Chapter 4: Problem 68
Water is added to \(25.0 \mathrm{~mL}\) of a \(0.866 \mathrm{M} \mathrm{KNO}_{3}\) solution until the volume of the solution is exactly \(500 \mathrm{~mL}\). What is the concentration of the final solution?
Short Answer
Expert verified
The final concentration is \(0.0433 \mathrm{M}\).
Step by step solution
01
Identify the Known Quantities
The initial concentration of the solution is given as \(0.866 \mathrm{M}\) and the initial volume is \(25.0 \mathrm{~mL}\). The final volume after dilution is \(500.0 \mathrm{~mL}\).
02
Define the Formula for Dilution
To find the concentration after dilution, use the formula for dilution: \(C_1V_1 = C_2V_2\), where \(C_1\) and \(V_1\) are the initial concentration and volume, and \(C_2\) and \(V_2\) are the final concentration and volume.
03
Substitute the Known Values
Substitute the known values into the dilution formula: \(0.866 \mathrm{M} \times 25.0 \mathrm{~mL} = C_2 \times 500.0 \mathrm{~mL}\).
04
Calculate the Final Concentration (\(C_2\))
Solve the equation for \(C_2\): \[C_2 = \frac{0.866 \times 25.0}{500.0} \] Calculating this gives: \[C_2 = \frac{21.65}{500.0} = 0.0433 \mathrm{M}\].
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Concentration
Concentration refers to the amount of a substance present in a certain volume of solution. It tells us how much of a solute (the substance being dissolved) is contained within a solvent (the liquid it's dissolved in). Understanding concentration is crucial in chemistry since it affects how reactions occur, how solutions appear, and their overall properties. Concentration can be expressed in different ways, including:
- Molality: Moles of solute per kilogram of solvent.
- Molarity: Moles of solute per liter of solution.
- Mass percent: Mass of solute divided by the total mass of the solution, multiplied by 100.
Molarity
Molarity is a measure of concentration that is particularly useful in the world of chemistry. It is defined as the number of moles of solute per liter of solution. The formula is:\[ M = \frac{n}{V} \]Where:
- \(M\) refers to molarity.
- \(n\) is the number of moles of solute.
- \(V\) is the volume of the solution in liters.
Solution Preparation
Preparing a solution in chemistry involves dissolving a specific amount of solute in a solvent to achieve a desired concentration. This process may require careful measurement of both components:
- The solute provides the active chemical component, while the solvent, often water in many chemistry labs, disperses the solute molecules.
- To ensure accuracy, it's important to measure both the solute and total volume of the solution precisely.
Chemistry
Chemistry is the scientific discipline that investigates the properties, composition, and behavior of matter. It explores how substances interact with each other and transform, which is where the concept of solution and dilution comes into play:
- Solutions are homogeneous mixtures formed when solutes dissolve in solvents, allowing for uniform distribution.
- Dilution is an integral concept in chemistry that involves reducing the concentration of a solution by increasing the solvent volume. It is crucial in reactions where specific chemical concentrations are necessary to observe or measure outcomes accurately.