Question

Specifications for lactated Ringer’s solution, which is used for intravenous (IV) injections, are as follows to reach 100. mL of solution: \(285-315 \mathrm{mg} \mathrm{Na}^{+}\) \(14.1-17.3 \mathrm{mg} \mathrm{K}^{+}\) \(4.9-6.0 \mathrm{mg} \mathrm{Ca}^{2+}\) \(368-408 \mathrm{mg} \mathrm{Cl}^{-}\) \(231-261 \mathrm{mg}\) lactate, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) a. Specify the amount of \(\mathrm{NaCl}, \mathrm{KCl}, \mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\) needed to prepare \(100 . \mathrm{mL}\) lactated Ringer's solution. b. What is the range of the osmotic pressure of the solution at \(37^{\circ} \mathrm{C},\) given the preceding specifications?

Short answer

To prepare 100 mL of lactated Ringer's solution, we need: - 759 mg of NaCl - 29.9 mg of KCl - 20.0 mg of CaCl2·2H2O - 309 mg of NaC3H5O3 The range of osmotic pressure of the solution at 37°C can be calculated by applying van't Hoff's law, considering the given mass ranges and converting them into molar concentrations. The final range will be the sum of the partial osmotic pressures for each component.

Step-by-step solution

Determine the number of moles of each ion needed

First, we need to find out the number of moles of each ion needed in the solution. To do this, we can use the mass of the given ion (mg) and its molar mass (g/mol). \[moles \ of \ an \ ion = \frac{mass \ of \ the \ ion}{molar \ mass \ of \ the \ ion}\]

Calculating the number of moles of Na^+

Take the average mass of Na^+ mid-range (300 mg) and divide it by the molar mass of Na^+ (22.99 g/mol). \[moles \ of \ Na^+ = \frac{300 \ mg}{22.99 \ g/mol} = 0.0130 \ mol\]

Calculating the number of moles of K^+

Take the average mass of K^+ mid-range (15.7 mg) and divide it by the molar mass of K^+ (39.10 g/mol). \[moles \ of \ K^+ = \frac{15.7 \ mg}{39.10 \ g/mol} = 0.000401 \ mol\]

Calculating the number of moles of Ca^2+

Take the average mass of Ca^2+ mid-range (5.45 mg) and divide it by the molar mass of Ca^2+ (40.08 g/mol). \[moles \ of \ Ca^{2+} = \frac{5.45 \ mg}{40.08 \ g/mol} = 0.000136 \ mol\]

Calculating the number of moles of Cl^−

Take the average mass of Cl^− mid-range (388 mg) and divide it by the molar mass of Cl^− (35.45 g/mol). \[moles \ of \ Cl^- = \frac{388 \ mg}{35.45 \ g/mol} = 0.01095 \ mol\]

Calculating the number of moles of lactate ion (C3H5O3^−)

Take the average mass of lactate ion mid-range (246 mg) and divide it by the molar mass of lactate ion (89.07 g/mol). \[moles \ of \ C_3H_5O^{-}_3 = \frac{246 \ mg}{89.07 \ g/mol} = 0.00276 \ mol\]

Calculate the amount of NaCl, KCl, CaCl2·2H2O, and NaC3H5O3 needed

Using the mole ratios of each component and their molar masses, we find the mass of each substance needed to prepare the lactated Ringer's solution: NaCl: Since NaCl contains 1 Na^+ and 1 Cl^− ion, moles of NaCl = moles of Na^+ = 0.0130 mol. Mass of NaCl needed = moles of NaCl × molar mass of NaCl = 0.0130 mol × 58.44 g/mol = 0.759 g (or 759 mg) KCl: Moles of KCl = moles of K^+ = 0.000401 mol Mass of KCl needed = moles of KCl × molar mass of KCl = 0.000401 mol × 74.55 g/mol = 0.0299 g (or 29.9 mg) CaCl2·2H2O: Moles of CaCl2·2H2O = moles of Ca^2+ = 0.000136 mol Mass of CaCl2·2H2O needed = moles of CaCl2·2H2O × molar mass of CaCl2·2H2O = 0.000136 mol × 147.02 g/mol = 0.0200 g (or 20.0 mg) NaC3H5O3: Moles of NaC3H5O3 = moles of C3H5O3^− = 0.00276 mol Mass of NaC3H5O3 needed = moles of NaC3H5O3 × molar mass of NaC3H5O3 = 0.00276 mol × 112.06 g/mol = 0.309 g (or 309 mg) So, to prepare 100 mL lactated Ringer's solution, we need: - 759 mg of NaCl - 29.9 mg of KCl - 20.0 mg of CaCl2·2H2O - 309 mg of NaC3H5O3

