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What is the molar chloride ion concentration resulting from mixing of \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) sodium chloride and \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) potassium chloride?

Short Answer

Expert verified
The molar chloride ion concentration is 0.100 M.

Step by step solution

01

Understand the problem

We need to find the molar chloride ion concentration in a solution formed by mixing two solutions: sodium chloride (NaCl) and potassium chloride (KCl). Both solutions contribute chloride ions (Cl鈦) to the final mixture.
02

Calculate moles of chloride ion from NaCl

Since NaCl dissociates fully into Na鈦 and Cl鈦 in solution, calculate the moles of chloride ions in the sodium chloride solution. Use the formula: \( ext{moles} = ext{concentration} \times ext{volume} \). For the 50.0 mL NaCl solution: \( ext{moles of Cl}^- = 0.100 ext{ M} \times 0.0500 ext{ L} = 0.00500 ext{ moles} \).
03

Calculate moles of chloride ion from KCl

Potassium chloride (KCl) also dissociates fully into K鈦 and Cl鈦 in solution. For the 25.0 mL KCl solution, calculate the moles of chloride ions: \( ext{moles of Cl}^- = 0.100 ext{ M} \times 0.0250 ext{ L} = 0.00250 ext{ moles} \).
04

Determine total moles of chloride ions

Add the moles of chloride ions from both solutions to get the total moles of chloride ions: \( 0.00500 ext{ moles} + 0.00250 ext{ moles} = 0.00750 ext{ moles} \).
05

Calculate total volume of the mixture

Add the volumes of the two solutions to find the total volume of the mixed solution: \( 50.0 ext{ mL} + 25.0 ext{ mL} = 75.0 ext{ mL} = 0.0750 ext{ L} \).
06

Calculate molar chloride ion concentration

Use the formula for concentration: \( ext{Concentration} = \frac{ ext{total moles of Cl}^-}{ ext{total volume}} \). Substitute the values: \( ext{Concentration of Cl}^- = \frac{0.00750 ext{ moles}}{0.0750 ext{ L}} = 0.100 ext{ M} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chloride Ion Concentration
Chloride ion concentration determines how many chloride ions are present in a solution, expressed in moles per liter (M). To find the concentration of chloride ions, you have to consider how the solution is made. Mixing compounds that release chloride ions, like sodium chloride (NaCl) and potassium chloride (KCl), into a liquid, such as water, allows us to calculate the concentration of chloride ions. Each compound contributes to the total amount of chloride ions present in the solution. By knowing the concentration of each solution and the volume used, you can calculate the concentration of chloride ions in the mixed solution.
Solution Mixing
Solution mixing involves combining two or more solutions to form a single homogenous mixture. When mixing solutions like sodium chloride and potassium chloride, it's important to add their volumes to get the total volume of the resulting solution. This total volume will help in calculating concentrations accurately.
When solutions mix, the ions within each solution disperse evenly throughout the mixture. This ensures the chloride ions from all sources contribute to the overall concentration proportionally. Therefore, understanding the volume and concentration of each solution prior to mixing is crucial for determining the final ion concentrations post-mixing.
Moles Calculation
To calculate moles, which are elementary quantities of a substance, you multiply the concentration (in moles per liter) by the volume (in liters) of the solution. This process is crucial when dealing with ions in a solution since it helps identify how many moles of a substance, like chloride ions, are present. For our example, where both NaCl and KCl solutions are used, we calculate the moles separately and then combine them.
The mathematical representation is: - **For NaCl**: Moles = Concentration (0.100 M) 脳 Volume (0.0500 L) = 0.00500 moles - **For KCl**: Moles = Concentration (0.100 M) 脳 Volume (0.0250 L) = 0.00250 moles
Adding these moles gives the total moles of chloride ions in the resulting solution.
Sodium Chloride and Potassium Chloride
Sodium chloride (NaCl) and potassium chloride (KCl) are both common salts that fully dissociate into their respective ions in a solution:
  • NaCl dissociates into sodium ions (Na鈦) and chloride ions (Cl鈦).
  • KCl dissociates into potassium ions (K鈦) and chloride ions (Cl鈦).
Since both release the same chloride ion into a solution, they contribute to the chloride ion concentration proportionately. As they mix in a solution, their contributions are simply additive, meaning you sum up the moles of chloride ions they each provide. Understanding how these compounds behave in water helps in predicting the final composition and concentration of the ions in the solution.

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