Nurul Aini / 110405014

Rizka Rinda / 110405063

Ekstraksi Cair-cair Multitahap

Proses ekstraksi berlawanan arah 10 tahap dilakukan untuk mengekstrak solute A dari

campuran umpan W dengan menggunakan solvent S murni. Pada masing-masing tahap

diasumsikan terjadi kesetimbangan dengan persamaan : yi = K.xi.

Neraca komponen A untuk tahap ke-i:

xi-1.W + yi+1.S = xi.W + yi.S

Bila diketahui data berikut:

S = 1000 kg/jam

xAin = 0,05 K = 10

W = 2000 kg/jam

yAin = 0

Penyelesaian:

Tahap I

xi-1.W + yi+1.S = xi.W + yi.S

xin W + y2S = x1 W + y1 S

xin W + Kx2S = x1 W + Kx1 S

(0,05) (2000) + (10) (1000) x2 = 2000 x1 + (10) (1000) x1

100 + 10000 x2 = 12000 x1

-12000 x1 + 10000 x2 = 100 .....(1)

Tahap II

xi-1.W + yi+1.S = xi.W + yi.S

x1 W + y3S = x2 W + y2 S

x1 W + Kx3S = x2 W + Kx2 S

2000 x1 + (10) (1000) x3 = 2000 x2 + (10) (1000) x2

2000 x1 - 12000 x2 + 10000 x3 = 0..... (2)

Tahap III

xi-1.W + yi+1.S = xi.W + yi.S

x2 W + y4S = x3 W + y3 S

x2 W + Kx4S = x3 W + Kx3 S

2000 x2 + (10) (1000) x4 = 2000 x3 + (10) (1000) x3

2000 x2 - 12000 x3 + 10000 x4 = 0.....(3)

Tahap IV

xi-1.W + yi+1.S = xi.W + yi.S

x3 W + y5S = x4 W + y4 S

x3 W + Kx5S = x4 W + Kx4 S

2000 x3 + (10) (1000) x5 = 2000 x4 + (10) (1000) x4

2000 x3 - 12000 x4 + 10000 x5 = 0 ..... (4)

Tahap V

xi-1.W + yi+1.S = xi.W + yi.S

x4 W + y6S = x5 W + y5 S

x4 W + Kx6S = x5 W + Kx5 S

2000 x4 + (10) (1000) x6 = 2000 x5 + (10) (1000) x5

2000 4 - 12000 x5 + 10000 x6 = 0 ...... (5)

Tahap VI

xi-1.W + yi+1.S = xi.W + yi.S

x5 W + y7S = x6 W + y6 S

x5 W + Kx7S = x6 W + Kx6 S

2000 x5 + (10) (1000) x7 = 2000 x6 + (10) (1000) x6

2000 5 - 12000 x6 + 10000 x7 = 0 .....(6)

Tahap VII

xi-1.W + yi+1.S = xi.W + yi.S

x6 W + y8S = x7 W + y7 S

x6 W + Kx8S = x7 W + Kx7 S

2000 x6 + (10) (1000) x8 = 2000 x7 + (10) (1000) x7

2000 6 - 12000 x7 + 10000 x8 = 0 .... (7)

Tahap VIII

xi-1.W + yi+1.S = xi.W + yi.S

x7 W + y9S = x8 W + y8 S

x7 W + Kx9S = x8 W + Kx8 S

2000 x7 + (10) (1000) x9 = 2000 x8 + (10) (1000) x8

2000 7 – 12000 x8 + 10000 x9 = 0 .... (8)

Tahap IX

xi-1.W + yi+1.S = xi.W + yi.S

x8 W + y10S = x9 W + y9 S

x8 W + Kx10S = x9 W + Kx9 S

2000 x8 + (10) (1000) x10 = 2000 x9 + (10) (1000) x9

2000 8 – 12000 x9 + 10000 x10 = 0 .... (9)

Tahap X

xi-1.W + yi+1.S = xi.W + yi.S

x9 W + y11S = x10 W + y10 S

x9 W + Kx11S = x10 W + Kx10 S

2000 x9 + (10) (1000) (0) = 2000 x10 + (10) (1000) x10

2000 x9 – 12000 x10 = 0 ..... (10)

Maka dapat dibuat ke dalam bentuk matriksnya:

-6 5 0 0 0 0 0 0 0 0 x1 -0,05

1 -6 5 0 0 0 0 0 0 0 x2 0

0 1 -6 5 0 0 0 0 0 0 x3 0

0 0 1 -6 5 0 0 0 0 0 x4 0

0 0 0 1 -6 5 0 0 0 0 x5 0

0 0 0 0 1 -6 5 0 0 0 x6 0

0 0 0 0 0 1 -6 5 0 0 x7 0

0 0 0 0 0 0 1 -6 5 0 x8 0

0 0 0 0 0 0 0 1 -6 5 x9 0

0 0 0 0 0 0 0 0 1 -6 x10 0

Hasil dari program MATLAB:

Sehingga diperoleh hasil sebagai berikut:

x1 = 0,01

x2 = 0,002

x3 = 0,0004

x4 = 0,0001

x5 = 0,0000

x6 = 0,0000

x7 = 0,0000

x8 = 0,0000

x9 = 0,0000

x10 = 0,0000