Question

A chemist mixed a 15 glucose solution with a 35 glucose solution this mixture produced 35 liters of a 19% glucose solution how many liters of each solution did the chemist use in the mixture

Answer 1

To find how many liters of each glucose solution the chemist used, we establish two equations: one for total volume and another for glucose content, then solve for the variables representing the volume of each solution.

Step-by-step explanation:

The chemist is looking to find the amount of each solution needed to mix a total of 35 liters of 19% glucose solution from a 15% glucose solution and a 35% glucose solution. To solve this, we set up a system of linear equations representing the total volume and the amount of glucose.

Let x be the liters of 15% glucose solution and y be the liters of 35% glucose solution. The first equation represents the total volume:

1. x + y = 35 (total volume equation)

The second equation represents the glucose content:

2. 0.15x + 0.35y = 0.19 × 35 (glucose content equation)

Solving this system of equations, we find x and y which represent the liters of each solution the chemist must mix to achieve the desired concentration.

Answer 2

w₁=0.15 (15%)
p₁=1.0582 g/ml=1058.2 g/L
v₁-?
w₂=0.35 (35%)
p₂=1.1482 g/ml=1148.2 g/L
v₂-?
w₃=0.19 (19%)
v₃=35L

v₁+v₂=v₃ (1)

w₁=m₁/v₁p₁ m₁=v₁p₁w₁
w₂=m₂/v₂p₂ m₂=v₂p₂w₂

w₃=(v₁p₁w₁+v₂p₂w₂)/(v₁p₁+v₂p₂)
v₁p₁(w₃-w₁)=v₂p₂(w₂-w₃)
v₁/v₂=p₂(w₂-w₃)/[p₁(w₃-w₁)] (2)

We solve the equations (1) and (2).
v₁+v₂=35
v₁/v₂=1148.2*0.16/[1058.2*0.04]=4.34

v₁=28.446 L
v₂=6.554 L