Problem 95 - Chemistry and Chemical Reactivity

Question

An unknown metal reacts with oxygen to give the metal oxide, \(\mathrm{MO}_{2}\). Identify the metal if a \(0.356-\mathrm{g}\) sample of the metal produces \(0.452 \mathrm{g}\) of the metal oxide.

Step-by-Step Solution

Answer

The metal is tin (Sn).

Step 1: Determine the Mass of Oxygen

First, find the mass of oxygen that has combined with the metal to form the metal oxide. Subtract the mass of the metal from the mass of the metal oxide: \[ 0.452 \, \text{g metal oxide} - 0.356 \, \text{g metal} = 0.096 \, \text{g oxygen} \]

Step 2: Calculate Moles of Oxygen

Next, calculate the moles of oxygen atoms. The molar mass of oxygen is approximately 16.00 g/mol. Since we have one mole of \( O_2 \) containing two moles of oxygen atoms, we use:\[ \text{Moles of } O = \frac{0.096 \, \text{g}}{16.00 \, \text{g/mol}} = 0.006 \text{ mol} \]

Step 3: Moles of Metal Correspondence

In the formula \( \text{MO}_2 \), each metal atom is associated with two oxygen atoms. Thus, the moles of metal should be half the moles of the \( O_2 \) atoms present:\[ \text{Moles of metal} = \frac{0.006 \text{ mol}}{2} = 0.003 \text{ mol} \]

Step 4: Calculate Molar Mass of the Metal

Using the moles of the metal and its mass, calculate its molar mass:\[ \text{Molar Mass} = \frac{0.356 \, \text{g}}{0.003 \, \text{mol}} = 118.67 \, \text{g/mol} \]

Step 5: Identify the Metal

Finally, compare the calculated molar mass with the periodic table. A molar mass of approximately 118.67 g/mol corresponds to the element tin (Sn).

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a substance is crucial for identifying an unknown element or compound. The molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It is the same as the atomic mass unit (amu) value found on the periodic table.
To determine the molar mass of an unknown metal in a compound, such as in our exercise, you divide the mass of the metal sample by the number of moles of the element you calculated. The formula is:

• \(\text{Molar Mass} = \frac{\text{Mass of Sample in grams}}{\text{Moles of Sample}}\)

For example, if the mass of the metal is 0.356 grams and the moles calculated from prior steps are 0.003 moles, the molar mass calculation would be:

• \(\text{Molar Mass} = \frac{0.356}{0.003} = 118.67 \, \text{g/mol}\)

This value can then be used to identify the element by comparing it with standard values found in the periodic table.

Metal Oxide Identification

Identifying a metal oxide involves understanding its chemical formula and the stoichiometry related to its formation. In our case, the compound is represented as \(\text{MO}_2\), indicating it consists of one metal atom and two oxygen atoms. This stoichiometry is typical for oxides of elements such as tin (Sn) in this molecular arrangement.
Knowing the stoichiometry helps determine how the elements are combined in the compound. When identifying the metal in \(\text{MO}_2\), one must consider the proportion of each element and use the actual masses from the experiment.
First, understand that the total mass of the oxide is a sum of its respective elements. Then, using the provided sample and oxide mass, you can identify the metal by deciding which element matches the calculated atomic or molar mass.

Oxygen Mass Calculation

Determining the mass of oxygen in a metal oxide is a straightforward process once you have the total mass of the oxide and the metal. The difference between these two values gives the mass of the oxygen combined with the metal.
The formula for calculating the mass of oxygen is:

• \(\text{Mass of Oxygen} = \text{Mass of Metal Oxide} - \text{Mass of Metal}\)

In our exercise, the metal oxide mass is 0.452 grams and the metal is 0.356 grams. Therefore, the mass of oxygen is:

• \(0.452 - 0.356 = 0.096 \, \text{g of oxygen}\)

By knowing the mass of oxygen, you can further determine the moles of oxygen present, providing crucial data needed for solving stoichiometric calculations related to the compound formation. This step is vital in metal identification processes when paired with other stoichiometric results.