Question

a lab technician needs to combine 30% alcohol solution with 35% alcohol solution to make 5l of 33% alcohol solution . how many luters of the 30% solutio and of the 35% solution will be used

Answer 1

To create a 5-liter 33% alcohol solution, the lab technician needs to mix 2 liters of the 30% alcohol solution with 3 liters of the 35% alcohol solution. We find this by setting up an equation based on the proportion of alcohol in each solution and solving for the unknown quantity.

Step-by-step explanation:

To solve this problem, we will use the concept of mixtures in algebra, which involves creating equations based on the concentration of solutions. The lab technician wants to combine a 30% alcohol solution with a 35% alcohol solution to create 5 liters of a 33% alcohol solution. Let's let x be the amount of the 30% solution and 5 - x be the amount of the 35% solution. The total volume of the solution is 5 liters. So, we can set up an equation based on the amounts of pure alcohol from both solutions:

• 0.30x (alcohol from the 30% solution)
• + 0.35(5 - x) (alcohol from the 35% solution)
• = 0.33(5) (total alcohol in the 33% solution)

Solving the equation:

1. 0.30x + 0.35(5 - x) = 1.65
2. 0.30x + 1.75 - 0.35x = 1.65
3. -0.05x = -0.10
4. x = 2 liters

Therefore, the lab technician needs 2 liters of the 30% alcohol solution and 3 liters (5 - 2) of the 35% alcohol solution to create the desired mixture.

Answer 2

To answer the problem, use the material and component balance. Let x and y be the volume of 30% and 35% solution, respectively. The balances are shown below,

Overall Material Balance: x + y = 5
Component Balance: 0.30x + 0.35y = 5 x 0.33

Solving simultaneously for the values of the variables gives x = 2 and y = 3.

Thus, the technician needs 2L of 30% alcohol and 3L of 35% alcohol.