Question

The absorbance of 0.1 M solution (A) of a compound "X" is 0.5, when measured using a cuvette of 1 cm length. Another solution (B) of the same compound, with unknown concentration, gave an absorbance of 0.125 using same cuvette. What is the expected concentration of solution B?

• A. 0.025 M
• B. 0.1 M
• C. 0.05 M
• D. 0.4 M

Hint:

Beer-Lambert law: \(A = \varepsilon c l\).
Absorbance is directly proportional to concentration.
\(c_2 = c_1 \times (A_2 / A_1)\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question tests the application of the Beer-Lambert law.

Step 2: Key Formula or Approach:
Beer-Lambert law: \(A = \varepsilon c l\).
For the same compound and cuvette, \(\varepsilon\) and \(l\) are constant.
So, \(A_1 / c_1 = A_2 / c_2\) (concentration is proportional to absorbance).

Step 3: Detailed Explanation:
Given:
A1 = 0.5, c1 = 0.1 M
A2 = 0.125, l = 1 cm (same)
Using the proportionality:
\[ \frac{A_1}{c_1} = \frac{A_2}{c_2} \] \[ \frac{0.5}{0.1} = \frac{0.125}{c_2} \] \[ 5 = \frac{0.125}{c_2} \] \[ c_2 = \frac{0.125}{5} = 0.025 \mathrm{M} \] Thus, the concentration of solution B is 0.025 M.

Step 4: Final Answer:
Thus, the expected concentration of solution B is 0.025 M, which corresponds to option (A).
[0.5cm]