Question

A person suffering from hyponatremia has a sodium ion concentration in the blood of \(0.118 M\) and a total blood volume of 4.6 L. What mass of sodium chloride would need to be added to the blood to bring the sodium ion concentration up to \(0.138 \mathrm{M}\), assuming no change in blood volume?

Short answer

First, let's calculate the initial moles of sodium ions: Initial moles of sodium ions = 0.118 M × 4.6 L = 0.5428 moles Next, find the moles of sodium ions required for the target molarity: Moles of sodium ions required = 0.138 M × 4.6 L = 0.6348 moles Now, calculate the moles of sodium ions to be added: Moles of sodium ions to be added = 0.6348 moles - 0.5428 moles = 0.092 moles Finally, calculate the mass of sodium chloride to be added: Mass of NaCl = 0.092 moles × 58.44 g/mol = 5.38 g So, 5.38 grams of sodium chloride would need to be added to the blood to bring the sodium ion concentration up to 0.138 M, assuming no change in blood volume.

Step-by-step solution

Calculate the moles of sodium ions initially present

First, let's find the initial moles of sodium ions in the blood using the formula: Moles = Molarity × Volume Initial moles of sodium ions = 0.118 M × 4.6 L

Calculate the moles of sodium ions required for the target molarity

Next, let's find the moles of sodium ions required to achieve a molarity of 0.138 M using the same formula: Moles = Molarity × Volume Moles of sodium ions required = 0.138 M × 4.6 L

Calculate the moles of sodium ions to be added

Now we need to find the moles of sodium ions that need to be added to the blood by subtracting the initial moles of sodium ions from the required moles of sodium ions: Moles of sodium ions to be added = Moles of sodium ions required – Initial moles of sodium ions

Calculate the mass of sodium chloride to be added

Since each mole of sodium chloride (NaCl) produces one mole of sodium ions (Na+), the moles of NaCl to be added would be equal to the moles of sodium ions to be added. Now we can find the mass of NaCl required using the molar mass of NaCl (58.44 g/mol): Mass of NaCl = Moles of NaCl × Molar mass of NaCl Now let's plug in the values and do the calculations.

Key concepts

Sodium Ion Concentration

Sodium ion concentration is a critical measure of health in the human body, especially concerning blood composition. The concentration of sodium ions in the blood helps regulate nerve and muscle function, as well as maintain fluid balance. In individuals suffering from hyponatremia, the sodium ion concentration is lower than normal, which can lead to symptoms like headache, confusion, fatigue, and, in severe cases, seizures or coma.
Understanding and managing sodium ion concentration is crucial, particularly in medical conditions where it is not naturally maintained at healthy levels. The concentration is typically expressed in molarity, denoted as M, which represents moles of solute per liter of solution. Monitoring and adjusting sodium ion concentration can involve careful calculation of both existing levels and the amounts needed to reach a target concentration.

Molarity Calculations

Molarity calculations are a fundamental part of chemistry, especially when adjusting the concentration of ions in a solution. Molarity (\(M\)) is defined as the number of moles of a solute divided by the volume of the solution in liters. This makes it a valuable tool for determining how much of a substance, like sodium chloride, needs to be added to a solution to achieve a desired concentration.
To perform molarity calculations:

• Determine the initial moles of solute by multiplying the initial molarity by the volume of the solution (\(0.118 \, M \times 4.6 \, L\)).
• Find the target moles required by using the target molarity and the solution volume (\(0.138 \, M \times 4.6 \, L\)).
• Subtract the initial moles from the target moles to find the moles needed to be added.

These calculations are essential for accurately increasing the concentration of sodium ions in the blood when treating conditions like hyponatremia.

Blood Volume

Blood volume is an important concept in physiology that represents the total amount of blood circulating within an individual's body. In this exercise, blood volume is considered a constant, remaining at 4.6 liters, as changes in sodium ion concentration are calculated without altering the volume. It's vital to understand how blood volume affects overall health, fluid balance, and the concentration of various substances within the bloodstream. When adjusting solute levels, like that of sodium ions, it's important to do so carefully to maintain a constant blood volume, ensuring effective distribution throughout the body.
In clinical settings, correct estimates of blood volume are essential. They allow for accurate adjustments in medical treatments, ensuring safe and efficient patient recovery. Understanding blood volume also aids in the comprehension of how different substances disperse and affect bodily functions.