Dilution is the process of reducing the concentration of a solution by adding more solvent, such as water, to the original solution. This lowers the amount of solute per unit volume, resulting in a less concentrated mixture.
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Dilution is commonly used in chemistry to prepare solutions of a desired concentration from more concentrated stock solutions.
The dilution factor, which is the ratio of the final volume to the initial volume, can be used to calculate the new concentration of the diluted solution.
Dilution is an important concept in mixture problems, as it helps determine the final composition of a mixture after combining solutions with different concentrations.
Uniform motion applications, such as those involving the flow of liquids, often involve dilution calculations to determine the properties of the resulting mixture.
Systems of equations can be used to solve complex mixture problems that involve dilution, allowing for the determination of unknown concentrations or volumes.
Review Questions
Explain how the dilution factor is used to calculate the new concentration of a diluted solution.
The dilution factor is the ratio of the final volume to the initial volume of the solution. It can be used to calculate the new concentration of the diluted solution using the formula: $C_1V_1 = C_2V_2$, where $C_1$ is the initial concentration, $V_1$ is the initial volume, $C_2$ is the final concentration, and $V_2$ is the final volume. Rearranging this equation allows you to solve for the final concentration, $C_2$, which will be lower than the initial concentration due to the addition of more solvent.
Describe how dilution is used in the context of mixture problems and uniform motion applications.
In mixture problems, dilution is a key concept for determining the final composition of a mixture after combining solutions with different concentrations. The dilution factor is used to calculate the new concentrations of the solutes in the final mixture. Similarly, in uniform motion applications, such as the flow of liquids, dilution calculations are important for understanding the properties of the resulting mixture, which may have different concentrations or flow rates compared to the individual components.
Explain how systems of equations can be used to solve complex mixture problems involving dilution.
When dealing with mixture problems that involve dilution, systems of equations can be used to solve for unknown concentrations or volumes. This is particularly useful when there are multiple components or constraints in the problem. The equations typically involve the dilution formula, $C_1V_1 = C_2V_2$, as well as other relationships between the quantities in the mixture. By setting up and solving these systems of equations, you can determine the final concentrations and volumes of the diluted solution, which is essential for understanding the overall composition of the mixture.