Question

If you calculated the concentration of β-carotene in your 2.50 mL sample to be 2.209×10−6 M, how many grams of β-carotene are in your sample? The molar mass of β-carotene is 536.85 g/mole.

Answer 1

Mass β-carotene = 0.000002964754125 grams = 0.002964754125 mg = 2.964754125 µgrams

Step-by-step explanation:

Step1: Data given

Volume = 2.50 mL = 0.0025 L

Molarity = 2.209 * 10^-6 M

The molar mass of β-carotene is 536.85 g/mol

Step 2: Calculate moles β-carotene

Moles β-carotene = molarity * volume

Moles β-carotene = 2.209 * 10^-6 M * 0.0025 L

Moles β-carotene = 0.0000000055225 = 5.5*10^-9 moles

Step 3: Calculate mass of β-carotene

Mass β-carotene = moles β-carotene ¨molar mass β-carotene

Mass β-carotene = 5.5*10^-9 moles *536.85 g/mol

Mass β-carotene = 0.000002964754125 grams = 0.002964754125 mg = 2.964754125 µgrams

Answer 2

Answer: The mass of β-carotene in the sample is
`2.43* 10^(-6)g`

Step-by-step explanation:

To calculate the mass of solute, we use the equation used to calculate the molarity of solution:

`\text{Molarity of the solution}=\frac{\text{Mass of solute}* 1000}{\text{Molar mass of solute}* \text{Volume of solution (in mL)}}`

Given mass of β-carotene = ? g

Molar mass of β-carotene = 536.85 g/mol

Molarity of solution =
`2.209* 10^(-6)mol/L`

Volume of solution = 2.50 mL

Putting values in above equation, we get:

`2.209* 10^(-6)mol/L=\frac{\text{Mass of }\beta\text{ -carotene}* 1000}{536.85* 2.05}\\\\\text{Mass of }\beta\text{ -carotene}=(2.209* 10^(-6)* 536.85* 2.05)/(1000)=2.43* 10^(-6)g`

Hence, the mass of β-carotene in the sample is
`2.43* 10^(-6)g`