
Since saponification of 1 mole of fat requires 1 mole of KOH, the number of moles of fat is also 0.00339 mol.
Finally, divide the gram weight of fat by the number of moles of fat to get the average molecular weight:
molecular weight of fat = 1 g / 0.00339 mol = 294.98 g/mol
Therefore, the average molecular weight of the fatty acids in the olive oil is 294.98 g/mol.