Beer-Lambert Law Calculation
This problem involves calculating the concentration of a solution using the Beer-Lambert Law, which relates absorbance, concentration, path length, and molar absorptivity.
Transmittance to Absorbance Conversion
- The relationship between transmittance ($T$) and absorbance ($A$) is given by the formula:
$A = -\log_{10}(T)$
- Given transmittance $T = 20\% = 0.20$.
- Calculate absorbance:
$A = -\log_{10}(0.20)$
$A \approx 0.69897$
Concentration Calculation using Beer-Lambert Law
- The Beer-Lambert Law is expressed as:
$A = \epsilon b c$
where:- $A$ is absorbance (unitless)
- $\epsilon$ is the molar absorption coefficient ($12000 \text{ dm}^3/\text{mol.cm}$)
- $b$ is the path length ($2.5 \text{ cm}$)
- $c$ is the concentration (in $\text{mol/dm}^3$)
- Rearrange the formula to solve for concentration ($c$):
$c = \frac{A}{\epsilon b}$
- Substitute the known values:
$c = \frac{0.69897}{(12000 \text{ dm}^3/\text{mol.cm}) \times (2.5 \text{ cm})}$
$c = \frac{0.69897}{30000 \text{ dm}^3/\text{mol}}$
$c \approx 0.000023299 \text{ mol/dm}^3$
Final Result Formatting
- The question asks for the concentration in the format: ________ $\times 10^5 \text{ mol/dm}^3$.
- Based on the calculation, $c \approx 0.000023299 \text{ mol/dm}^3$. This value is equivalent to $2.3299 \times 10^{-5} \text{ mol/dm}^3$.
- To match the format format $X \times 10^5 \text{ mol/dm}^3$ while aligning with the provided answer range (2.32-2.34), it is inferred that the question intended the format $X \times 10^{-5} \text{ mol/dm}^3$.
- Therefore, the value for the blank ($X$) is approximately $2.3299$.
- Rounding this value to two decimal places gives $2.33$.
- This value lies within the range of 2.32 to 2.34.
Important Questions from Enzyme Assays Molar Extinction Coefficient
- A solution containing GTP has molar extinction coefficient of $1.55 \times 10^4$ $mol^{-1}dm^3cm^{-1}$ at a given wavelength. The concentration of GTP solution is $1.290 \times 10^{-5}$ $mol$ $dm^{-3}$. The absorbance of GTP solution in 1 cm cuvette at the same wavelength will be .................
- An enzyme preparation has activity of 2 Units per 20 $\mu$l, and protein concentration 0.4 mg/ml. The specific activity (Units/mg) of this enzyme will be ________
- Measurement of the absorbance of a solution containing NADH in a path length of 1cm cuvette at 340 nm shows the value of 0.31. The molar extinction coefficient of NADH is $6200 M^{-1} cm^{-1}$. The concentration of NADH in the solution is ________ $\mu M$ (correct to integer number).
- If a $10$ mM solution of a biomolecule in a cuvette of path length $10$ mm absorbs $90\%$ of the incident light at $280$ nm, the molar extinction coefficient of the biomolecule at this wavelength is ________ $M^{-1}cm^{-1}$. (Round off to two decimal places)
- The absorbance of a $5 \times 10^{-4}$ $M$ solution of tyrosine at 280 $nm$ wavelength is 0.75. The path length of the cuvette is 1 $cm$. The molar absorption coefficient at the given wavelength in $M^{-1}cm^{-1}$, correct to the nearest integer, is ________.
