A health clinic uses a solution of bleach to sterilize petri...

A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 100 gal of a solution of $2 \%$ ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be $5 \%$ for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

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Key Concepts

Conservation of Mass

Conservation of mass in the context of mixture problems dictates that the total mass of the solute remains constant, apart from what is added or removed. This principle is applied to equate the amount of solute before and after the process of draining and replacing parts of a solution.

Replacement Method in Mixture Problems

The replacement method is a strategy used to modify the concentration of a solution by removing a portion of the original mixture and replacing it with another solution of a different concentration. This method utilizes the conservation of mass to determine the resulting concentration after the exchange.

Mixture Problems

Mixture problems involve combining two or more solutions with different concentrations to achieve a desired concentration. These problems typically require setting up a balance equation that accounts for the quantities and concentrations of the individual components, ensuring that the total amount of the solute remains consistent throughout the process.

Percentage Concentration

Percentage concentration is a measure used to describe the ratio of the quantity of a solute to the total quantity of the solution, usually expressed as a percentage. It allows for easy comparison and calculation of how much of a substance is present in a mixture relative to its total volume or mass.

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