Question

1. According to equation $25-2$if all conditions are constant, but particle size is reduced from$3\mathrm{\mu m}$to$0.7\mathrm{\mu m}$by what factor must pressure be increased to maintain constant linear velocity?
2. If all conditions except pressure are constant, by what factor will linear velocity increase if column pressure is increased by a factor of $10?$
3. With $0.7\mathrm{\mu m}$particles in a $9\mathrm{cm}\times 50$column, increasing pressure from $70\mathrm{MPa}\mathrm{to}700\mathrm{MPa}$ decreased analysis time by approximately a factor of $10$while increasing plate count from
4. $12000\mathrm{to}45{000}^{59}$Explain why small particles permit faster flow without losing efficiency or,in this case,with improved efficiency.

Short answer

Must pressure be increased to maintain constant linear velocity.

If all conditions except pressure are constant, by what factor will linear velocity.

small particles permit faster flow without losing efficiency or,in this case,with improved efficiency.

The equation$25-2$

$\mathrm{p}={\mathrm{f}}_{.}\frac{{\mathrm{u}}_{\mathrm{v}}.\mathrm{n}.\mathrm{L}.}{{\mathrm{\pi r}}^2.{\mathrm{d}}_{\mathrm{p}}^2}$

If all conditions except pressure are constant.

$$\begin{gathered} \mathrm{a})18.37\mathrm{times}\mathrm{greater} \\ \mathrm{b})10\mathrm{times} \end{gathered}$$

c) The small particles permit 10-fold faster flow without losing efficiency because small particles has faster transfer than large particles. So, velocity for maximum efficiency (highest plate number) increases.

Step-by-step solution

define constant linear

a) Must pressure be increased to maintain constant linear velocity.

The equation$25-2$

$\mathrm{p}=\mathrm{f}.\frac{{\mathrm{u}}_{\mathrm{v}}.\mathrm{n}.\mathrm{L}}{{\mathrm{\pi r}}^2.{{\mathrm{d}}_{\mathrm{p}}}^2}$

If all conditions are constant, but particle size $\left({\mathrm{d}}_{\mathrm{p}}\right)$is reduced from$3\mathrm{mm}$to $0.77\mathrm{mm}$the factor by the pressure must be increased to maintain constant linear velocity is:

$\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1}=\frac{{{\mathrm{d}}_1}^2}{{{\mathrm{d}}_2}^2}=\frac{3^2}{0.7^2}=18.37$

So, pressure must be$18.37$times greater.

b)If all conditions except pressure are constant, by what factor will linear velocity $\left({\mathrm{u}}_{\mathrm{v}}\right)$.

If all conditions except pressure are constant, the factor by linear velocity will increase if column pressure is increased by a factor of $10$is$10$because according to the equation in task a), we see that pressure is proportional to the velocity.

particles permit

C) small particles permit faster flow without losing efficiency or,in this case,with improved efficiency.

The small particles permit 10-fold faster flow without losing efficiency because small particles has faster transfer than large particles. So, velocity for maximum efficiency (highest plate number) increases.

$$\begin{gathered} \mathrm{Hence}, \\ \mathrm{a})18.37\mathrm{times}\mathrm{greater} \\ \mathrm{b})10\mathrm{times} \end{gathered}$$

c) The small particles permit 10-fold faster flow without losing efficiency because small particles has faster transfer than large particles. So, velocity for maximum efficiency (highest plate number) increases.