Concentration of syrup containing 24% sugar by weight by evaporation How much water should be evaporated for 100 kg of syrup containing 64% sugar to be obtained

1 answer

Let's assume that the initial volume of syrup is V and the initial weight of syrup is W.

We know that the concentration of the syrup is 24%, so the weight of sugar in the initial syrup is:

0.24W

We want to obtain 100 kg of syrup containing 64% sugar, so the weight of sugar in the final syrup is:

0.64 x 100 kg = 64 kg

Let's assume that we need to evaporate x kg of water to obtain the final syrup.

The weight of sugar in the evaporated water is:

0.24x

The weight of sugar in the remaining syrup is:

0.24W - 0.24x

We want the weight of sugar in the final syrup to be 64 kg, so we can write the following equation:

0.24W - 0.24x = 64

We know that the initial concentration of the syrup is 24%, so we can write:

W = V x 0.24

If we assume that the density of the syrup is 1 kg/L, then:

W/V = 1 kg/L

W = V

Substituting W in the first equation, we get:

0.24V - 0.24x = 64

Dividing by 0.24, we get:

V - x = 266.67

We want to obtain 100 kg of syrup, so:

V - x = 100

Substituting V - x in the previous equation, we get:

V - x = 266.67

x = 166.67 kg

Therefore, we need to evaporate 166.67 kg of water to obtain 100 kg of syrup containing 64% sugar.