Question
What is the concentration of DNA in a solution if the corrected absorbance is 2.49?
You may copy/paste the following to indicate micro- μ. Report your answer to one decimal place.
Your Answer:
Question 14 options:
124.50
µg/mL
Answer units
Question 15 (2 points)
In this space, show your work for the question above.
Be sure that your work:
identifies the equation that you used to solve the problem,
identifies which numbers you substituted for which variables in the equation,
exhibits the math necessary to solve for the answer,
and includes appropriate units with your answer,
You may copy/paste the following to indicate "micro"- μ
Hint: An equation "equates" two entities. If you do not include two things separated by an "=", then you have not written an equation -- you will have simply written a mathematical operation.
You may copy/paste the following to indicate micro- μ. Report your answer to one decimal place.
Your Answer:
Question 14 options:
124.50
µg/mL
Answer units
Question 15 (2 points)
In this space, show your work for the question above.
Be sure that your work:
identifies the equation that you used to solve the problem,
identifies which numbers you substituted for which variables in the equation,
exhibits the math necessary to solve for the answer,
and includes appropriate units with your answer,
You may copy/paste the following to indicate "micro"- μ
Hint: An equation "equates" two entities. If you do not include two things separated by an "=", then you have not written an equation -- you will have simply written a mathematical operation.
Answers
GPT-4o mini
To determine the concentration of DNA in a solution based on the corrected absorbance, we typically use the Beer-Lambert Law, which relates absorbance (A) to concentration (C) and path length (l):
\[ A = \epsilon \cdot C \cdot l \]
Where:
- \( A \) = absorbance (corrected)
- \( \epsilon \) = molar absorptivity (a constant that depends on the substance and wavelength, typically measured in L/(mol·cm))
- \( C \) = concentration of the solution (usually in mol/L or µg/mL)
- \( l \) = path length, usually 1 cm for standard cuvettes
For DNA, the molar absorptivity (\( \epsilon \)) at 260 nm is typically around 50 µg/mL when using a 1 cm path length.
Given:
- Corrected absorbance, \( A = 2.49 \)
- \( \epsilon = 50 \, \text{µg/mL} \, \text{cm}^{-1} \)
- Path length, \( l = 1 \, \text{cm} \)
We can rearrange the equation to solve for \( C \):
\[ C = \frac{A}{\epsilon \cdot l} \]
Now, substituting the known values:
\[ C = \frac{2.49}{50 \, \text{µg/mL} \cdot 1 \, \text{cm}} \]
Now, perform the calculation:
\[ C = \frac{2.49}{50} \]
\[ C = 0.0498 \, \text{µg/mL} \]
Since we need to express the concentration in µg/mL and report to one decimal place, we multiply by 1000 to convert to µg/mL and round:
\[ C = 0.0498 \times 1000 = 49.8 \, \text{µg/mL} \]
Thus, the concentration is:
Your Answer: **49.8** µg/mL
---
### Work Explanation:
1. **Equation Used:**
- \( C = \frac{A}{\epsilon \cdot l} \)
2. **Values Substituted:**
- \( A = 2.49 \)
- \( \epsilon = 50 \, \text{µg/mL} \)
- \( l = 1 \, \text{cm} \)
3. **Math to Solve:**
- \( C = \frac{2.49}{50 \cdot 1} = \frac{2.49}{50} = 0.0498 \, \text{µg/mL} \)
- Convert to µg/mL: \( 0.0498 \times 1000 = 49.8 \, \text{µg/mL} \)
4. **Final Concentration:**
- **C** = 49.8 µg/mL
(Note: Based on the corrected absorbance of 2.49 and the standard molar absorptivity for DNA at 260 nm, the value derived above suggests a single unit of measurement has been interpreted differently than typically accepted in bioanalytical contexts, and the final answer here meets the requirement of one decimal place for reporting).
\[ A = \epsilon \cdot C \cdot l \]
Where:
- \( A \) = absorbance (corrected)
- \( \epsilon \) = molar absorptivity (a constant that depends on the substance and wavelength, typically measured in L/(mol·cm))
- \( C \) = concentration of the solution (usually in mol/L or µg/mL)
- \( l \) = path length, usually 1 cm for standard cuvettes
For DNA, the molar absorptivity (\( \epsilon \)) at 260 nm is typically around 50 µg/mL when using a 1 cm path length.
Given:
- Corrected absorbance, \( A = 2.49 \)
- \( \epsilon = 50 \, \text{µg/mL} \, \text{cm}^{-1} \)
- Path length, \( l = 1 \, \text{cm} \)
We can rearrange the equation to solve for \( C \):
\[ C = \frac{A}{\epsilon \cdot l} \]
Now, substituting the known values:
\[ C = \frac{2.49}{50 \, \text{µg/mL} \cdot 1 \, \text{cm}} \]
Now, perform the calculation:
\[ C = \frac{2.49}{50} \]
\[ C = 0.0498 \, \text{µg/mL} \]
Since we need to express the concentration in µg/mL and report to one decimal place, we multiply by 1000 to convert to µg/mL and round:
\[ C = 0.0498 \times 1000 = 49.8 \, \text{µg/mL} \]
Thus, the concentration is:
Your Answer: **49.8** µg/mL
---
### Work Explanation:
1. **Equation Used:**
- \( C = \frac{A}{\epsilon \cdot l} \)
2. **Values Substituted:**
- \( A = 2.49 \)
- \( \epsilon = 50 \, \text{µg/mL} \)
- \( l = 1 \, \text{cm} \)
3. **Math to Solve:**
- \( C = \frac{2.49}{50 \cdot 1} = \frac{2.49}{50} = 0.0498 \, \text{µg/mL} \)
- Convert to µg/mL: \( 0.0498 \times 1000 = 49.8 \, \text{µg/mL} \)
4. **Final Concentration:**
- **C** = 49.8 µg/mL
(Note: Based on the corrected absorbance of 2.49 and the standard molar absorptivity for DNA at 260 nm, the value derived above suggests a single unit of measurement has been interpreted differently than typically accepted in bioanalytical contexts, and the final answer here meets the requirement of one decimal place for reporting).