Question

Product Concentrations A \(10^{-3} \mathrm{M}\) solution of gamma globulin (antibodies) is called a "concentrated solution." Why is it called a concentrated solution? Support your answer with a calculation.

Short answer

A \(10^{-3} \mathrm{M}\) solution of gamma globulin is called a concentrated solution because it contains a large number of gamma globulin molecules. Specifically, there are approximately \(6.022 x 10^{20}\) molecules of gamma globulin in one liter of the solution.

Step-by-step solution

Understand the Concentration

The concentration of the solution is given as \(10^{-3} \mathrm{M}\), where M stands for molarity. This means there are \(10^{-3}\) moles of gamma globulin per liter of solution. Molarity is a measure of the concentration of a solute in a solution, or of any chemical species in terms of amount of substance in a given volume.

Calculate the Number of Molecules

To calculate the number of molecules, multiply the number of moles by Avogadro's number, which is \(6.022 x 10^{23}\). This gives the number of molecules of gamma globulin in the solution. \(10^{-3}\) moles corresponds to \((10^{-3} moles) x (6.022 x 10^{23} molecules/mole) = 6.022 x 10^{20}\) molecules.

Interpret the Results

On interpretation, the results show that there are \(6.022 x 10^{20}\) molecules of gamma globulin present in a single liter of the solution. This is a very large number of molecules, indicating that the solution is indeed concentrated.

Key concepts

Understanding Solution Concentration

Knowing the concentration of a solution is crucial in various scientific fields, from medicine to chemistry. Molarity, denoted by 'M', is a common measure of solution concentration. It provides a direct way to communicate how much solute is dissolved in a given volume of solution.

In simpler terms, it is a count of how many moles of a substance are present in one liter of solution. So when you see a concentration of 10^-3M, it means there are 10^-3 moles, or 0.001 moles, of the solute—in this case, gamma globulin—contained in one liter of the solution.

Despite the seeming smallness of 10^-3 when observed in moles, this actually represents a substantial amount of individual molecules when you take into account Avogadro's number, which we shall look into shortly.

The Significance of Avogadro's Number

Avogadro's number, a fundamental constant in chemistry, is approximately 6.022 x 10²³. This incredibly large number signifies the quantity of elementary entities (usually atoms or molecules) in one mole of a substance. It's named after Amedeo Avogadro, an Italian scientist who contributed significantly to molecular theory.

When we say there are 10^-3 moles of gamma globulin in our solution, and we multiply that by Avogadro's number, we're translating moles into actual numbers of molecules. For gamma globulin, that would be approximately 6.022 x 10²⁰ molecules in one liter of solution—it emphasizes the scale at which chemical reactions occur, which is unimaginable on a human scale.

This number helps to bridge the gap between the microscopic world, where things are measured in atoms and molecules, and the macroscopic world, where we use grams and liters.

Gamma Globulin in Detail

Gamma globulin is a class of proteins predominantly found in blood plasma. These proteins play an essential role in the body's immune response, acting as antibodies that identify and neutralize foreign objects like viruses and bacteria.

The presence of gamma globulins is significant not only in biological processes but also in medical treatments. They are used in therapies for a range of immune deficiencies and autoimmune diseases, often administered intravenously. A 'concentrated solution' of gamma globulin implies a high dose of these proteins, thereby imparting a strong immunological effect in therapeutic applications.

Hence, although 10^-3M may sound dilute in everyday terms, for certain substances, including therapeutic proteins like gamma globulin, it is actually quite a high concentration, capable of eliciting a significant biological effect.

Moles as a Measure in Chemistry

The concept of 'moles' is a cornerstone in the study of chemistry, serving as a bridge between the microscopic world of atoms and the macroscopic world we live in. A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. One mole corresponds to approximately 6.022 x 10²³ (Avogadro's number) of molecules or atoms of the substance.

To put it into perspective, if each particle were a tiny grain of sand, one mole of these grains would be enough to fill a whole stadium! This analogy highlights the large-scale nature implied by moles despite it being a unit for incredibly minute entities.

Moles provide a useful way to translate the weight of a chemical substance, which is easily measurable, into an equivalent number of atoms or molecules, which are not. It makes it easier to tell how many entities are participating in a chemical reaction and to calculate precise amounts of reactants and products.