Problem 63 - Chemistry: The Central Science

Question

Theaverage 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?

Step-by-Step Solution

Answer

The mass of sodium ions circulating in the average adult human male's blood is 15.52 g. This is calculated by first finding the moles of sodium ions in 5.0 L of blood with a concentration of 0.135 M, and then multiplying this by the molar mass of sodium (22.99 g/mol).

Step 1: Calculate moles of sodium ions

Given, the total blood volume is 5.0 L, and the concentration of sodium ions is 0.135 M. We can calculate the moles of sodium ions using the formula: Moles of sodium ions = Concentration × Volume of blood Moles of sodium ions = 0.135 M × 5.0 L

Step 2: Find the molar mass of sodium

The molar mass of sodium (Na) is 22.99 g/mol.

Step 3: Calculate the mass of sodium ions

Now, to find the mass of sodium ions, we'll multiply the moles of sodium ions by the molar mass of sodium (Na). Mass of sodium ions = Moles of sodium ions × Molar mass of sodium Mass of sodium ions = (0.135 M × 5.0 L) × 22.99 g/mol Mass of sodium ions = \(0.675 \text{ moles} \times 22.99 \frac{\text{g}}{\text{mol}}\) Mass of sodium ions = 15.52 g Therefore, the mass of sodium ions circulating in the blood is 15.52 g.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. It is expressed in units of grams per mole (g/mol). The molar mass is used to convert between the mass of a substance and the number of moles.
For individual atoms, like sodium (Na), the molar mass is numerically equal to the atomic mass of the element, typically found on the periodic table. In our example, the molar mass of sodium is 22.99 g/mol.

• This means that one mole of sodium atoms weighs 22.99 grams.
• This value allows chemists to easily move between grams and moles in calculations, an essential skill when working with chemical equations and reactions.

Understanding molar mass is crucial because it serves as a bridge between the microscopic world of atoms and the macroscopic world that we can measure and observe in the lab.

Concentration Calculations

Concentration calculations are a key part of chemistry and describe the amount of a substance present in a given volume of solution. The most common unit of concentration is molarity (M), defined as moles of solute per liter of solution.
In the given exercise, the sodium ion concentration is given as 0.135 M, meaning there are 0.135 moles of sodium ions in every liter of blood.

• This type of calculation is particularly useful in scenarios like blood chemistry, where it is important to maintain certain concentrations for proper physiological function.
• Knowing the concentration allows for determining the total amount of substance in a given volume, which informs decisions in both medical and chemical contexts.

Calculating concentration is straightforward when volume and moles are known, as seen in the calculation of moles of sodium ions provided above.

Sodium Ion Concentration

Sodium ions are a critical component of human blood chemistry, playing key roles in nerve function, muscle contraction, and maintaining fluid balance. The concentration of sodium ions in blood is typically tightly regulated. In chemistry terms, this concentration is often expressed using molarity.
The exercise provides a sodium ion concentration of 0.135 M in 5.0 liters of blood. This concentration measurement helps convert volume data into enzyme activity, ion balance, and physiological implications.

• A deviation in normal sodium ion concentration can lead to serious health consequences, emphasizing the need for accurate calculation and monitoring.
• In practical applications, this concentration helps us calculate the total moles and thus the total mass of sodium ions present, which is crucial for diagnosing or treating medical conditions.

This illustrates how chemistry concepts directly impact health science and medical practices.

Moles to Grams Conversion

Converting moles to grams is an essential skill in chemistry that involves using the molar mass of a substance. Once the number of moles is established, multiplying by the molar mass yields the mass in grams.
In the example problem, we calculated that there were 0.675 moles of sodium ions in 5 liters of blood. Multiplying by the molar mass of sodium (22.99 g/mol) gives the mass of the sodium ions as 15.52 grams.

• This conversion is valuable because mass is a more tangible and commonly measured property than moles.
• It is particularly useful in laboratory settings, where precise measurements are critical.

A deep understanding of moles to grams conversion helps in balancing chemical equations, preparing solutions, and conducting accurate experimental work.