Find the range of osmotic pressure of the solution at 37°C

We will use van't Hoff's law to calculate the osmotic pressure, considering the lowest and highest concentrations given. \(p_i = c_iRT\) where: - \(p_i\) = osmotic pressure of the solution - \(c_i\) = molar concentration of the ith solute in the solution - R = universal gas constant = 0.0821 atm·L/mol·K - T = temperature in Kelvin = 37 °C + 273.15 = 310.15 K To find osmotic pressures, substitute the minimum and maximum moles of each component (considering the given mass ranges) divided by 100 mL into the equation. Calculate the osmotic pressure for the lowest and highest values, sum up the partial osmotic pressures for each component, and thus find the range of the osmotic pressure.

Key concepts

Ionic Composition in Lactated Ringer's Solution

Lactated Ringer's solution is a carefully balanced mixture used in IV therapies. This solution contains several key ions each playing a unique role in maintaining physiological function. In a typical solution, you will find the following ionic components:

• Sodium ions (\( \mathrm{Na^+} \))
• Potassium ions (\( \mathrm{K^+} \))
• Calcium ions (\( \mathrm{Ca^{2+}} \))
• Chloride ions (\( \mathrm{Cl^-} \))
• Lactate ions (\( \mathrm{C_3H_5O_3^-} \))

These ions are essential as they mimic the body’s natural plasma environment, aiding in the restoration of fluid and electrolyte balance.
Each component has its specific range, for example, sodium ions range from 285-315 mg per 100 mL, ensuring the solution's effectiveness and safety.
Understanding the precise ionic composition helps in tailoring the solution specifically to certain medical scenarios, like dehydration or electrolyte imbalance.

Molar Mass Calculations

Calculating the molar mass is a fundamental step in preparing solutions like lactated Ringer's. It allows us to determine the appropriate amount of each compound needed. Here's how it's done:

• First, understand that molar mass is the mass of one mole of a substance, expressed in \( \text{g/mol} \).
• To find the number of moles of each ion, divide the mass of the ion in milligrams by its molar mass in \( \text{g/mol} \).

For instance, to find the moles of sodium ions, use the conversion:\[\text{moles of } \mathrm{Na^+} = \frac{300 \text{ mg}}{22.99 \text{ g/mol}} = 0.0130 \text{ mol}\]This process is applied to each ion in the solution, and ensures the exact proportions necessary to maintain the intended ionic balance. Accurately calculating moles allows us to precisely prepare substances, which in turn ensures the effectiveness and safety of the resultant solutions.

Understanding Osmotic Pressure

Osmotic pressure is a crucial concept when dealing with solutions such as lactated Ringer's. It is defined as the pressure required to prevent the inward flow of water across a semipermeable membrane. Osmotic pressure depends on the concentration of solutes in a solution:

• To calculate it, we use van't Hoff's law: \( p_i = c_iRT \).
• \( c_i \) represents the molar concentration of each solute.
• R is the universal gas constant (0.0821 atm·L/mol·K).
• T is the temperature in Kelvin.

For lactated Ringer's, the calculations involve substituting the minimum and maximum molar concentrations of the ingredients to find a pressure range.
This pressure range helps in determining how the solution will interact with the body's cells, making it vital in clinical settings. It ensures that the solution does not cause harm by either taking too much water into cells or drawing too much water out from them.

Solute Preparation for Solutions

Preparing solutes in lactated Ringer's solution involves calculating precise amounts of each compound to achieve the right concentrations of ions. This is crucial to ensure the solution's effectiveness and safety. Here's a step-by-step guide:

• After determining the moles of each ion, calculate the amount of compound needed using their molar masses.
• This involves using stoichiometric relationships, considering compounds like NaCl for \( \text{Na}^+ \) and \( \text{Cl}^- \).

For example, to prepare 100 mL of lactated Ringer's, derive the necessary mass of NaCl through the moles of sodium ions calculated as:\[\text{Mass of NaCl} = \text{moles of } \mathrm{NaCl} \times \text{molar mass of NaCl}\]By doing these calculations meticulously for each component, the solute preparation ensures that the solution is uniformly mixed and ready for clinical use. This precision helps in maintaining the delicate balance needed in a medical solution like lactated Ringer's.