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A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]
Correct answer is '0.40 to 0.42'. Can you explain this answer?
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A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. ...
Given information:
- Concentration of protein solution: 0.1% (w/v)
- Absorbance of the solution at this concentration: 20%
To find:
- Fraction of light transmitted when the concentration is increased to 0.4%
Solution:
Step 1: Understanding Absorbance
Absorbance is a measure of how much light is absorbed by a solution. It is calculated using the equation: A = log(Io/I), where A is the absorbance, Io is the intensity of the incident light, and I is the intensity of the transmitted light.
The absorbance can be converted to a percentage by multiplying it by 100.
Step 2: Relationship between Concentration and Absorbance
The absorbance of a solution is directly proportional to the concentration of the solute. This relationship is described by the Beer-Lambert Law, which states that the absorbance is equal to the product of the molar absorptivity (ε), the path length (l), and the concentration of the solute (c): A = εcl.
In this case, the concentration of the protein solution is given as 0.1% (w/v) and the absorbance is given as 20%. We can use these values to determine the molar absorptivity.
Step 3: Calculating Molar Absorptivity
Using the equation A = εcl, we can rearrange it to solve for ε: ε = A/(cl).
Given:
- Concentration (c) = 0.1% (w/v) = 0.1 g/100 mL = 0.001 g/mL
- Absorbance (A) = 20%
- Path length (l) = 1 cm (assuming standard cuvette)
Substituting these values into the equation, ε = (0.2)/(0.001 * 1) = 200 mL/g/cm.
Step 4: Calculating Fraction of Light Transmitted
Now that we have determined the molar absorptivity, we can calculate the fraction of light transmitted at a new concentration of 0.4%.
Given:
- Concentration (c) = 0.4% (w/v) = 0.4 g/100 mL = 0.004 g/mL
- Path length (l) = 1 cm (assuming standard cuvette)
Using the Beer-Lambert Law (A = εcl), we can rearrange it to solve for the absorbance (A): A = εcl.
Substituting the values into the equation, A = (200 mL/g/cm) * (0.004 g/mL) * (1 cm) = 0.8.
The absorbance at the new concentration is 0.8. Since absorbance is directly proportional to the fraction of light absorbed, the fraction of light transmitted is 1 - absorbance = 1 - 0.8 = 0.2.
Final Answer:
The fraction of light transmitted when the concentration is increased to 0.4% is approximately 0.20, or 20%.
- Concentration of protein solution: 0.1% (w/v)
- Absorbance of the solution at this concentration: 20%
To find:
- Fraction of light transmitted when the concentration is increased to 0.4%
Solution:
Step 1: Understanding Absorbance
Absorbance is a measure of how much light is absorbed by a solution. It is calculated using the equation: A = log(Io/I), where A is the absorbance, Io is the intensity of the incident light, and I is the intensity of the transmitted light.
The absorbance can be converted to a percentage by multiplying it by 100.
Step 2: Relationship between Concentration and Absorbance
The absorbance of a solution is directly proportional to the concentration of the solute. This relationship is described by the Beer-Lambert Law, which states that the absorbance is equal to the product of the molar absorptivity (ε), the path length (l), and the concentration of the solute (c): A = εcl.
In this case, the concentration of the protein solution is given as 0.1% (w/v) and the absorbance is given as 20%. We can use these values to determine the molar absorptivity.
Step 3: Calculating Molar Absorptivity
Using the equation A = εcl, we can rearrange it to solve for ε: ε = A/(cl).
Given:
- Concentration (c) = 0.1% (w/v) = 0.1 g/100 mL = 0.001 g/mL
- Absorbance (A) = 20%
- Path length (l) = 1 cm (assuming standard cuvette)
Substituting these values into the equation, ε = (0.2)/(0.001 * 1) = 200 mL/g/cm.
Step 4: Calculating Fraction of Light Transmitted
Now that we have determined the molar absorptivity, we can calculate the fraction of light transmitted at a new concentration of 0.4%.
Given:
- Concentration (c) = 0.4% (w/v) = 0.4 g/100 mL = 0.004 g/mL
- Path length (l) = 1 cm (assuming standard cuvette)
Using the Beer-Lambert Law (A = εcl), we can rearrange it to solve for the absorbance (A): A = εcl.
Substituting the values into the equation, A = (200 mL/g/cm) * (0.004 g/mL) * (1 cm) = 0.8.
The absorbance at the new concentration is 0.8. Since absorbance is directly proportional to the fraction of light absorbed, the fraction of light transmitted is 1 - absorbance = 1 - 0.8 = 0.2.
Final Answer:
The fraction of light transmitted when the concentration is increased to 0.4% is approximately 0.20, or 20%.
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A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]Correct answer is '0.40 to 0.42'. Can you explain this answer?
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A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]Correct answer is '0.40 to 0.42'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]Correct answer is '0.40 to 0.42'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 0.1% (w/v) solution of a protein absorbs 20% of the incident light. What fraction of light is transmitted if the concentration is increased to 0.4%? [Correct to two decimal places]Correct answer is '0.40 to 0.42'. Can you explain this answer?.
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