Question

An unknown metal (M) was found not to react with either water or steam, but its reactivity with aqueous acid was not investigated. When a \(1.000 \mathrm{~g}\) sample of the metal was burned in oxygen and the resulting metal oxide converted to a metal sulfide, \(1.504 \mathrm{~g}\) of sulfide was obtained. What is the identity of the metal?

Short answer

The metal is Copper (Cu).

Step-by-step solution

Determine the General Equation

The metal (M) reacts with oxygen to form metal oxide, then the metal oxide reacts to form a metal sulfide. These reactions can be represented as:\[ 2M + O_2 \rightarrow 2MO \] (Formation of Metal Oxide) \[ MO + H_2S \rightarrow MS + H_2O \] (Formation of Metal Sulfide)

Calculate Molar Mass of Metal Sulfide

The mass of the metal sulfide obtained is given as 1.504 g. The molar mass of the metal sulfide (MS) is the sum of the atomic masses of the metal (M) and sulfur. Assuming complete conversion, the mass of M in the sulfide is 1 g.

Establish Mass Equation

Using the mass of sulfur (S = 32.07 g/mol), set up the equation for the formation of metal sulfide:\[ m_M + m_S = 1.504 \text{ g} \] where \( m_M \) = mass of the metal, and \( m_S \) = mass of sulfur in the sulfide. Since \( m_M = 1 \text{ g} \), the equation for sulfur becomes:\[ 1 + m_S = 1.504 \text{ g} \]

Solve for Mass of Sulfur

From the equation \( 1 + m_S = 1.504 \), solve for \( m_S \) to find the mass of sulfur in the metal sulfide:\[ m_S = 1.504 - 1 = 0.504 \text{ g} \]

Calculate Atomic Mass of Metal

Now, calculate the moles of sulfur using its atomic mass (32.07 g/mol):\[ \text{Moles of S} = \frac{0.504}{32.07} \approx 0.0157 \text{ moles} \] Since the mole ratio of M to S is 1:1 in the sulfide, the moles of M = moles of S = 0.0157 moles. Then, the atomic mass of M is given by:\[ \text{Atomic mass of M} = \frac{1}{0.0157} = 63.69 \text{ g/mol} \]

Identify the Metal

The calculated atomic mass of the unknown metal (M) is approximately 63.69 g/mol. Based on this atomic mass, the metal is likely Copper (Cu), which has an atomic mass of about 63.55 g/mol.

Key concepts

Metal Oxide Formation

Metal oxide is formed when a metal reacts with oxygen. In our exercise, the unknown metal (M) reacts with oxygen to form the metal oxide (MO). This process, also known as oxidation, involves the transfer of oxygen atoms to the metal element, creating a compound where metal ions are combined with oxide ions. The general balanced chemical equation for this reaction is: \[ 2M + O_2 \rightarrow 2MO \] This equation tells us that two atoms of metal (M) react with one molecule of oxygen producing two units of metal oxide (MO). Understanding this equation helps us predict the outcomes of reactions based on the stoichiometric coefficients. They represent the ratios of reactants and products, crucial in calculating how much of each substance is used and produced. Metal oxide formation is a common process in geology, materials science, and chemistry. It's foundational for understanding how metals behave in natural environments and when processed industrially.

Metal Sulfide Formation

Metal sulfide forms when metal oxide reacts with hydrogen sulfide. This substitute reaction involves metal oxides being converted into metal sulfides. The sulfide ion replaces the oxide ion, producing a new compound. The chemical equation that represents this conversion is:\[ MO + H_2S \rightarrow MS + H_2O \]This shows the metal oxide reacting with hydrogen sulfide, resulting in the formation of metal sulfide (MS) and water (H₂O). In this reaction, the oxygen from the metal oxide bonds with the hydrogen from hydrogen sulfide to produce water as a byproduct, leaving the sulfur to bind with the metal.Metal sulfide formation is significant in various industries, including metal extraction and processing. This reaction is helpful for recovering metals from their ores or refining metals for practical use. Understanding this is vital for those studying geochemistry, metallurgy, and applied chemistry.

Atomic Mass Calculation

Atomic mass calculation is an essential step in identifying unknown substances in chemistry. In our problem, we have determined the mass of the sample, which allows us to calculate the atomic mass of metal (M). The atomic mass of an element is the mass of a single atom, typically expressed in atomic mass units (g/mol). To find the atomic mass of M, we first calculate the moles of sulfur in the metal sulfide, using its atomic mass of 32.07 g/mol. Given the weight of sulfur is 0.504 g, the moles are:\[ \text{Moles of S} = \frac{0.504}{32.07} \approx 0.0157 \text{ moles} \]Because our metal sulfide has a 1:1 molar ratio of metal (M) to sulfur (S), the moles of M are the same. Since the mass of M is given as 1 g, the atomic mass can be found by:\[ \text{Atomic mass of M} = \frac{1}{0.0157} = 63.69 \text{ g/mol} \]This calculated atomic mass is close to the known atomic mass of copper, approximately 63.55 g/mol, identifying copper as the metal (M). Mastering atomic mass calculation is crucial for recognizing substances, understanding their properties, and predicting reactions in chemistry.