Question

Consider the balanced equation: $$ \mathrm{SiO}_{2}(s)+3 \mathrm{C}(s) \longrightarrow \mathrm{SiC}(s)+2 \mathrm{CO}(g) $$ Complete the table showing the appropriate number of moles of reactants and products. If the number of moles of a reactant is provided, fill in the required amount of the other reactant, as well as the moles of each product that forms. If the number of moles of a product is provided, fill in the required amount of each reactant to make that amount of product, as well as the amount of the other product that forms.

Short answer

To complete the table, utilize the balanced equation ratios: 1 SiO2 : 3 C : 1 SiC : 2 CO. Multiply or divide by appropriate stoichiometric coefficients based on the data given for reactants or products.

Step-by-step solution

Understand the Stoichiometry of the Balanced Equation

First, note the stoichiometry of the balanced equation: one mole of silicon dioxide reacts with three moles of carbon to produce one mole of silicon carbide and two moles of carbon monoxide. This stoichiometric relationship is represented by the coefficients in the balanced equation: 1 SiO2 : 3 C : 1 SiC : 2 CO.

Setting Up Ratios for Given Moles of Reactant

If the number of moles of one reactant is provided, use the stoichiometric ratio from the balanced equation to calculate the required moles of other reactants and the moles of products formed. For example, if you have n moles of SiO2, the required moles of C will be 3n, moles of SiC will be n, and moles of CO will be 2n.

Setting Up Ratios for Given Moles of Product

If the number of moles of one product is provided, use the stoichiometric ratio from the balanced chemical equation in reverse to calculate the required moles of reactants to produce that amount of product as well as the moles of the other product that forms. For example, if n moles of SiC are required, then you will need n moles of SiO2, 3n moles of C, and will produce 2n moles of CO.

Key concepts

Chemical Equations

Chemical equations are much like mathematical equations, but instead of numbers, they involve chemical substances. A chemical equation represents a chemical reaction that occurs between reactants to form products.

For instance, in the reaction \(\mathrm{SiO}_2(s) + 3\mathrm{C}(s) \longrightarrow \mathrm{SiC}(s) + 2\mathrm{CO}(g)\), \(\mathrm{SiO}_2\) and \(\mathrm{C}\) are the reactants, and \(\mathrm{SiC}\) and \(\mathrm{CO}\) are the products. The symbols \((s)\) and \((g)\) indicate that \(\mathrm{SiO}_2\) and \(\mathrm{C}\) are solids and \(\mathrm{CO}\) is a gas, respectively. The numbers in front of each chemical formula are coefficients that provide the ratios of the reactants and products; they ensure the equation obeys the law of conservation of mass.

To better understand these ratios, picture baking a cake that requires three eggs for every two cups of flour. Similarly, the given reaction requires three atoms of carbon for every molecule of silicon dioxide used.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we observe. A mole is a unit that denotes a specific number of particles, just like a dozen represents 12 of anything.

Avogadro's number \(6.022 \times 10^{23}\) tells us how many particles are in one mole of a substance. This large number evens the playing field and allows chemists to count atoms and molecules by weighing them, as directly counting entities like atoms would be impractical.

Understanding the mole concept is crucial in stoichiometry as it allows us to convert between the mass of a substance and the amount in moles. For example, if we know the molar mass of \(\mathrm{SiO}_2\) is about 60 g/mol, we can calculate that 120 grams of \(\mathrm{SiO}_2\) equals 2 moles. This fundamental conversion factor is instrumental in solving stoichiometric problems.

Stoichiometric Calculations

Stoichiometric calculations are the heart of solving chemical equations quantitatively. These calculations allow us to convert moles of one substance in a reaction to moles of another substance using the coefficients in the balanced equation as conversion factors.

Applying Stoichiometry

In the balanced equation for our silicon carbide synthesis, stoichiometry tells us that for every 1 mole of \(\mathrm{SiO}_2\), 3 moles of \(\mathrm{C}\) are needed, yielding 1 mole of \(\mathrm{SiC}\) and 2 moles of \(\mathrm{CO}\). To calculate how much of each reactant is required or how much of each product will be formed, simply multiply the given moles of one substance by the ratio deduced from the balanced equation.

Example Calculation

If given 4 moles of \(\mathrm{SiO}_2\), we can determine the needed moles of \(\mathrm{C}\) by multiplying 4 moles by the ratio of \(\mathrm{C}\) to \(\mathrm{SiO}_2\), which is 3:1. This results in 12 moles of \(\mathrm{C}\). Similarly, we'd obtain 4 moles of \(\mathrm{SiC}\) and 8 moles of \(\mathrm{CO}\).

Understanding stoichiometry enables the precise calculation of reactants and products, ensuring reactions are efficient and resources aren't wasted.