Problem 45 - Chemistry Matter and Change

Question

Smelting When tin(IV) oxide is heated with carbon in a process called smelting, the element tin can be extracted. \begin{equation} \mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Sn}(1)+2 \mathrm{CO}(\mathrm{g}) \end{equation} Interpret the chemical equation in terms of particles, moles, and mass.

Step-by-Step Solution

Answer

The equation shows 1 molecule/1 mole of SnO₂ reacting with 2 atoms/2 moles of C, producing 1 atom/1 mole of Sn and 2 molecules/2 moles of CO, conserving mass.

Step 1: Interpret in Terms of Particles

The chemical equation \( ext{SnO}_2(s) + 2 ext{C}(s) \rightarrow ext{Sn}(l) + 2 ext{CO}(g)\) represents a reaction at a particle level where 1 molecule of tin(IV) oxide reacts with 2 atoms of carbon to produce 1 atom of tin and 2 molecules of carbon monoxide.

Step 2: Interpret in Terms of Moles

In terms of moles, the equation shows that 1 mole of tin(IV) oxide reacts with 2 moles of carbon to produce 1 mole of tin and 2 moles of carbon monoxide. Moles are a way to count particles using Avogadro's number \(6.022 \times 10^{23}\).

Step 3: Interpret in Terms of Mass

To interpret the equation in terms of mass, calculate the molar masses of each substance involved: \(\text{SnO}_2\) (150.71 g/mol), \(\text{C}\) (12.01 g/mol), \(\text{Sn}\) (118.71 g/mol), \(\text{CO}\) (28.01 g/mol). According to the equation, 1 mole of \(\text{SnO}_2\) (150.71 g) reacts with 2 moles of \(\text{C}\) (2 x 12.01 g = 24.02 g) to yield 1 mole of \(\text{Sn}\) (118.71 g) and 2 moles of \(\text{CO}\) (2 x 28.01 g = 56.02 g), ensuring mass is conserved.

Key Concepts

Stoichiometry

Stoichiometry is the heart of chemical reactions, guiding us to understand how reactants transform into products. It's like a recipe, where the chemical equation provides the exact amounts of each component. In the smelting process of tin, the equation \( \text{SnO}_2 + 2\, \text{C} \rightarrow \text{Sn} + 2\, \text{CO} \) shows the precise ratio of substances involved. Stoichiometry helps illustrate that 1 mole of \( \text{SnO}_2 \) reacts with 2 moles of carbon to yield 1 mole of tin and 2 moles of carbon monoxide. A stoichiometric calculation involves the following steps:

• Balancing the equation: Ensures both sides have the same number of atoms for each element.
• Converting quantities: Use molar mass to convert grams to moles.
• Using mole ratios: Derive ratios from the balanced equation to calculate desired quantities.

This careful balancing ensures no excess or deficit in the prediction of product formed or reactant used.

Moles

The concept of moles is fundamental in chemistry as it serves as a bridge between the microscopic world of atoms and the macroscopic world of grams and liters. A mole is like a counting unit, much like a dozen, but instead of 12, a mole contains \( 6.022 \times 10^{23} \) particles, known as Avogadro's number. In our smelting example, when we say 1 mole of \( \text{SnO}_2 \) reacts, we mean \( 1 \times 6.022 \times 10^{23} \) molecules of tin(IV) oxide react. This large number helps chemists perform calculations on a practical scale because dealing directly with such small particles would be otherwise impossible. Understanding moles bridges the gap between the recipe provided by stoichiometry and actual laboratory work, enabling precise measurements and reactions.

Molar Mass

Molar mass is crucial in translating between moles and grams, the units we often deal with practically. It's the mass of one mole of a substance, expressed in grams per mole (g/mol). Each element's molar mass corresponds to its atomic weight on the periodic table.For example, the molar mass of \( \text{SnO}_2 \) is calculated by summing the atomic masses of tin (Sn), approximately 118.71 g/mol, and oxygen (O) which is about 16.00 g/mol each in this molecule. Thus, \( \text{SnO}_2 \)'s molar mass becomes 150.71 g/mol. Knowing molar masses allows chemists to convert between mass and moles:

• To convert grams to moles: Divide the mass of the substance by its molar mass.
• To convert moles to grams: Multiply the number of moles by the molar mass.

This conversion is crucial for preparing reagents and predicting the amount of products formed in chemical reactions.

Smelting Process

The smelting process is an ancient technique used to extract metals from their ores. In the case of tin, tin(IV) oxide is heated with carbon to produce pure tin and carbon monoxide gas. This reduction reaction is expressed in the equation \( \text{SnO}_2 + 2\, \text{C} \rightarrow \text{Sn} + 2\, \text{CO} \). Smelting involves:

• Heating: The ore is heated to high temperatures to initiate the chemical reaction.
• Reduction: The ore's metal is reduced, commonly with a reducing agent like carbon, to separate the metal from oxygen.
• Collection: The molten metal (tin in this case) is then collected after it separates from the other substances.

Through smelting, valuable pure metals are recovered from their natural ore forms, allowing them to be used in various applications around the world. Understanding the chemical equations and physical conditions in smelting is key for efficient metal extraction and industrial applications.