Problem 124 - Chemistry Matter and Change

Question

A 12.0 -g sample of an element contains \(5.94 \times 10^{22}\) atoms. What is the unknown element? (Chapter 10\()\)

Step-by-Step Solution

Answer

The unknown element is antimony (Sb).

Step 1: Determine the Moles of Atoms

To find the number of moles of atoms, use Avogadro's number. Avogadro's number is \(6.022 \times 10^{23}\) atoms/mol, so the number of moles is calculated by dividing the number of atoms by Avogadro's number. \[\text{moles of atoms} = \frac{5.94 \times 10^{22}}{6.022 \times 10^{23}} = 0.0986 \text{ mol}\]

Step 2: Calculate the Molar Mass of the Element

The molar mass is calculated by dividing the mass of the sample by the moles of atoms calculated. With a sample mass of 12.0 g:\[\text{Molar mass} = \frac{12.0 \, \text{g}}{0.0986 \, \text{mol}} = 121.7 \, \text{g/mol}\]

Step 3: Identify the Element

Using the calculated molar mass of approximately \(121.7 \, \text{g/mol}\), we check the periodic table to find that this matches the molar mass of antimony (Sb), which has a molar mass close to 121.7 g/mol.

Key Concepts

Avogadro's Number

Avogadro's Number, named after the Italian scientist Amedeo Avogadro, is a fundamental constant used in chemistry. It tells us how many atoms or molecules are in a mole of a substance. This number is incredibly large:

• Avogadro's Number is precisely defined as \(6.022 \times 10^{23}\).
• It serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world that we can observe and measure.

When dealing with chemical reactions, Avogadro's number allows chemists to convert between moles and numbers of atoms or molecules easily. For instance, in the exercise given, we used it to find out how many moles are in the sample based on the number of atoms present. This conversion is essential for stoichiometry, ensuring accurate calculations in chemical equations.

Molar Mass

Molar Mass is a key concept in chemistry that refers to the mass of a given substance (chemical element or chemical compound) divided by the amount of substance, measured in moles. It allows us to convert a known substance mass into moles, facilitating calculations involving other reactants or products. Characteristics include:

• Molar mass is expressed in grams per mole (g/mol).
• For an element, it is numerically equal to the atomic mass when considering a single-mole sample.

In calculating molar mass, one divides the given mass by the number of moles obtained. In our example, a 12.0 g sample containing \(0.0986\) moles corresponds to a molar mass of \(121.7 \text{ g/mol}\). This calculation tells us the weight per mole of the element and helps identify it by matching with known molar masses.

Element Identification

Element Identification involves determining which element corresponds to a specific set of chemical or physical properties, such as molar mass or atomic structure.

• This process often involves comparing calculated values, such as molar mass, to known values from sources like the periodic table.
• An accurate molar mass helps to pinpoint the element uniquely among others.

In this context, by calculating a molar mass of \(121.7 \text{ g/mol}\), we can cross-reference with the periodic table and identify the element as antimony (Sb). This method is straightforward yet powerful, helping chemists identify unknown elements in a sample.