Problem 63 - Chemistry: The Central Science in SI Units, Global Edition

Question

The average adult human male has a total blood volume of 5.0 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?

Step-by-Step Solution

Answer

The mass of sodium ions circulating in the average adult human male's blood is approximately 15.5 g. This calculation is based on a blood volume of 5.0 L and a sodium ion concentration of \(0.135 \mathrm{M}\).

Step 1: Calculate moles of sodium ions in the blood

To determine the moles of sodium ions in the blood, we can use the formula: Moles of solute = Molarity × Volume of solution Here, the Molarity of sodium ions is \(0.135 \mathrm{M}\) and the volume of the blood is 5.0 L.

Step 2: Convert volume to liters

The volume of blood is given in liters, so we don't need to make any conversion. We can directly use the given volume: Volume of blood = 5.0 L

Step 3: Calculate moles of sodium ions

Now, we can calculate the moles of sodium ions using the molarity and volume: Moles of sodium ions = \(0.135 \mathrm{M} \times 5.0\, \mathrm{L}\) Moles of sodium ions = \(0.675 \, \mathrm{moles}\)

Step 4: Calculate the mass of sodium ions

To calculate the mass of sodium ions, we can use the formula: Mass = Moles × Molar mass The molar mass of sodium ion (Na+) is approximately \(23 \, \mathrm{g/mol}\) (we consider only the sodium part of the ion, ignoring the charge). So, the mass of sodium ions in the blood: Mass of sodium ions = \(0.675 \, \mathrm{moles} \times 23\, \mathrm{g/mol}\) Mass of sodium ions = \(15.525 \, \mathrm{g}\)

Step 5: Round the answer to the appropriate decimal place

The mass of sodium ions circulating in the blood is approximately 15.5 g, after rounding off to one decimal place.

Key Concepts

Molarity

Molarity is a central concept in chemistry calculations, particularly when discussing solutions. It measures the concentration of a solute within a given volume of solution. The formula to calculate molarity is:

• Molarity (M) = Moles of solute / Liters of solution

Understanding molarity helps chemists determine how much of a substance is present in a given volume of liquid. For instance, in our problem, the sodium ion concentration is given as 0.135 M, indicating that there are 0.135 moles of sodium ions in every liter of blood. This becomes particularly useful when calculating other properties like moles or mass, as we can directly relate these quantities to the volume of the solution.

Moles

Moles are a fundamental unit in chemistry that represent a specific number of particles, usually atoms or molecules. A single mole is equal to Avogadro's number, which is approximately 6.022 × 10²³ particles. This concept provides a bridge between the atomic scale and the macroscopic measurements we use in the laboratory.When calculating moles in a solution, the formula used is:

• Moles = Molarity (M) × Volume (L)

In the given exercise, with a blood volume of 5.0 liters and a sodium ion concentration of 0.135 M, we find the moles of sodium ions by multiplying these values: \(0.135 imes 5.0 = 0.675\) moles. This quantifies the amount of sodium ions present in the bloodstream, forming a basis for further calculations like determining the mass.

Sodium Ion Concentration

Sodium ions play a vital role in bodily functions, and their concentration within the blood needs to be tightly regulated. In chemistry terms, concentration often refers to molarity, as discussed. In our problem, we have a sodium ion concentration of 0.135 M, indicating that every liter of blood contains 0.135 moles of sodium ions. The measurement of sodium ion concentration is essential for understanding electrolyte balance and several physiological processes, such as nerve signaling and muscle contraction. Knowing this concentration allows chemists or medical professionals to precisely calculate related chemical quantities, such as the number of moles or the mass of the ions, to ensure proper physiological functionality.

Blood Volume

Blood volume is an important parameter in physiological studies and medical diagnoses. It refers to the total amount of blood circulating within the body. In the context of the exercise, we considered an average adult male with a blood volume of 5.0 liters. This constant value allows us to calculate the total moles of a solute, such as sodium ions, by applying it in the molarity equation. The calculation of solute quantity in the blood helps in assessing and managing conditions related to blood composition. Blood volume's relevance extends to determining dosages of medication and understanding the dynamics of blood circulation in the body.

Molar Mass

Molar mass is a key concept in converting moles to grams, which provides practical, tangible measurements. It represents the mass of one mole of a substance, usually expressed in grams per mole (g/mol). For sodium ions ( ext{Na}^+), the molar mass is approximately 23 g/mol.In our exercise, after calculating the moles of sodium ions present in the blood (0.675 moles), we use the molar mass to find the total mass. The formula applied is:

• Mass = Moles × Molar Mass

Applying this, we get:\(0.675 imes 23 = 15.525\) grams.This calculation allows us to express the amount of sodium ions in a format that is easy to measure experimentally, providing a basis for practical applications in both laboratory and clinical settings.