Problem 26 - Chemistry Matter and Change

Question

Arrange these quantities from smallest to largest in terms of mass: 1.0 mol of \(\mathrm{Ar}, 3.0 \times 10^{24}\) atoms of Ne, and 20 \(\mathrm{g}\) of \(\mathrm{Kr}\) .

Step-by-Step Solution

Answer

The correct order from smallest to largest in terms of mass is 20 g of Krypton (Kr), 1.0 mol of Argon (Ar), and \(3.0 \times 10^{24}\) atoms of Neon (Ne).

Step 1: Write down the molar mass of the elements and Avogadro's number

We need the molar mass of the elements involved and Avogadro's number to determine the number of atoms/molecules involved in each mass. The molar mass of Argon (Ar) is 39.95 g/mol, Neon (Ne) is 20.18 g/mol, and Krypton (Kr) is 83.80 g/mol. Avogadro's number is \(6.022 \times 10^{23}\) particles/mol.

Step 2: Find the mass of 1.0 mol of Argon

Since the mass of Argon (Ar) is already given in moles, we can directly determine its mass using the molar mass of Ar. The mass of Ar is equal to the molar amount multiplied by the molar mass: Mass of Ar = 1.0 mol × 39.95 g/mol = 39.95 g

Step 3: Find the mass of \(3.0 \times 10^{24}\) atoms of Neon

First, we need to convert the given number of atoms of Neon (Ne) to moles using Avogadro's number. Then, we will use the molar mass of Ne to find the mass in grams. Moles of Ne = \(\frac{3.0 \times 10^{24}\ \text{atoms}}{6.022 \times 10^{23}\ \text{atoms/mol}} = 4.985 \ \text{mol}\) Now, we find the mass of Ne using its molar mass: Mass of Ne = 4.985 mol × 20.18 g/mol = 100.498 g

Step 4: Find the mass of 20 g of Krypton

The mass of Krypton is already given in grams, so we do not need to do any further calculations: Mass of Kr = 20 g

Step 5: Arrange the elements in order of mass

We now have the masses of the three elements: Argon (Ar) is 39.95 g, Neon (Ne) is 100.498 g, and Krypton (Kr) is 20 g. To arrange them from the smallest to largest in terms of mass, we simply list them in the ascending order of their masses: 20 g of Krypton (Kr) < 1.0 mol of Argon (Ar) < \(3.0 \times 10^{24}\) atoms of Neon (Ne) Therefore, the correct order from smallest to the largest mass is 20 g of Krypton, 1.0 mol of Argon, and \(3.0 \times 10^{24}\) atoms of Neon.

Key Concepts

Avogadro's Number

When diving into the world of chemistry, Avogadro's number is a constant that frequently appears in molar mass calculations. It represents the number of particles—atoms, molecules, ions, or others—contained in one mole of a substance. The established value is approximately \(6.022 \times 10^{23}\) particles per mole.

This number is pivotal when converting between the number of particles and the amount of substance in moles. For instance, if a question asks about a certain quantity of atoms, like in the exercise involving Neon (Ne), you utilize Avogadro's number to convert that quantity into moles, which can then be easily related to grams with the help of the substance's molar mass.

Atomic Mass Units

The atomic mass unit is a standard unit of mass that quantifies mass on an atomic or molecular scale. Abbreviated as amu, one atomic mass unit is defined as one-twelfth the mass of one carbon-12 atom. In practical terms, it's a way to express the mass of atoms or molecules on a scale that makes sense when dealing in microscopic amounts.

An atom's mass stated in atomic mass units nearly matches the number you'd use to calculate moles using Avogadro's number. This is because the relative atomic mass (atomic weight) displayed on the periodic table is measured in amu and essentially tells you how many grams per mole of that atom you would weigh out - which was crucial for the molar mass calculations in our original exercise. For example, Argon (Ar) has a molar mass of 39.95 g/mol which means one mole, or \(6.022 \times 10^{23}\) atoms, of Argon weighs 39.95 grams.

Mole-to-Gram Conversion

Understanding mole-to-gram conversion is key for solving quantitive problems in chemistry. This conversion process is the very foundation for comparing amounts of substances chemically. To convert moles to grams, you simply multiply the number of moles by the molar mass of the substance.

As an example from our solution, the mass of 1.0 mole of Argon (Ar) is calculated by multiplying the number of moles by Argon's molar mass, resulting in 39.95 g. This conversion enables chemists to measure out precise amounts of a substance for reactions, just like in cooking, where you measure ingredients like flour or sugar by weight for accuracy. If reversed, to convert grams to moles, you'd divide the mass of the substance by its molar mass - a process used when you start with a measured mass of a substance, as in the case with the 20 g of Krypton (Kr).