Chapter 2, Problem 1ASA

Interpretation Introduction

Interpretation:

The $R_f$ values for the given chromatograph of a mixture are to be stated.

Concept introduction:

Chromatography is the technique used to identify the components of a mixture. The division of the distance covered by the component of a compound to the distance covered by solvent in the chromatography technique is known as the $R_f$ value. The full form of $R_f$ value is retention value.

Answer to Problem 1ASA

The $R_f$ values for the given chromatograph of a mixture which contains compounds A, B, C and D are $0.25$, $0.5$, $0.75$ and $1$ respectively.

Explanation of Solution

The chromatograph for a mixture that is prepared by a student is shown below.

Figure 1

The modified chromatogram with proper divided parts is shown below.

Figure 2

According to the above shown chromatogram, four compounds A, B, C and D are present in the mixture.

The total distance travelled by the solvent is $\text{L}$.

The total distance travelled by the compound A is $\text{L}/\text{4}$.

The total distance travelled by the compound B is $\text{L}/\text{2}$.

The total distance travelled by the compound C is $\text{3L}/\text{4}$.

The total distance travelled by the compound D is $\text{L}$.

The expression to represent the $R_f$ value is given below.

$R_f=\frac{\text{Distance}\text{travelled}\text{by}\text{the}\text{solute}\text{from}\text{baseline}}{\text{Distance}\text{travelled}\text{by}\text{the}\text{solvent from}\text{baseline}}$ …(1)

To calculate the $R_f$ value for compound A, substitute the value of distance travelled by compound A and distance travelled by solute in equation (1).

$\begin{array}{rll}{R}_f& =& \frac{\text{L}/\text{4}}{\text{L}}\\ & =& \frac{1}{4}\\ & =& 0.25\end{array}$

To calculate the $R_f$ value for compound B, substitute the value of distance travelled by compound A and distance travelled by solute in equation (1).

$\begin{array}{rll}{R}_f& =& \frac{\text{L}/\text{2}}{\text{L}}\\ & =& \frac{1}{2}\\ & =& 0.5\end{array}$

To calculate the $R_f$ value for compound C, substitute the value of distance travelled by compound A and distance travelled by solute in equation (1).

$\begin{array}{rll}{R}_f& =& \frac{\text{3L}/\text{4}}{\text{L}}\\ & =& \frac{3}{4}\\ & =& 0.75\end{array}$

To calculate the $R_f$ value for compound D, substitute the value of distance travelled by compound A and distance travelled by solute in equation (1).

$\begin{array}{rll}{R}_f& =& \frac{\text{L}}{\text{L}}\\ & =& 1\end{array}$

Therefore, the $R_f$ values are $0.25$, $0.5$, $0.75$ and $1$.

Conclusion

The $R_f$ values for the given chromatograph of a mixture which contains compounds A, B, C and D are $0.25$, $0.5$, $0.75$ and $1$ respectively.