Using the given figure, the ratio of \(R_f\) values of sample A and sample C is x × 10–2. Value of x is __________.
Correct Answer: 50
Approach Solution - 1
The \(R_f\) value in chromatography is given by:
\[R_f = \frac{\text{Distance traveled by the sample spot}}{\text{Distance traveled by the solvent front}}.\]
Step 1: Calculate \(R_f\) for sample \(A\)
For sample \(A\):
\[R_f(A) = \frac{\text{Distance traveled by sample } A}{\text{Distance traveled by solvent front}} = \frac{5}{12.5}.\]
\[R_f(A) = 0.4.\]
Step 2: Calculate \(R_f\) for sample \(C\)
For sample \(C\):
\[R_f(C) = \frac{\text{Distance traveled by sample } C}{\text{Distance traveled by solvent front}} = \frac{10}{12.5}.\]
\[R_f(C) = 0.8.\]
Step 3: Calculate the ratio of \(R_f\) values
The ratio of \(R_f\) values for sample \(A\) and sample \(C\) is:
\[\text{Ratio} = \frac{R_f(A)}{R_f(C)} = \frac{0.4}{0.8} = 0.5.\]
Expressing the ratio as \(x \times 10^{-2}\):
\[\text{Ratio} = 50 \times 10^{-2}.\]
Final Answer: \(x = 50\).
Approach Solution -2
Distance of solvent front from base line = 12.5 cm
Distance travelled by sample A = 5.0 cm
Distance travelled by sample C = 10.0 cm
Step 2: Formula for Rf value.
\[ R_f = \frac{\text{Distance travelled by the sample}}{\text{Distance travelled by the solvent front}} \]
Step 3: Calculate Rf values.
For sample A:
\[ R_f(A) = \frac{5.0}{12.5} = 0.4 \]
For sample C:
\[ R_f(C) = \frac{10.0}{12.5} = 0.8 \]
Step 4: Find the ratio of Rf values.
\[ \frac{R_f(A)}{R_f(C)} = \frac{0.4}{0.8} = 0.5 = 50 \times 10^{-2} \]
Step 5: Final Answer.
Value of x = 50
Final Answer: 50
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