Question

The molecule β-carotene has λ 450 nm, and ɛ = 15,000 m2 mol-1. Calculate the absorption (A) expected for a solution in which 0.1 mg has been dissolved in 10 ml of water (given: the molecular weight of β-carotene, C40H56, as 536) with a path length of 1 cm. Group of answer choices

Answer 1

The absorption (A) can be calculated using the Beer-Lambert Law by multiplying the molar absorptivity (ɛ), concentration (c), and path length (l). The expected absorption (A) for the given solution is approximately 0.028.

Step-by-step explanation:

The calculation of absorption (A) can be done using the Beer-Lambert Law, which states that the absorbance (A) is equal to the molar absorptivity (ɛ), the concentration of the sample (c), and the path length (l). The formula is given by:

A = ɛ * c * l

In this case, the molar absorptivity (ɛ) is given as 15,000 m2 mol-1. The concentration (c) can be calculated by dividing the mass of β-carotene (0.1 mg) by its molar mass (536 g/mol) and converting it to moles. The path length (l) is given as 1 cm.

Using the given values, the calculation becomes:

A = (15,000 m2 mol-1) * (0.0001 g / 536 g/mol / 1 L) * (0.01 L)

A = 0.028

Therefore, the expected absorption (A) for the solution is approximately 0.028.

Answer 2

Answer: The absorbance for a solution is 0.0028

Step-by-step explanation:

To calculate the absorption of a solution, the equation by Beer-Lambert law is used:

`A=\varepsilon * b* C`

OR

`A=\varepsilon * b* \frac{\text{Given mass of solute}* 1000}{\text{Molar mass of solute}* \text{Volume of solution (mL)}}`

where,

A = absorbance = ?

`\varepsilon` = molar absorptivity = [/tex]15000m^2mol^{-1}L[/tex]

b = path length = 1 cm = 0.01 m (Conversion factor: 1 m = 100 cm)

Given mass of
`\beta-` carotene = 0.1 mg = 0.0001 g (Conversion factor: 1 g = 1000 mg)

Molar mass of
`\beta-` carotene = 536 g/mol

Volume of solution = 10 mL

Putting values in equation 1:

`A=15000* 0.01* (0.0001* 1000)/(536* 10)\\\\A=0.0028`

Hence, the absorbance for a solution is 0.0028