Question

Silicon carbide, \(\mathrm{SiC},\) is one of the hardest materials known. Surpassed in hardness only by diamond, it is sometimes known commercially as carborundum. Silicon carbide is used primarily as an abrasive for sandpaper and is manufactured by heating common sand (silicon dioxide, \(\mathrm{SiO}_{2}\) ) with carbon in a furnace. $$\mathrm{SiO}_{2}(s)+\mathrm{C}(s) \rightarrow \mathrm{CO}(g)+\mathrm{SiC}(s)$$ What mass of silicon carbide should result when 1.0 kg of pure sand is heated with an excess of carbon?

Short answer

When 1.0 kg of pure sand is heated with an excess of carbon, 667 g of silicon carbide should be produced.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the formation of silicon carbide from silicon dioxide and carbon is already provided: $$\mathrm{SiO}_{2}(s)+\mathrm{C}(s) \rightarrow \mathrm{CO}(g)+\mathrm{SiC}(s)$$

Convert the mass of silicon dioxide to moles

We are given 1.0 kg of silicon dioxide. To convert this mass to moles, we'll use the molar mass of silicon dioxide. The molar mass of SiO2 is \((1\times28.09\:\text{g/mol})+(2\times16.00\:\text{g/mol}) = 60.09\:\text{g/mol}\). First, convert the mass of silicon dioxide from kg to grams: \(1.0\:\text{kg} = 1000\:\text{g}\) Now, calculate the moles of silicon dioxide: $$\text{moles\:of\:SiO}_{2} = \frac{\text{mass}}{\text{molar\:mass}} = \frac{1000\:\text{g}}{60.09\:\text{g/mol}} = 16.63\:\text{mol}$$

Use the stoichiometry of the reaction to find moles of silicon carbide

From the balanced chemical equation, we can see that every mole of SiO2 used in the reaction produces one mole of SiC. So, 16.63 moles of silicon dioxide will produce 16.63 moles of silicon carbide.

Convert the moles of silicon carbide to mass

Finally, we need to convert the moles of silicon carbide to mass. To do this, we'll use the molar mass of silicon carbide. The molar mass of SiC is \(1\times28.09\:\text{g/mol} + 1\times12.01\:\text{g/mol} = 40.10\:\text{g/mol}\). Now, calculate the mass of silicon carbide produced: $$\text{mass\:of\:SiC} =\text{moles} \times \text{molar\:mass} = 16.63\:\text{mol} \times 40.10\:\text{g/mol} = 667\:\text{g}$$ So, when 1.0 kg of pure sand is heated with an excess of carbon, 667 g of silicon carbide should be produced.

Key concepts

Chemical Reactions

Chemical reactions are central to the study of chemistry, connecting the rearrangement of atoms to create new substances. Understanding these transformations requires deciphering chemical equations that represent the process. In our exercise, the chemical reaction involves the production of silicon carbide (SiC), a material known for its hardness. This reaction takes place when silicon dioxide (SiO₂) is heated with carbon (C) to produce silicon carbide (SiC) and carbon monoxide (CO) as byproducts.

For each substance involved, the physical state is indicated in parentheses—solid (s), gas (g). Reactants and products are connected by an arrow, signifying the direction of the reaction. The importance of these notations lies in providing a visual representation of the actual lab process, enabling us to anticipate the output of silicon carbide from a given input of sand—in this case, expressed as 1.0 kg.

Molar Mass Calculation

Molar mass acts as a bridge linking the mass of a substance with the amount in moles. When handling chemical reactions, it's essential to convert the mass of reactants or products into moles, as it allows for the use of the balanced equation to predict quantities. This process is termed molar mass calculation.

In the given exercise, we calculated the molar masses of silicon dioxide and silicon carbide to transition from grams to moles and vice versa. The molar mass is found by summing the masses of the individual atoms in the compound's formula. For complex substances, this involves multiplying the atomic masses from the periodic table by the number of each type of atom in the molecule and adding them together. Carrying out this step accurately is crucial, as it underpins the subsequent stoichiometric calculations that determine the final mass of the silicon carbide produced.

Balanced Chemical Equation

A balanced chemical equation is critical in ensuring the Law of Conservation of Mass is adhered to, meaning no atoms are lost or gained during the reaction. It provides a proportional relationship between reactants and products and is an indispensable tool for stoichiometric calculations.

The equation from our exercise indicates that one mole of SiO₂ reacts with one mole of C to produce one mole of CO and one mole of SiC. The balanced nature of the equation helps us deduce that the moles of silicon dioxide directly equate to the moles of silicon carbide formed—a 1:1 ratio. Understanding and applying the mole ratios from balanced equations enable us to accurately predict the outcomes of chemical reactions, as seen in the exercise where we could determine the expected mass of the abrasive silicon carbide from a known quantity of sand.