A solution (A) with concentration of 0.010 mol L^{-1} gives an absorbance of 0.5. What concentration of this solution will give an absorbance reading of 0.25? Assume that both meas... A solution (A) with concentration of 0.010 mol L^{-1} gives an absorbance of 0.5. What concentration of this solution will give an absorbance reading of 0.25? Assume that both measurements were done using the same optical cell and at the same wavelength.
Understand the Problem
The question is asking about the unit of absorbance derived from Beer Lambert's law and provides a scenario involving a solution's concentration and absorbance. It seeks to determine the concentration of a solution that gives a specific absorbance reading based on a known measurement.
Answer
The concentration of the solution is $0.005 \text{ mol L}^{-1}$.
Answer for screen readers
The concentration of the solution that gives an absorbance reading of 0.25 is $0.005 \text{ mol L}^{-1}$.
Steps to Solve
- Understanding Beer-Lambert Law
Beer-Lambert Law is represented by the equation:
$$ A = \varepsilon c l $$
where:
( A ) = absorbance
( \varepsilon ) = molar absorptivity (in L mol(^{-1}) cm(^{-1}))
( c ) = concentration (in mol L(^{-1}))
( l ) = path length (in cm)
Since both solutions use the same optical cell, the path length ( l ) remains constant.
- Setting Up the Initial Condition
Given that the concentration ( c_1 = 0.010 ) mol L(^{-1}) results in an absorbance ( A_1 = 0.5 ), we can express this as:
$$ A_1 = \varepsilon c_1 l $$
Substituting known values:
$$ 0.5 = \varepsilon \cdot 0.010 \cdot l $$
- Calculating the Required Absorbance
We need to find the concentration ( c_2 ) that gives an absorbance ( A_2 = 0.25 ):
$$ A_2 = \varepsilon c_2 l $$
Substituting the known absorbance:
$$ 0.25 = \varepsilon c_2 l $$
- Calculating the Ratio of Absorbances
We can create a ratio of the two equations:
$$ \frac{A_1}{A_2} = \frac{\varepsilon c_1 l}{\varepsilon c_2 l} $$
This simplifies to:
$$ \frac{0.5}{0.25} = \frac{0.010}{c_2} $$
- Solving for ( c_2 )
Calculate the ratio:
$$ 2 = \frac{0.010}{c_2} $$
Cross-multiplying gives:
$$ c_2 = \frac{0.010}{2} = 0.005 \text{ mol L}^{-1} $$
The concentration of the solution that gives an absorbance reading of 0.25 is $0.005 \text{ mol L}^{-1}$.
More Information
The Beer-Lambert Law relates the absorbance of light by a solution to its concentration and the path length of the light through the solution. It is widely used in chemistry to determine the concentration of a solute in solution.
Tips
- Not recognizing that absorbance is directly proportional to concentration and path length.
- Confusing the units; ensuring correct unit conversions can prevent errors.
- Forgetting to set the same path length for different absorbance readings, which is crucial for comparisons.
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