SEPTEMBER, 1937
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INDUSTRIAL AND ENGINEERING CHEMISTRY
V"i dt = 100 [l
-
The per cent of the total amount of substance distilled between the temperatures T$-I and Ti is,
D "i
(O)] [l
Q"i
- e-=]
(11)
. O
The elimination curve calculated from this equation (Figure 5 c ) is lower and flatter than that for the first hypothetical distillation calculated by Equation 9.
Distillation from a Nonvolatile Solvent at a Continuously Increasing Temperature
.
For some distillations, it is convenient to have the distillability increase continuously instead of by discrete jumps This situation might arise when a still is being supplied more power than necessary to maintain constant temperature, or when the distilland trickles down a column heated a t the bottom. The ways in which the distillability can vary with time are infinite, but for the simplest equations, let it be assumed that the distillability increases by the factor r every rn units of time. Then, D = br ( t / m ) if we let b represent the distillability and the rate of distillation at t = 0. The distillation starts at the temperature To. After m units of time, the temperature is T I , after 2m units of time it is T z , and after irn units of time it is Ti. Since a dilute solution in a nonvolatile solvent is again assumed, the mole fraction AT at any time t during the distillation is given h y
N
=
(1
979
100 [Qi.- Qi-l] = 100 [exp. -
bm(ri-1 l ) - exp. 100 lnr bm(r' 100 lnr -
"I
(I2)
Figure 6a shows the eliminatiQn curve for this type of distillation if b = 1, r = 2("*), and m = 1. The shape of this curve is almost the same as that for the distillation with discontinuous temperature changes shown in Figure 1. The effect of raising the temperature more slowly by letting m = 2 and also 4 is shown in Figure 6b and G . This shifting of the temperature of the maximum yield to a lower value when more time is taken is similar to that of the first type of distillation shown in Figure 2 . S
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