Question

Each liter of human blood serum contains about \(3.4 \mathrm{~g}\) of sodium ions \(\left(\mathrm{Na}^{+}\right.\), ionic weight \(=23 \mathrm{~g} /\) mole \() .\) What is the molarity of \(\mathrm{Na}^{+}\) in human blood serum?

Short answer

The molarity of Na+ ions in human blood serum is approximately 0.1478 M.

Step-by-step solution

Convert mass to moles

Using the given mass of sodium ions (3.4 g) and the ionic weight of sodium (23 g/mol), we can find the number of moles present in 1 L of human blood serum by using the formula: Moles of sodium ions (Na+) = (Mass of Na+ ions) / (Ionic weight of Na+)

Calculate the moles of Na+ ions

By substituting the given values (mass of Na+ ions = 3.4 g and ionic weight of Na+ = 23 g/mol) into the formula from Step 1, we can calculate the moles of Na+ ions present: Moles of sodium ions (Na+) = (3.4 g) / (23 g/mol) = 0.1478 mol

Calculate the molarity of Na+ ions

Molarity is the number of moles of solute (in this case, Na+ ions) per liter of solution. Since we have 1 L of human blood serum, the molarity of Na+ ions can be calculated as: Molarity of Na+ ions = (Moles of Na+ ions) / (Volume of solution)

Find the molarity of Na+ ions in human blood serum

Substitute the calculated moles of Na+ ions (0.1478 mol) and the volume of blood serum (1 L) into the formula from Step 3 to find the molarity: Molarity of Na+ ions = (0.1478 mol) / (1 L) = 0.1478 M So, the molarity of Na+ ions in human blood serum is approximately 0.1478 M.

Key concepts

Molarity

Understanding molarity is essential for anyone involved in chemistry, as it is a standard measure of concentration in the field. Simply put, molarity denotes the number of moles of a substance contained in one liter of solution. It is expressed by the capital letter M. For instance, a 1 M solution contains one mole of solute per liter of solution.

To calculate molarity, we use the formula:
\[ Molarity = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \].

For the exercise focused on sodium ions in human blood, the molarity calculation helps determine the concentration of these ions, which are vital for physiological functions including nerve impulse transmission and muscle contraction.

Sodium Ions in Human Blood

In the context of biology and medicine, sodium ions (\r\(Na^+\)) play a pivotal role in the human body. They're involved in various functions like regulating blood pressure, maintaining fluid balance, and enabling nerve and muscle function. Normally, the concentration of sodium ions in human blood is tightly controlled, as both deficient and excessive levels can lead to health issues. Normal blood serum levels range from 135 to 145 millimoles per liter (mmol/L), and the molarity concept is used to express these levels in a clear, quantifiable manner.

Understanding the molarity of sodium ions in our blood is therefore vital not just for chemists, but also for healthcare professionals who monitor and manage patients' electrolyte balance.

Moles Calculation

The mole is a fundamental unit in chemistry that provides a bridge between the atomic or molecular scale and a scale that chemists can work with. One mole of any substance contains Avogadro's number of particles (approximately \(6.022 \times 10^{23}\)) of that substance.

When calculating moles from mass, we use the formula:
\[ Moles = \frac{\text{Mass of the substance (g)}}{\text{Molar mass of the substance (g/mol)}} \].

The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol), and it equals the sum of the atomic masses of all atoms in a molecule. In the exercise about sodium ions, we use the molar mass of \(Na^+\), which is 23 g/mol, to find the number of moles from the given mass.

Chemical Concentration

Chemical concentration refers to the amount of a substance in a specified volume of solution or mixture. There are several ways to express chemical concentration, including molarity, mass percent, volume percent, and molality. However, molarity is one of the most common and convenient methods, especially in aqueous solutions.

Understanding concentrations is crucial in many areas such as pharmacology, where precise dosages of medication are required, and in environmental science, where the pollutant levels in air, water, and soil are monitored. My tip for students is to always double-check which unit of concentration is being used, as confusing different units can lead to significant errors in calculations and results.