Problem 66 - Chemistry and Chemical Reactivity

Question

An unknown metal reacts with oxygen to give the metal oxide, MO \(_{2} .\) Identify the metal based on the following information: Mass of metal \(=0.356 \mathrm{g}\) Mass of sample after converting metal completely to oxide \(=0.452 \mathrm{g}\)

Step-by-Step Solution

Answer

The metal is Uranium.

Step 1: Calculate the mass of oxygen in the oxide

To find the mass of oxygen that reacted with the metal, subtract the initial mass of the metal from the mass of the metal oxide. \[ \text{Mass of Oxygen} = \text{Mass of Metal Oxide} - \text{Mass of Metal} = 0.452 \text{ g} - 0.356 \text{ g} = 0.096 \text{ g}\]

Step 2: Write the formula of the oxide

The unknown metal reacts with oxygen to form the metal oxide, which is represented as \(MO_2\). This indicates that two moles of oxygen atoms combine with one mole of metal atoms.

Step 3: Calculate the moles of oxygen

The molar mass of oxygen is \(16 \text{ g/mol}\). Since the oxide is \(MO_2\), the oxygen content in the compound is \(2\times 16 = 32 \text{ g/mol}\). Calculate the moles of oxygen used:\[ \text{Moles of } O = \frac{0.096 \text{ g}}{32 \text{ g/mol}} = 0.003 \text{ mol}\]

Step 4: Determine moles of the unknown metal

Based on the formula \(MO_2\), one mole of metal combines with two moles of oxygen atoms. Therefore, the number of moles of metal is:\[ \text{Moles of metal} = \frac{0.003}{2} = 0.0015 \text{ mol}\]

Step 5: Calculate the molar mass of the metal

Knowing the mass of the metal and the moles, calculate the molar mass of the metal using the formula:\[ \text{Molar Mass of Metal} = \frac{\text{Mass of Metal}}{\text{Moles of Metal}} = \frac{0.356 \text{ g}}{0.0015 \text{ mol}} \approx 237.33 \text{ g/mol}\]

Step 6: Identify the metal

Compare the calculated molar mass of the metal with known molar masses of elements. The molar mass of approximately 237.33 g/mol closely matches that of Uranium (U, 238.03 g/mol). Therefore, the metal is Uranium.

Key Concepts

Molar Mass Calculation

Understanding how to calculate molar mass is crucial for identifying unknown substances in chemical reactions. The molar mass is essentially the mass of one mole of a given substance, expressed in grams per mole (g/mol).

In the context of our exercise, it involves calculating the molar mass of an unknown metal. You begin by determining the number of moles present using the formula:

• Molar Mass = \( \frac{\text{Mass of Substance}}{\text{Moles of Substance}} \)

Calculating the molar mass allows us to compare it with known values for different elements. This step is vital for identifying unknown metals in chemical reactions.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry is the quantitative relationship between reactants and products in a chemical equation. It tells us the ratios in which substances react and are formed.

In this exercise, stoichiometry is crucial when determining the relationship between the metal and oxygen in the metal oxide, \( MO_2 \).

Given the formula \( MO_2 \), it signifies that one mole of metal reacts with two moles of oxygen. By knowing the exact proportions, we can establish that if we have 0.003 moles of \( O \), then there are \( \frac{0.003}{2} = 0.0015 \) moles of the metal.

This precision in measurement helps us further in calculating other vital statistics within the chemical equation.

Metal Identification

The process of metal identification involves comparing calculated properties, such as molar mass, with known properties of elements.

For the unknown metal that forms \( MO_2 \), we've calculated a molar mass of approximately 237.33 g/mol.

Using this information:

• We compare the calculated molar mass to known molar masses.
• We look for a close match to identify the element.

In this scenario, the calculated molar mass closely matches uranium, which has a molar mass of 238.03 g/mol.
Therefore, the unknown metal is identified as Uranium. Identifying metals is a valuable skill for correctly predicting reactions and properties in chemistry.