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. $$\mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Sn}(1)+2 \mathrm{CO}(\mathrm{g})$$ Interpret the chemical equation in terms of particles, moles, and mass.

Step-by-Step Solution

Answer

In the smelting process, one formula unit of tin(IV) oxide (SnO2) reacts with two atoms of carbon (C) to produce one atom of tin (Sn) and two molecules of carbon monoxide (CO). In terms of moles, 1 mole of SnO2 reacts with 2 moles of C to produce 1 mole of Sn and 2 moles of CO. In terms of mass, 150.71 g of SnO2 reacts with 24.02 g of carbon to produce 118.71 g of tin and 56.02 g of carbon monoxide.

Step 1: Identify the balanced chemical equation

The balanced chemical equation for the smelting process is given as: \[\mathrm{SnO}_{2(s)} + 2 \mathrm{C}_{(s)} \rightarrow \mathrm{Sn}_{(l)} + 2 \mathrm{CO}_{(g)}\] This equation tells us that one mole of tin(IV) oxide (SnO2) reacts with two moles of carbon (C) to produce one mole of tin (Sn) and two moles of carbon monoxide (CO).

Step 2: Interpret in terms of particles

In terms of particles, one formula unit of tin(IV) oxide reacts with two atoms of carbon to produce one atom of tin and two molecules of carbon monoxide. To relate particles to moles, we utilize Avogadro's number: \(6.022 \times 10^{23}\) particles per mole. So, \(6.022 \times 10^{23}\) formula units of SnO2 react with \(2 \times 6.022 \times 10^{23}\) carbon atoms to produce \(6.022 \times 10^{23}\) tin atoms and \(2 \times 6.022 \times 10^{23}\) CO molecules.

Step 3: Interpret in terms of moles

The balanced chemical equation tells us the molar ratios between the reactants and products: 1 mole of tin(IV) oxide (SnO2) reacts with 2 moles of carbon (C) to produce 1 mole of tin (Sn) and 2 moles of carbon monoxide (CO).

Step 4: Interpret in terms of mass

To interpret the chemical equation in terms of mass, calculate the molar masses of each species involved: Molar mass of SnO2: Sn (118.71 g/mol) + 2*O (2*16.00 g/mol) = 150.71 g/mol Molar mass of C: 12.01 g/mol Molar mass of Sn: 118.71 g/mol Molar mass of CO: C (12.01 g/mol) + O (16.00 g/mol) = 28.01 g/mol Using these molar masses, we can relate the moles to mass: 150.71 g of tin(IV) oxide reacts with 2*12.01 g (24.02 g) of carbon to produce 118.71 g of tin and 28.01 g*2 (56.02 g) of carbon monoxide.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, known as products. In the smelting process presented, tin(IV) oxide (SnO_2) and carbon (C) are the reactants, while tin (Sn) and carbon monoxide (CO) are the products.
To better understand chemical reactions, it is crucial to pay attention to the chemical equations that symbolize them. A chemical equation balances two sides: reactants on the left and products on the right.

• The equation\[\mathrm{SnO}_{2(s)} + 2 \mathrm{C}_{(s)} \rightarrow \mathrm{Sn}_{(l)} + 2 \mathrm{CO}_{(g)}\]shows a balanced chemical reaction.
• Balancing chemical equations means having an equal number of each type of atom on both sides of the equation.

In this equation, for each one molecule of tin(IV) oxide, there are two molecules of carbon needed to form one atom of tin and two molecules of carbon monoxide. Understanding this helps in predicting the amounts of substances consumed and produced in a reaction.

Mole Concept

The mole concept is a fundamental idea in chemistry that links the microscopic world of atoms and molecules to the macroscopic world we observe daily. One mole represents \(6.022 \times 10^{23} \) particles, a number known as Avogadro's number. This concept is key to quantifying substances in chemical reactions.
When we look at the smelting equation, each component can be considered in terms of moles:

• 1 mole of SnO_2 reacts with 2 moles of C to yield 1 mole of Sn and 2 moles of CO.
• The mole ratios, derived from the coefficients in the balanced equation, are critical in calculations involving stoichiometry.

These mole ratios help predict how much product we can expect when a given amount of reactants react completely. For instance, knowing the mole concept allows us to convert between moles and grams using molar mass, enabling more tangible measurements.

Molar Mass

Molar mass is the mass of one mole of any chemical substance and is expressed in grams per mole (g/mol). It serves as a bridge between the mole concept and the mass of substances, as it enables the conversion of moles to grams and vice versa.
For the smelting reaction, calculating molar masses involves adding together the atomic masses of the elements in each compound:

• For \( \mathrm{SnO}_2 \), molar mass is calculated as: Sn (118.71 g/mol) + 2 x O (16.00 g/mol) = 150.71 g/mol.
• Carbon (C) is simpler, with a molar mass of 12.01 g/mol.

From this information, the masses involved in the chemical equation become interpretable in a tangible way:

• 150.71 g of SnO_2 reacts with 24.02 g of C to produce 118.71 g of Sn and 56.02 g of CO.

Understanding molar mass is essential for converting amounts in chemical equations from moles to grams, which is crucial for practical laboratory and industrial applications.