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? Hint: try to think of a range of two values between which the concentration of the unknown falls.
20 x (0.01/0.09)= 2.22
Is this the right set up? I'm not sure where to go next to solve the problem
I would put this on a piece of graph paper, plot % vs density. You can look at it and tell that it must be just about 70%.
The setup you provided is incorrect. Let's work through the problem step by step to find the approximate concentration of the unknown solution.
1. Start by comparing the densities of the known solutions with their respective concentrations:
- 20% solution has a density of 0.69 g/mL.
- 50% solution has a density of 0.58 g/mL.
- 70% solution has a density of 0.49 g/mL.
2. We can see that as the concentration increases, the density decreases. This means that there is an inverse relationship between concentration and density.
3. Now, let's compare the density of the unknown solution (0.50 g/mL) with the densities of the known solutions:
- The density of the unknown solution (0.50 g/mL) is between the densities of the 50% (0.58 g/mL) and 70% (0.49 g/mL) solutions.
4. Since the unknown solution's density is closer to the density of the 50% solution, we can infer that the unknown solution has a concentration that is higher than 50% but lower than 70%.
5. To determine the approximate concentration of the unknown solution, we can use the range we have deduced. Taking 50% as the lower bound and 70% as the upper bound, we can say that the concentration of the unknown solution is between 50% and 70%.
Therefore, the approximate concentration of the unknown solution falls within the range of 50% to 70%.