Question

Referring to Problem 26-18, calculate the resolution for

(a) methylcyclohexene and methylcyclohexane.

(b) methylcyclohexene and toluene.

(c) methylcyclohexane and toluene.

Short answer

(a) Resolution between methylcyclohexene and methylcyclohexane is $1.13$.

(b) Resolution between methylcyclohexene and toluene is $2.65$.

(c) Resolution between methylcyclohexane and toluene is $3.73$.

Step-by-step solution

Part (a) Step 1: Given information 

The data given is as follows:

Compound	$t,\min$	$W,\min$
Air	1.9	-
Methylcyclohexane	10.0	0.76
Methylcyclohexene	10.9	0.82
Toluene	13.4	1.06

Part (a) Step 2: Resolution of a sample 

Resolution of a sample is as follows:

$R=\frac{2\left[{\left(t_R\right)}_B-{\left(t_R\right)}_A\right]}{W_A+W_B}............\left(1\right)$

Here, $R$is the resolution,${\left(t_R\right)}_B\mathrm{and}{\left(t_R\right)}_B$are retention time of A and B, $W_{\mathrm{A}}\mathrm{and}{W}_B$are the peaks widths for A and B.

Part (a) Step 3: Calculate resolution for methylcyclohexene and methylcyclohexane

Substitute the values for methylcyclohexene and methylcyclohexane in the above equation (1) as follows:

$$\begin{gathered} R=\frac{2\left[{\left(t_R\right)}_B-{\left(t_R\right)}_A\right]}{W_A+W_B} \\ =\frac{2\left[\left(10.9\right)-\left(10.0\right)\right]}{0.76+0.82} \\ =1.13 \end{gathered}$$

Part (b) Step 1: Calculate resolution for methylcyclohexene and toluene

Substitute the values for methylcyclohexene and toluene in the above equation (1) as follows:

$$\begin{gathered} R=\frac{2\left[{\left(t_R\right)}_B-{\left(t_R\right)}_A\right]}{W_A+W_B} \\ =\frac{2\left[\left(13.4\right)-\left(10.9\right)\right]}{1.06+0.82} \\ =2.65 \end{gathered}$$

Part (c) Step 1: Calculate resolution for methylcyclohexane and toluene

Substitute the values for methylcyclohexane and toluene in the above equation (1) as follows:

$$\begin{gathered} R=\frac{2\left[{\left(t_R\right)}_B-{\left(t_R\right)}_A\right]}{W_A+W_B} \\ =\frac{2\left[\left(13.4\right)-\left(10.0\right)\right]}{1.06+0.76} \\ =3.73 \end{gathered}$$