Problem 20 - Chemistry: Principles and Reactions

Question

How many protons are in (a) an atom of platinum? (b) one mole of platinum? (c) one gram of platinum?

Step-by-Step Solution

Answer

Answer: There are 2.40 x 10^23 protons in one gram of platinum.

Step 1: Find the atomic number of platinum

Check the periodic table and find that the atomic number of platinum (Pt) is 78, which means that there are 78 protons in the nucleus of a platinum atom.

Step 2: Calculate the number of protons in one mole of platinum

Using Avogadro's number (6.022 x 10^23), we can find out the number of protons in one mole of platinum atoms. The number of protons in one mole of platinum atoms is equal to the atomic number multiplied by Avogadro's number: Number of protons = atomic number × Avogadro's number = 78 × (6.022 x 10^23) = 4.69 x 10^25 protons

Step 3: Calculate the number of protons in one gram of platinum

First, we need to know the molar mass of platinum, which is 195.08 g/mol. To find out how many moles are in one gram of platinum, we can use the following formula: Moles of platinum = mass of platinum / molar mass of platinum = 1 g / 195.08 g/mol = 0.00512 moles Now, we can find the number of protons in one gram of platinum by multiplying the number of moles by the number of protons in one mole of platinum (from step 2): Number of protons in 1 gram of platinum = moles of platinum × number of protons in one mole of platinum = 0.00512 moles × 4.69 x 10^25 protons/mole = 2.40 x 10^23 protons So, there are 2.40 x 10^23 protons in one gram of platinum.

Key Concepts

Avogadro's Number

Imagine a very large number that's crucial in the world of chemistry; this number is known as Avogadro's number, which is approximately equal to \(6.022 \times 10^{23}\). It's named after the Italian scientist Amedeo Avogadro and is the number of units in one mole of any substance.

Think of it as the bridge between the microscopic world of atoms and molecules and our everyday, macroscopic world. Just as a dozen always refers to 12 things, one mole always contains Avogadro's number of particles, whether those particles are atoms, ions, or molecules. This concept is at the heart of many calculations in chemistry, including determining the number of atoms or molecules in a given mass of a substance—like how many protons are in a mole of platinum.

Mole Concept

To understand the mole concept, it helps to think about buying eggs. An egg carton typically holds a dozen eggs. In chemistry, instead of counting items one by one, we count them by the 'carton,' except this carton is called a mole, and it's a lot bigger, containing Avogadro's number of items.

The mole is a standard unit of measurement used in chemistry to express amounts of a chemical substance. It allows chemists to work with the subatomic world with macroscopic amounts of material. When we talk about one mole of an element or compound, we're referring to exactly \(6.022 \times 10^{23}\) of their fundamental units (atoms, molecules, ions, etc.). For example, one mole of platinum contains \(6.022 \times 10^{23}\) platinum atoms.

Molar Mass

Every chemist's toolbox includes the term 'molar mass', which represents the mass of one mole of a given substance. Expressed in grams per mole (g/mol), the molar mass is numerically equivalent to the atomic or molecular weight of a substance.

For instance, the molar mass of platinum is 195.08 g/mol, which means every mole of platinum has a mass of 195.08 grams. This concept is vitally important when converting between the number of moles and the mass of a substance. It provides a way to measure precise amounts of a substance in a lab by relating the mole (a count of particles) to mass (something we can measure on a scale).