Question

A person suffering from hyponatremia has a sodium ion concentration in the blood of \(0.118 \mathrm{M}\) and a total blood volume of \(4.6 \mathrm{~L} .\) What mass 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?

Short answer

Approximately 5.38 grams of sodium chloride are needed.

Step-by-step solution

Calculate initial moles of sodium ions

To find the initial moles of sodium ions, use the formula \( ext{moles} = ext{concentration} \times ext{volume} \). The initial concentration of sodium ions is \(0.118 \, \text{M}\) and the blood volume is \(4.6 \, \text{L}\). Thus, initial moles are \( 0.118 \, \text{mol/L} \times 4.6 \, \text{L} = 0.5428 \, \text{mol} \).

Calculate needed moles of sodium ions for desired concentration

For the desired concentration of sodium ions, use the same formula with \(0.138 \, \text{M}\) as the concentration. The required moles are \( 0.138 \, \text{mol/L} \times 4.6 \, \text{L} = 0.6348 \, \text{mol} \).

Calculate additional moles of sodium ions needed

Find the additional moles of sodium ions needed by subtracting the initial moles from the needed moles: \( 0.6348 \, \text{mol} - 0.5428 \, \text{mol} = 0.092 \, \text{mol} \).

Convert moles of sodium ions to moles of sodium chloride

Since one mole of sodium chloride \((\text{NaCl})\) dissociates completely into one mole of sodium ions \((\text{Na}^+)\) and one mole of chloride ions \((\text{Cl}^-)\), 0.092 moles of sodium ions require 0.092 moles of sodium chloride.

Calculate mass of sodium chloride needed

Use the molar mass of sodium chloride \((\text{NaCl})\), which is approximately \(58.44 \, \text{g/mol}\) to find the mass. Multiply the moles of sodium chloride by its molar mass: \(0.092 \, \text{mol} \times 58.44 \, \text{g/mol} = 5.37648 \, \text{g} \).

Conclusion

The mass of sodium chloride that needs to be added to the blood is approximately \(5.38 \text{g}\).

Key concepts

Sodium Ions

Sodium ions, chemically represented as \(\text{Na}^+\), are essential electrolytes in the human body. They play a pivotal role in maintaining fluid balance, nerve signal transmission, and muscle function. In our context with hyponatremia, the sodium ion concentration in the blood decreases below normal, resulting in various health issues. Normal sodium ion levels are crucial as they help control blood pressure and volume through the ion concentration gradient.

In the original exercise, the initial sodium ion concentration in a patient's blood was \(0.118 \, \text{M}\). This unit, "M," stands for molarity, which is the number of moles of a solute per liter of solution. Maintaining appropriate sodium ion levels is vital for health, and in our problem, an adjustment was needed to reach \(0.138 \, \text{M}\). By understanding the role of sodium ions, we see why precise calculations are critical when adjusting them in blood chemistry.

Sodium Chloride

Sodium chloride, commonly known as table salt, has the chemical formula \(\text{NaCl}\). It is a simple ionic compound, made up of sodium ions \(\text{Na}^+\) and chloride ions \(\text{Cl}^-\). One of the remarkable properties of sodium chloride is its ability to dissociate completely in water—meaning every mole of \(\text{NaCl}\) will produce one mole of \(\text{Na}^+\) and one mole of \(\text{Cl}^-\).

In our exercise, sodium chloride is used to adjust the sodium ion concentration in the blood. To find out how much sodium chloride is needed, we assumed complete dissociation in the aqueous blood medium. After calculating the extra sodium ions needed to reach a desired blood concentration, it was determined that \(0.092 \,\text{mol}\) of sodium ions was required. Therefore, \(0.092 \,\text{mol}\) of sodium chloride was also needed due to the 1:1 dissociation ratio.

This makes sodium chloride an effective, simple means of adjusting sodium ion levels in the body due to its consistent dissociation behavior in fluids like blood.

Molar Concentration

Molar concentration, or molarity, is pivotal in understanding solution chemistry, specifically when adjusting ion levels like sodium in solutions such as blood. Molar concentration is represented in mol/L and tells us how many moles of a given solute are present in one liter of solution. It provides a straightforward way to compare concentrations of substances and is especially useful in chemistry and medicine.

The exercise utilized this concept by calculating the molar concentration of sodium ions in blood, where initially it was \(0.118 \, \text{M}\). To correct the hyponatremia condition, a new target concentration of \(0.138 \, \text{M}\) was necessary. By employing the equation \(\text{moles} = \text{concentration} \times \text{volume}\), the change in moles required was determined so the right amount of sodium chloride could be added. This exemplified how molar concentration calculations are crucial for solving practical problems in health and chemistry.

• It allows precise measurements of substances in a solution.
• Provides a method to adjust concentrations in medical scenarios.
• Facilitates clear understanding of chemical reactions in solutions.