Question

Four hundred liters of a yeast suspension in water is initially at 1.21% solids. The density of the suspension is 1.003 g/cm3. How much water must be removed in order to concentrate the suspension to 2.66% solids? If the density of the solution is assumed to remain constant, what is the volume of the concentrated suspension?

Answer 1

density = mass/volume = 1.003 g/cm³

So mass 1.003 g per ml

1.003 g is 1.21 % in water

400 litre = 400 x 10³ cm³ [ since 1 litre = 10³ cm³ ]

mass/ 400 x 10³ cm³ = 1.003 g/ cm³

mass = 1.003 g/ cm³ x 400 x 10³ cm³ = 4.012 x 10⁵ g

Weight of water = volume of water

So weight of water = 4 x 10⁵ g

Weight of yeast =  4.012 x 10⁵ g - 4 x 10⁵ g = 0.012 x 10⁵ g

0.012 x 10⁵ g yeast is equivalent to 1.21% suspension

So 2.66 % suspension is 0.027x 10⁵ g yeast

But density is still same ((400- A) +  0.027 x 10⁵ g)/ A cm³ = 1.003 g/cm³ [where(400x 10³ - A) is volume of concentrated solution]

1.003(400x 10³ - A) = (400x 10³ -A) +  0.027 x 10⁵

A = 1.5/.003 = 500