Q36P Consider the chromatography of n... [FREE SOLUTION]

Chapter 24: Q36P (page 666)

Consider the chromatography of $n - c_{12} H_{26}$ on a 25 m 脳 0.53 mm open tubular column of 5% phenyl鈥�95% methyl polysiloxane with a stationary phase thickness of 3.0 $渭尘$ and He carrier gas at 125潞C. The observed retention factor for $n - c_{12} H_{26}$ is 8.0. Measurements were made of plate height, H, at various values of linear velocity, $渭_{x} (m / s)$ . A least-squares curve through the data points is given by
localid="1654864230381" $H (m) = (6.0 脳 10^{- 5} m^{2} / s) / 渭_{x} + (2.09 脳 10^{- 3} s) 渭_{x} the coefficients of the van Deemter equation, find the diffusion coefficient of n - c_{12} H_{26} in the mobile and stationary phases . Why is one of these diffusion coefficients so much greater than the other ?$

Short Answer

Expert verified

$From substituting the values we get the diffusion coefficient of n - C_{12} H_{26} i n m o b i l e p h a s e i s 3.0 脳 10^{- 5 \frac{m^{2}}{s}} and the diffusion coefficient of n - C_{12} H_{16} in stationary phase is 5.0 脳 10^{- 10} m^{2} / s . The diffusion coefficient of mobile is greater than the stationary phase because it is easier for the diffusion of solute through Helium gas than through a viscous liquid phase .$

Step by step solution

The deemter equation is taken in the form

$H = \frac{B}{渭_{x}} + C_{渭_{x}} = (C_{s} + C_{m}) 渭_{x} C_{s} = \frac{2 k}{3 {(k + 1)}^{2}} \frac{d^{2}}{d_{s}} C_{m} = \frac{1 + 6 k 11 k^{2}}{24 {(k + 1)}^{2}} \frac{r^{2}}{D_{m}} B = 2 D_{m}$

$Where D_{m} = diffusion coefficient of solute in mobile phase k = retention factor d = thickness of stationary phase D_{s} = diffusion coefficient of solute in stationary phase$

Diffusion coefficient of solute in mobile phase

$H = (6.0 脳 10^{- 5} m^{2} / s) 渭_{x} + (2.09 脳 10^{- 3} s) 渭_{x} B = 2 D_{M} = (6.0 脳 10^{- 5} m^{2} / s) D_{m} = 3.0 脳 10^{5} m^{2} / s F o r t h e s e c o n d t e r m, C_{s} + C_{m} = 2.09 脳 10^{- 3} s = \frac{2 k}{3 {(k + 1)}^{2}} \frac{d^{2}}{D_{s}} + \frac{1 + 6 k + 11 k^{2}}{24 {(k + 1)}^{2}} \frac{r^{2}}{d_{m}} c o n s u m p t i o n o f c i t r a t e a n d a c t i v a t i o n o f g l y c o l y s i s .$

Diffusion coefficient of solute in stationary phase

Substituting the values of all parameters to solve $D_{s}$

$2.09 脳 10^{- 3} s = \frac{2 (8.0)}{3 {(8.0 + 1)}^{2}} \frac{{(3.0 脳 10^{- 6} m)}^{2}}{D_{s}} + \frac{1 + 6 (8.0) + 11 {(80)}^{2}}{24 ({(8.0) + 1)}^{2}} \frac{{(2.65 脳 10^{- 4} m)}^{2}}{(3.0 脳 10^{- 5} m^{2} / s)} D_{s} = 5.0 脳 10^{- 10} m^{2} / s$

Diffusion coefficient in mobile phase

Diffusion coefficient in mobile phase= $\frac{3.0 脳 10^{- 5} m^{2} / s}{5.0 脳 10^{- 10} m^{2} / s} = 6.0 脳 10^{4}$

Reason why one of these diffusion coefficient is greater than the other

Diffusion coefficient in mobile phase is $6.0 脳 10^{- 4}$ times higher than the diffusion coefficient in stationary phase. The diffusion coefficient of mobile is greater than the diffusion coefficient in the stationary phase because it is easier for the diffusion of solute through Helium gas than through liquid phase.