The densities of three solutions with known concentrations ( 20% , 50%, and 70%), and one unknown solution were determined. If the densities of 20%, 50% and 70% solutions are 0.69 and 0.58 and 0.49 g/mL, respectively, and the denisty of the unknown solution is 0.50 g/mL, what is the approximate concentration of the unknown solution?

Question

The densities of three solutions with known concentrations ( 20% , 50%, and 70%), and one unknown solution were determined. If the densities of 20%, 50% and 70% solutions are 0.69 and 0.58 and 0.49 g/mL, respectively, and the denisty of the unknown solution is 0.50 g/mL, what is the approximate concentration of the unknown solution?

Answer 1

The density of the 70% solution is 0.49 g/mL then the concn of the 0.50 g/mL solution must be approximately 70%. Right?

Answer 2

To determine the approximate concentration of the unknown solution, we can use the concept of density and concentration. The density of a solution can be related to its concentration by a linear relationship, usually expressed as:

Density = Concentration × Volume

In this case, we have the densities of three known solutions (20%, 50%, and 70%) and their concentrations, as well as the density of the unknown solution. We can use these values to determine the concentration of the unknown solution.

Let's assign variables to the known and unknown values:
- Density of 20% solution: D1 = 0.69 g/mL
- Density of 50% solution: D2 = 0.58 g/mL
- Density of 70% solution: D3 = 0.49 g/mL
- Density of the unknown solution: D4 = 0.50 g/mL
- Concentration of 20% solution: C1 = 20%
- Concentration of 50% solution: C2 = 50%
- Concentration of 70% solution: C3 = 70%
- Concentration of the unknown solution: C4 (to be determined)

Now, we can set up the following equation to relate the concentrations and densities:

D1 = C1 × V (equation 1)
D2 = C2 × V (equation 2)
D3 = C3 × V (equation 3)
D4 = C4 × V (equation 4)

Since the volume (V) is the same for all solutions, we can cancel it out when comparing the equations. Dividing equation 2 by equation 1, we get:

D2 / D1 = C2 / C1

Using the given densities, we have:

0.58 g/mL / 0.69 g/mL = 50% / 20%

Simplifying this equation, we find:

0.841 = 2.5

Now, we can determine the ratio between the densities of the unknown solution and the 20% solution:

D4 / D1 = C4 / C1

Substituting the values, we have:

0.50 g/mL / 0.69 g/mL = C4 / 20%

Simplifying, we find:

0.725 = C4 / 20%

Solving for C4, we get:

C4 = 0.725 × 20% = 14.5%

Therefore, the approximate concentration of the unknown solution is 14.5%.