Fish-liver oil is a good source of Vitamin A. When 0.1232 g of fish liver oil is dissolved in 500. mL of solvent, an absorbance of 0.724 is recorded. When 0.00167 g of Vitamin A is dissolved in 250. mL of solvent, an absorbance of 1.018 is recorded. Calculate the mass percent of Vitamin A in fish-liver oil.
I have no idea where to go with this for an equation. any assistance would be greatly appreciated.
To calculate the mass percent of Vitamin A in fish-liver oil, we need to compare the absorbance values of both the fish liver oil and pure Vitamin A solutions.
We can start by figuring out the concentration of the fish liver oil solution and the pure Vitamin A solution.
For the fish liver oil solution:
- Mass of fish liver oil = 0.1232 g
- Volume of solvent = 500 mL = 0.5 L
- Absorbance = 0.724
For the pure Vitamin A solution:
- Mass of Vitamin A = 0.00167 g
- Volume of solvent = 250 mL = 0.25 L
- Absorbance = 1.018
Now, we can use the Beer-Lambert Law, which states that absorbance is directly proportional to concentration, to find the concentration of each solution.
For the fish liver oil solution:
Absorbance = ε × concentration × path length
Where ε is the molar absorptivity (a constant that depends on the substance), and the path length is typically 1 cm.
For the pure Vitamin A solution:
Absorbance = ε × concentration × path length
Since the path length is the same for both solutions (1 cm), we can ignore it for our calculation.
Rearranging the Beer-Lambert Law:
concentration = absorbance / ε
To find the mass percent of Vitamin A in fish-liver oil, we need to compare the concentration of Vitamin A in the fish liver oil solution to the concentration of Vitamin A in the pure Vitamin A solution.
Let's calculate the concentrations for both solutions:
For the fish liver oil solution:
concentration_fish_liver_oil = absorbance_fish_liver_oil / ε_fish_liver_oil
For the pure Vitamin A solution:
concentration_pure_A = absorbance_pure_A / ε_pure_A
Now, to find the mass percent of Vitamin A in fish-liver oil, we can use the equation:
mass percent = (mass of Vitamin A in fish liver oil / mass of fish liver oil) x 100
For that, we need to calculate the mass of Vitamin A in fish liver oil:
mass of Vitamin A in fish liver oil = concentration_fish_liver_oil x volume_fish_liver_oil x molar mass of Vitamin A
Finally, we can plug in the values and calculate the mass percent of Vitamin A in fish-liver oil.
To calculate the mass percent of Vitamin A in fish-liver oil, we can use the relationship between absorbance and concentration, known as Beer-Lambert Law.
The Beer-Lambert Law states that the absorbance of a sample is directly proportional to the concentration of the absorbing species and the path length of the light through the sample.
The equation is given as:
A = εbc
Where:
A is the absorbance,
ε is the molar absorptivity (a constant that relates the absorbance to the concentration of the absorbing species),
b is the path length (which is generally constant),
and c is the concentration of the absorbing species.
Now, let's solve the problem step by step:
1. Determine the molar absorptivity (ε):
To find ε, we need to use the given data. We have two solutions with known concentrations and absorbance values.
For the solution with fish-liver oil:
Concentration (c₁) = 0.1232 g / 500 mL = 0.0002464 g/mL
Absorbance (A₁) = 0.724
For the solution with vitamin A:
Concentration (c₂) = 0.00167 g / 250 mL = 0.00000668 g/mL
Absorbance (A₂) = 1.018
Now, we can use the formula ε = A / (bc) to find the ε values for each solution.
For the fish-liver oil solution:
ε₁ = A₁ / (c₁ * b)
For the vitamin A solution:
ε₂ = A₂ / (c₂ * b)
2. Calculate the mass percent of Vitamin A in fish-liver oil:
Now that we have the molar absorptivity values, we can calculate the concentration of Vitamin A in the fish-liver oil solution.
Using the Beer-Lambert Law equation, we can rearrange it to find the concentration of Vitamin A (c):
c = A / (ε * b)
For the fish-liver oil solution:
c₁ = 0.724 / (ε₁ * b)
Now calculate the mass of Vitamin A in the fish-liver oil solution:
mass of Vitamin A (m) = c₁ * volume of fish-liver oil solution
Finally, calculate the mass percent of Vitamin A:
mass percent of Vitamin A = (mass of Vitamin A / mass of fish-liver oil) * 100
Substitute the values into the equations and solve for the mass percent.
A = kc
A = 1.018 for 250 mL.
1.018 = k*0.00167
Solve for k
For the unknown, assuming a straight line relationship, we want to compare the same volume of material; therefore, if we took 0.1232 g fish liver oil and dissolved it in 250 mL volume, the A would be twice that in the problem or 0.724*2
0.724*2 = k(from above)*C.
Solve for C which will be grams/250 mL.
%vitaminA = (g vit A in the sample/0.1232)*100 = ??% vit A.