Logan wants to mix an 18 % acid solution with a 45 % acid...

Logan wants to mix an $18 \%$ acid solution with a $45 \%$ acid solution to get $16 \mathrm{L}$ of a $36 \%$ acid solution. How many liters of the $18 \%$ solution and how many liters of the $45 \%$ solution should be mixed?

Key Concepts

Mixture Problems

This concept involves combining solutions with different properties to form a new solution with a desired property. Typically, this requires setting up equations that account for the total volume and the total amount of the substance of interest (in this case, acid), ensuring that both the quantity of solution and the concentration are conserved.

Percent Concentrations

Percent concentration is a measure of how much solute is present in a solution relative to its total volume, usually expressed as a percentage. It is important to convert these percentages into decimals when performing calculations with volumes, as this conversion allows you to compute the actual quantity of the solute present in each solution.

System of Linear Equations

To solve mixture problems, one typically establishes a system of linear equations—one equation representing the total volume and another representing the total amount of the substance (acid) based on its percent concentration. Solving this system yields the volumes of the component solutions required to achieve the mixture’s desired properties.

Weighted Averages

This concept is used when combining two or more different concentrations to find an overall average concentration. The final concentration is determined by the weighted contributions of each individual solution’s concentration and their respective volumes, reflecting the balance needed in the mixture.

Transcript

Please give Ace some feedback