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Magazine Chapter 5: Problem 30
You have a 250 -ppm solution of \(K^{+}\) as \(K C l\). You wish to prepare from this a \(0.00100 M\) solution of \(\mathrm{Cl}^{-} .\) How many. milliliters must be diluted to \(1 \mathrm{~L} ?\)
Short Answer
Expert verified
Dilute 298.5 mL of the 250 ppm solution to 1 L to get a 0.00100 M solution of \(\text{Cl}^-\).
Step by step solution
01
Understand What is Given and What is Required
We are given a 250 ppm (parts per million) solution of potassium ions \(K^{+}\) as potassium chloride \(KCl\). From this, we need to prepare a 0.00100 M solution of \(\text{Cl}^-\) ions. We need to determine how much of the original solution is required to make 1 liter of this new solution.
02
Convert ppm to Molarity
Given a 250 ppm solution, this means there are 250 mg of \(K^{+}\) ions per liter. The molar mass of \(KCl\) is 74.55 g/mol, which combines the masses of \(K^+\) and \(Cl^-\). To convert ppm to molarity, we first convert mg to grams: 250 mg = 0.250 g. Then, divide by the molar mass to convert grams to moles: \(\frac{0.250}{74.55} \approx 0.00335\, \text{moles/L}\).
03
Relate Potassium and Chloride Ion Concentrations
Each mole of \(KCl\) dissociates into one mole of \(K^+\) and one mole of \(Cl^-\). Therefore, the concentration of \(\text{Cl}^-\) ions is equal to the concentration of \(K^{+}\) ions in the solution. So, the \(\text{Cl}^-\) concentration is also 0.00335 M.
04
Use Dilution Formula to Find Required Volume
We will use the dilution equation \(C_1 V_1 = C_2 V_2\), where \(C_1\) is the initial concentration (0.00335 M), \(V_1\) is the unknown volume in liters, \(C_2\) is the final concentration (0.00100 M), and \(V_2\) is the final volume (1 L). Substituting, we have:\[ 0.00335 \times V_1 = 0.00100 \times 1 \]Solving for \(V_1\), we get \(V_1 = \frac{0.00100}{0.00335} \approx 0.2985 \text{ L} \) or 298.5 mL.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molarity Conversion
Molarity is a measure of concentration, specifically the number of moles of a solute per liter of solution. It helps us understand how much of a given substance is in a certain volume. Converting parts per million (ppm) to molarity involves a few steps. First, understand that ppm means the amount of a substance in a million parts of solution, typically measured as milligrams per liter for solutions.
To convert ppm to molarity:
To convert ppm to molarity:
- Convert milligrams to grams by dividing by 1000: 250 mg = 0.250 g.
- Determine the molar mass of the compound, such as potassium chloride, which is 74.55 g/mol.
- Calculate moles by dividing the mass in grams by molar mass: \ \(\frac{0.250}{74.55} \approx 0.00335\, \text{moles/L}\).
Dilution Equation
The dilution equation is a useful tool for preparing the desired concentrations of solutions in different volumes. The fundamental principle behind the dilution equation is conservation of moles, which mathematically is expressed as \(C_1V_1 = C_2V_2\).
Here's how to use it:
Here's how to use it:
- \(C_1\) is the initial concentration of the solution.
- \(V_1\) is the volume of this concentrated solution you'll need.
- \(C_2\) is the desired concentration after dilution.
- \(V_2\) is the final volume, often made up to a specific amount, such as 1 liter in this problem.
Potassium Chloride
Potassium chloride (KCl) is a salt commonly used in chemistry and medicine. In aqueous solutions, KCl dissociates into potassium ions \((K^+)\) and chloride ions \((Cl^-)\).
When dealing with KCl solutions:
When dealing with KCl solutions:
- Each formula unit of KCl provides one \(K^+\) and one \(Cl^-\).
- Thus, the concentration of one ion mirrors that of the other when the salt dissociates completely in water.
Parts Per Million
Parts per million, or ppm, is a unit of concentration. It signifies milligrams of solute dissolved in one liter of solution (mg/L). It's particularly useful for tracing small amounts of substances.
Key points for ppm calculations:
Key points for ppm calculations:
- 250 ppm means there are 250 mg of solute per liter of solvent.
- Often used in water quality measurements and solution preparations involving trace concentrations.
Chemical Concentration
Chemical concentration refers to the amount of a substance in a given volume, influencing the solution's properties and reactions. Concentration may be expressed in multiple ways, such as molarity (M), parts per million (ppm), or mass/volume percent.
When calculating chemical concentrations:
When calculating chemical concentrations:
- Define the unit you are working with, such as moles per liter for molarity.
- Acknowledge that concentration affects reaction rates and the physical properties of the solution.
- Proper concentration understanding and management are crucial for experimental accuracy and safety.
