Question

Oleic acid, a component of olive oil, is 76.54% C, 12.13% H, and 11.33% 0. The

experimental value of the molar mass is 282 g/mol.
a. What is the molecular formula of oleic acid?
b. If oleic acid has a density of 0.895 g/mL, how many molecules of oleic acid
are in 3.00 mL of oleic acid?

Answer 1

To determine the molecular formula of oleic acid, we first calculate the empirical formula by converting the mass of carbon, hydrogen, and oxygen to moles and finding the ratio. The empirical formula of oleic acid is C9H18O2. The molecular formula is determined by comparing the experimental molar mass to the empirical molar mass and finding how many times the empirical formula must be repeated, resulting in a molecular formula of C17H34O4.

Step-by-step explanation:

To determine the molecular formula of oleic acid, we need to calculate the empirical formula first. Given the percentages of carbon, hydrogen, and oxygen in the compound, we can assume a 100g sample. This means we have 76.54g of carbon, 12.13g of hydrogen, and 11.33g of oxygen. Next, we convert these masses to moles by dividing by their respective molar masses: 76.54g of carbon is approximately 6.376 moles, 12.13g of hydrogen is approximately 12.06 moles, and 11.33g of oxygen is approximately 0.708 moles.
The empirical formula of oleic acid can be found by dividing the number of moles of each element by the smallest number of moles. In this case, oxygen has the fewest moles, so we divide each value by 0.708. This gives us a ratio of approximately 9 carbons, 18 hydrogens, and 2 oxygens. Therefore, the empirical formula is C9H18O2.
To find the molecular formula, we need to know the molar mass. Given that the experimental value of the molar mass is 282 g/mol, we compare this to the empirical formula's molar mass, which is approximately 170 g/mol.
To determine the number of times the empirical formula must be repeated to reach the molar mass of 282 g/mol, we divide the experimental molar mass by the empirical molar mass: 282 g/mol divided by 170 g/mol gives us approximately 1.66. Rounding this value, we find that the molecular formula of oleic acid is C17H34O4.

Answer 2

a) The molecular formula of oleic acid is:
`C_(18)H_(34)O_(2)`

b) There are 5.74 x 10^21 molecules of oleic acid in a 3.00 mL sample.

Step-by-step explanation:

a)

First, let's determine the empirical formula of oleic acid from the percentage composition provided by the question:

- Assuming a 100g sample of oleic acid, the correspondent mass of C, H and O would be:

mass of C = 76.54g

mass of H = 12.13g

mass of O = 11.33g

- We must determine the number of moles contained in each of the masses determined above. For that, let's use the atomic masses of C (12.01 u), H (1.007 u) and O (15.99 u) and the following equation:

`number of moles = (mass of sample)/(molar mass)`

number of moles of C = 76.54g / 12.01 g/mol = 6.373 mol C

number of moles of H = 12.13g / 1.007 g/mol = 12.04 mol H

number of moles of O = 11.33g / 15.99 g/mol = 0.7086 mol O

- Next, we'll try to find whole-number ratios by dividing each number of moles obtained by the smallest value obtained (0.7086):

C = 6.373 / 0.7086 = 8.994 ≅ 9

H = 12.04 / 0.7086 = 16.99 ≅ 17

O = 0.7086 / 0.7086 = 1.000

- Now, we can write the empirical formula of oleic acid as:
`C_(9)H_(17)O`

Now that we have the empirical formula for oleic acid (C9H17O), let's check its molar mass and compare it to the experimental value provided by the question (282 g/mol):

molar mass (C9H17O) = 9 * 12.01 + 17 * 1.007 + 1 * 15.99 = 141.9 g/mol

Note that the molar mass obtained from the empirical formula (141.9 g/mol) and the experimental molar mass (282 g/mol) are different, thus we need to find an integer multiple to determine the molecular formula (keep in mind that molecular formulas always present kind and number of atoms of each element present in the molecular compound, while the empirical formula presents the smallest coefficients for each atom).

Molecular formula = n × Empirical formula

This integer multiple, n, can be obtained by dividing the molar mass, MM , of the compound by the empirical formula mass, EFM (the molar mass represented by the empirical formula):

n = MM / EFM

n = 282 / 141.9

n = 1.987 ≅ 2

Since the integer multiple is 2, we can multiply all coefficients in the empirical formula by 2 to find the molecular formula of oleic acid:

C9 H17 O x 2 = C18 H34 O2

Therefore, the molecular formula of oleic acid is:
`C_(18)H_(34)O_(2)`

b)

We need to calculate the amount of molecules of oleic acid in a 3.00mL sample, considering the density as 0.895 g/mL.

From the density provided, we can calculate the mass, in grams, of oleic acid contained in 3.00 mL of this compound:

1 mL ----------------------- 0.895 g oleic acid

3.00 mL ----------------- x

Solving for x, we have that there are 2.69 g of oleic acid in a 3.00 mL sample.

Next, considering the molar mass of oleic acid (282 g/mol), we can calculate the number of moles contained in 2.685g of the acid:

282 g -------------------- 1 mol oleic acid

2.69 g ----------------- y

Solving for y, we have that there are 0.00953 moles of oleic acid in a 3.00 mL sample.

Now, using the Avogadro's number (6.022 x 10^23 particles/mol), we can calculate the amount of molecules of oleic acid in the sample:

1 mol oleic acid ------------------------------- 6.022 x 10^23 molecules oleic acid

0.00953 mol oleic acid ------------------- z

Solving for z, we have that there are 5.74 x 10^21 molecules of oleic acid in a 3.00 mL sample.