Question

The average adult human male has a total blood volume of 5.0 \(\mathrm{L}\). If the concentration of sodium ion in this average individual is \(0.135 \mathrm{M},\) what is the mass of sodium ion circulating in the blood?

Short answer

The mass of sodium ion is approximately 15.52 g.

Step-by-step solution

Understand the Problem

We need to find the mass of sodium ions in an average adult male's blood. We know the blood volume is 5.0 L and the sodium ion concentration is 0.135 M. Molarity (M) is the number of moles of solute per liter of solution. Hence, we need to convert these into moles and then into mass.

Calculate Moles of Sodium Ions

Using the molarity formula: \[ \text{moles of sodium ions} = \text{molarity} \times \text{volume} \]Substitute the given values: \[ 0.135 \text{ M} \times 5.0 \text{ L} = 0.675 \text{ moles of sodium ions} \]

Convert Moles to Mass

The next step is to convert moles into mass using the molar mass of sodium. The molar mass of sodium (Na) is approximately 22.99 g/mol. Therefore, the mass is calculated using: \[ \text{mass} = \text{moles} \times \text{molar mass} \]\[ 0.675 \text{ moles} \times 22.99 \text{ g/mol} = 15.52 \text{ g} \]

Verify and Conclude

Review the calculations to ensure all steps were followed correctly and accurately. The calculated mass of sodium ions in the blood is the final result.

Key concepts

Moles

When we talk about moles in chemistry, we're referring to a unit that measures the amount of a substance. Think of a mole as a dozen. Just as a dozen refers to 12 items, a mole refers to approximately \(6.022 \times 10^{23}\) entities, which could be atoms, molecules, or ions. This number is known as Avogadro's number.
Moles help us bridge the gap between the atomic scale and the real world. Since atoms and molecules are incredibly small, measuring them in grams directly doesn't make sense, because they wouldn’t even register! By using moles, we can count these particles in a way that is meaningful and practical.
**How Moles Work in Calculations:**- When you know the molarity (the number of moles per liter), you can find the actual number of moles in a liquid by multiplying the molarity by the volume in liters.- Once you have the moles, you can convert it into mass using the molar mass (the mass of one mole of a substance in grams).
In our exercise, once we had the molarity of sodium ions and the blood volume, we calculated the moles of sodium ions by simply multiplying these two values, allowing us to proceed to find out the mass.

Blood volume

Blood volume is the total amount of blood circulating within the body. For an average adult human male, this is about 5.0 liters. Knowing the blood volume is crucial for various medical and scientific calculations, as it provides necessary context for measuring substances dissolved in the blood.
**Importance of Blood Volume:** - **Medical Diagnostics:** It helps in determining baseline conditions and diagnosing abnormalities. - **Fluid Therapies:** For treatments involving intravenous fluids or medications, it's crucial to know blood volume to avoid over or under-dosing.
In chemistry, such as in our exercise, blood volume aids in calculating how much of a particular substance (like sodium ions) is present in the blood. By knowing the blood's volume, you can easily translate the concentration of substances in blood to their actual amounts using molarity as a stepping stone.

Sodium ion concentration

The concentration of sodium ions in the blood is a measure of how many sodium ions are present per liter of blood. It is usually expressed in terms of molarity, which is moles of solute per liter of solution. In our scenario, the sodium ion concentration is given as 0.135 M.
**Why Sodium Ion Concentration Matters:** - **Body Function Regulation:** Sodium ions play critical roles in muscle function, nerve signaling, and fluid balance. Their concentration affects blood pressure and volume regulation. - **Health Monitoring:** Proper sodium levels are essential for overall health, making its concentration in the blood a key diagnostic marker for medical professionals.
**Calculating Mass from Concentration:** To find the mass of sodium ions circulating in the blood, we need to convert from molarity to mass. This is done in two steps: - Calculate the number of moles of sodium ions, by multiplying the ion concentration (0.135 M) by the blood volume (5.0 L). - Convert the moles to mass using the molar mass of sodium (22.99 g/mol).
This approach not only applies to sodium ions, but to any solute where you know the concentration and volume, making this a vital skill in chemistry.