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
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.
To find out how much water should be evaporated from the syrup, we first need to determine the initial amount of sugar in the syrup and the desired final amount of sugar.
1. Initial amount of sugar in the syrup:
The syrup contains 24% sugar by weight, which means that 100 kg of syrup contains 24 kg of sugar (100 kg x 0.24 = 24 kg).
2. Desired amount of sugar in the final syrup:
We want to obtain a syrup containing 64% sugar by weight. Let's assume the final weight of the syrup after evaporation is W kg.
Therefore, the desired amount of sugar in the final syrup is 64% of W kg, which is 0.64W kg.
3. Amount of water to be evaporated:
The amount of water to be evaporated is equal to the initial amount of syrup minus the desired amount of sugar in the final syrup.
Therefore, the amount of water to be evaporated is (100 kg - 24 kg) - (0.64W kg) = 76 kg - 0.64W kg.
Therefore, to obtain a final syrup containing 64% sugar by weight, you need to evaporate (76 kg - 0.64W kg) of water from 100 kg of syrup.