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Chapter 3: Problem 102

Ringer's solution, used in the treatment of burns and wounds, is prepared by dissolving \(4.30 \mathrm{~g}\) of \(\mathrm{NaCl}, 0.150 \mathrm{~g}\) of \(\mathrm{KCl}\), and \(0.165 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\) in water and diluting to a volume of \(500.0 \mathrm{~mL}\). What is the molarity of each of the component ions in the solution?

Short Answer

Expert verified
Molarities: Na+ = 0.1472 M, K+ = 0.00402 M, Ca2+ = 0.00298 M, Cl- = 0.15718 M.

Step by step solution

01

Calculate Moles of NaCl

First, find the moles of NaCl. The molar mass of NaCl is approximately 58.44 g/mol. Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). So, \( \frac{4.30 \text{ g}}{58.44 \text{ g/mol}} = 0.0736 \text{ moles} \).
02

Calculate Moles of KCl

Next, calculate the moles of KCl. The molar mass of KCl is approximately 74.55 g/mol. Using the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), we have \( \frac{0.150 \text{ g}}{74.55 \text{ g/mol}} = 0.00201 \text{ moles} \).
03

Calculate Moles of CaCl2

Now, find the moles of CaCl2. The molar mass of CaCl2 is approximately 110.98 g/mol. Using \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), we find \( \frac{0.165 \text{ g}}{110.98 \text{ g/mol}} = 0.00149 \text{ moles} \).
04

Moles to Molarity Conversion

To find molarity, we use the formula \( \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \). The solution is 500.0 mL, which is 0.500 L.
05

Calculate Molarity of Na+ Ions

NaCl dissociates completely in water to produce Na+ and Cl-. Since there are 0.0736 moles of NaCl, there are 0.0736 moles of Na+. The molarity of Na+ ions is \( \frac{0.0736}{0.500} = 0.1472 \text{ M} \).
06

Calculate Molarity of K+ Ions

KCl dissociates completely to produce K+ and Cl-. There are 0.00201 moles of KCl, so 0.00201 moles of K+. The molarity of K+ ions is \( \frac{0.00201}{0.500} = 0.00402 \text{ M} \).
07

Calculate Molarity of Ca2+ Ions

CaCl2 dissociates to provide one Ca2+ ion. So, the moles of Ca2+ is equal to the moles of CaCl2, which is 0.00149. The molarity of Ca2+ ions is \( \frac{0.00149}{0.500} = 0.00298 \text{ M} \).
08

Calculate Molarity of Cl- Ions

NaCl provides 0.0736 moles of Cl-, KCl 0.00201 moles, and CaCl2 provides 2 \times 0.00149 = 0.00298 moles of Cl-. Total moles of Cl- is \( 0.0736 + 0.00201 + 0.00298 = 0.07859 \text{ moles} \). The molarity is \( \frac{0.07859}{0.500} = 0.15718 \text{ M} \).

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Key Concepts

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

Ringer's Solution
Ringer's solution is a well-known isotonic fluid often used in medical settings for treating burns and wounds. It consists of a balanced mix of key electrolytes: sodium chloride (NaCl), potassium chloride (KCl), and calcium chloride (CaCl鈧�), dissolved in water. The purpose of this solution is to mimic physiological conditions, maintaining proper osmotic balance and providing essential ions to the tissues. This balance helps in wound healing and can aid in rehydrating tissues after burns. It's crucial to prepare Ringer's solution with precise measurements to ensure its effectiveness and safety as an intravenous fluid therapy.
Ionic Dissociation
Ionic dissociation occurs when ionic compounds dissolve in water and their ions separate, or "dissociate," from each other. This process is essential to understanding the behavior of Ringer's solution once it is prepared.
  • When NaCl dissolves, it dissociates into sodium (Na鈦�) and chloride (Cl鈦�) ions.
  • KCl separates into potassium (K鈦�) and chloride (Cl鈦�) ions.
  • CaCl鈧� dissociates into calcium (Ca虏鈦�) ions and, importantly, two chloride (Cl鈦�) ions per formula unit.
This dissociation is vital because it determines the ionic strength and, consequently, the therapeutic properties of Ringer's solution.
Solution Preparation
Preparing a solution correctly is fundamental to achieving the intended concentration and effectiveness. For Ringer's solution, it involves the precise weighing and mixing of the individual ionic compounds.
Step-by-step, here鈥檚 how to prepare it:
  • Calculate the mass of each compound needed as per the desired concentration.
  • Dissolve NaCl, KCl, and CaCl鈧� separately in a portion of the total water volume.
  • Gradually mix these dissolved compounds to avoid precipitation or unwanted reactions.
  • Finally, dilute the entire mixture to the specified total volume, making sure to mix thoroughly.
Every step ensures that ions are adequately mixed and remain evenly distributed throughout the solution, key for consistent physiological effects.
Concentration Calculation
To understand the effects of a solution, calculating the concentration of its components is important. Molarity, a common concentration measure, expresses the amount of solute in a solution in moles per liter (mol/L).
Here鈥檚 how to perform concentration calculation:
  • First, find the number of moles of each dissolving compound using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
  • Determine the molarity by dividing the moles of each ion by the total solution volume in liters.
  • Remember that compounds like CaCl鈧� create multiple ions per molecule (e.g., Ca虏鈦� and two Cl鈦� ions).
This precise calculation allows you to identify the molarity of each ionic component, ensuring that the mixture mimics the intended natural balance crucial for medical applications.

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