soap made by primitive methods was likely
very
4. If the saponification value of olive oil is 190 mg KOH per gram, what is the SAP value of olive oil when using NaOH to
make soap? Hint: What is the ratio of the molar mass of NaOH to the molar mass of KOH?
Materials



Answer :

Sure, let's solve this problem step-by-step.

1. Understand the Saponification Value:
- The saponification value is the amount of potassium hydroxide (KOH), in milligrams, needed to saponify 1 gram of fat or oil.
- For olive oil, this value is given as 190 mg KOH per gram of oil.

2. Determine the Ratio of Molar Masses:
- The molar mass of KOH (potassium hydroxide) is approximately 56 g/mol.
- The molar mass of NaOH (sodium hydroxide) is approximately 40 g/mol.
- The ratio of the molar mass of NaOH to the molar mass of KOH is:

[tex]\[ \text{Ratio} = \frac{\text{Molar mass of NaOH}}{\text{Molar mass of KOH}} = \frac{40 \, \text{g/mol}}{56 \, \text{g/mol}} \][/tex]

Simplifying this ratio:

[tex]\[ \text{Ratio} = \frac{40}{56} = \frac{5}{7} \][/tex]

3. Calculate the Saponification Value with NaOH:
- Since the saponification value with KOH is given as 190 mg KOH per gram of oil, we need to convert this to the equivalent value using NaOH.
- Let's denote the saponification value with NaOH as [tex]\(SV_{NaOH}\)[/tex].

To find [tex]\(SV_{NaOH}\)[/tex], we use the ratio we determined above:

[tex]\[ SV_{NaOH} = 190 \, \text{mg KOH/g oil} \times \frac{5}{7} \][/tex]

Carry out the multiplication:

[tex]\[ SV_{NaOH} = 190 \times \frac{5}{7} = 190 \times 0.7142857 \][/tex]

[tex]\[ SV_{NaOH} \approx 135.71 \, \text{mg NaOH/g oil} \][/tex]

Thus, the saponification value of olive oil when using NaOH (sodium hydroxide) to make soap is approximately 135.71 mg NaOH per gram of oil.