Problem 3 - Chemistry Matter and Change

Question

Silver nitrate \(\left(\mathrm{Ag} \mathrm{NO}_{3}\right)\) is used to make several different silver halides used in photographic films. How many formula units of \(\mathrm{AgNO}_{3}\) are there in 3.25 \(\mathrm{mol}\) of \(\mathrm{AgNO}_{3} ?\)

Step-by-Step Solution

Answer

In 3.25 mol of silver nitrate (AgNO₃), there are approximately \(19.5715 \times 10^{23}\) formula units.

Step 1: Recall the concept of a mole

A mole is a unit of measurement for the amount of substance. It allows us to compare different substances and perform calculations involving chemical reactions. One mole of any substance contains Avogadro's number of entities, which is approximately 6.022 x 10²³ entities/mol.

Step 2: Identify the given information

In this problem, we are given 3.25 mol of silver nitrate (AgNO₃). Our goal is to find the number of formula units in this amount of AgNO₃.

Step 3: Use Avogadro's number to find the number of formula units

To find the number of formula units of AgNO₃ in 3.25 mol, we will use Avogadro's number (6.022 x 10²³ entities/mol). Multiply the given number of moles by Avogadro's number: Number of formula units = (moles of AgNO₃) x (Avogadro's number) Number of formula units = (3.25 mol) x (6.022 x 10²³ entities/mol)

Step 4: Perform the calculation

Multiply the number of moles (3.25) by Avogadro's number (6.022 x 10²³): Number of formula units = (3.25) x (6.022 x 10²³) Number of formula units = 19.5715 x 10²³

Step 5: Present the final answer

The number of formula units of silver nitrate (AgNO₃) in 3.25 mol is approximately 19.5715 x 10²³ formula units.

Key Concepts

Avogadro's Number

In the world of chemistry, Avogadro's number is crucial for understanding the mole concept. It signifies the number of particles, such as atoms or molecules, in one mole of a substance. The value of Avogadro's number is approximately 6.022 x 10^{23}. This is an unimaginably large number, which echoes the immense quantity of molecules or atoms in a relatively small amount of material.
Avogadro's number serves as a bridge between the microscopic world of atoms and molecules, and the macroscopic world in which we weigh substances in grams or observe reactions on a macroscopic scale. This allows chemists to count entities by weighing a sample. Thus, if you're calculating the number of formula units or particles in a certain amount of a substance, you multiply the number of moles by Avogadro's number. This is how you can go from moles to actual numbers of atoms or molecules.

Chemical Calculations

The ability to perform chemical calculations is essential for solving problems in chemistry. These calculations often involve converting between mass, moles, and the number of particles. They enable chemists to predict the outcomes of reactions and to express quantities of substances in a workable form.
A common calculation involves determining the number of particles in a substance using its mole quantity, as demonstrated in the problem about silver nitrate. To perform such a calculation:

• Identify the amount of substance in moles.
• Multiply it by Avogadro's number to find the number of formula units or molecules.

For instance, if you have 3.25 moles of a substance, you would multiply this by 6.022 x 10^{23} to determine the actual number of formula units. These calculations can also go in the opposite direction, such as finding the moles from a number of particles, by dividing the particle number by Avogadro's number.

Silver Nitrate Formulas

Silver nitrate, with the chemical formula AgNO_{3}, is a well-known compound in the field of chemistry and has quite a few applications, particularly in photography and as a reagent in labs. Understanding its chemical formula is crucial for performing chemical calculations involving this substance.
This compound consists of:

• One silver (Ag) atom
• One nitrogen (N) atom
• Three oxygen (O) atoms

When tasked with finding formula units in a sample of silver nitrate, such as in the exercise given, it's vital to understand how this formula translates to actual molecules. Knowing the chemical formula lets you perform stoichiometric calculations and understand reactions in which silver nitrate is involved. This knowledge is also pivotal when working with its derivatives or when it's part of more complex reactions, as it relates directly to the number of molecules or formula units. By mastering the chemical formula, one can seamlessly integrate knowledge from molecular composition to practical applications.