Sand consists mainly of silicon dioxide. When sand is heated with an excess of coke (carbon), pure silicon and carbon monoxide are produced. (a) Write a balanced equation for the reaction. (b) How many moles of silicon dioxide are required to form \(12.72 \mathrm{~g}\) of silicon? (c) How many grams of carbon monoxide are formed when \(44.99 \mathrm{~g}\) of silicon is produced?

Understanding chemical reaction balancing is essential for studying and executing chemical reactions. Balancing a chemical equation means ensuring that the number of atoms for each element is the same on both the reactant and the product sides of the reaction. This is in accordance with the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

For example, the reaction of silicon dioxide with carbon to produce silicon and carbon monoxide must be balanced to show the conservation of silicon, oxygen, and carbon atoms. Initially, the equation may look like this: \[\text{SiO}_2(s) + \text{C}(s) \rightarrow \text{Si}(s) + \text{CO}(g)\]

However, this is not balanced, as there are two oxygen atoms on the reactant side and only one on the product side. To correct this, we adjust the coefficients, which are the numbers in front of the chemical formulas that indicate the relative number of moles of each substance needed to balance the equation. The balanced equation becomes: \[\text{SiO}_2(s) + 2\text{C}(s) \rightarrow \text{Si}(s) + 2\text{CO}(g)\]

The coefficients tell us the stoichiometry of the reaction - for every mole of silicon dioxide that reacts, two moles of carbon monoxide are produced.

The mole concept is a fundamental principle in chemistry that helps us quantify the amount of a substance. One mole is defined as exactly 6.022 x 10^23 (Avogadro's number) particles of that substance, which could be atoms, molecules, ions, or electrons.

To relate moles to a quantity we can weigh, we use molar mass, which is the mass of one mole of a substance. The molar mass is numerically equal to the atomic or molecular weight of the substance in grams per mole. For instance, the molar mass of silicon (Si) is 28.09 g/mol. This implies that one mole of silicon atoms weighs 28.09 grams.

When calculating how many moles of a substance are present in a given mass, the formula is: \[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]

In our textbook example, for the 12.72 g of silicon (Si), we find the number of moles by dividing the mass by the molar mass of silicon, leading to the calculation: \[\frac{12.72 \text{ g}}{28.09 \text{ g/mol}}\].

Molar mass is a crucial characteristic of substances that bridges the gap between the microscale (atoms and molecules) and the macroscale (grams and kilograms) of matter. It represents the mass of one mole of a compound and is measured in grams per mole (g/mol).

As each element has a unique molar mass, compounds will have molar masses that are the sum total of the molar masses of the individual elements in the molecular formula, each weighted by the number of atoms of that element in the formula.

For example, the molar mass of carbon monoxide (CO) is calculated by adding the molar masses of carbon (12.01 g/mol) and oxygen (16.00 g/mol), resulting in 28.01 g/mol. Knowing the molar mass allows us to find the mass of gases produced, as shown in the solution to our textbook exercise where the formation of carbon monoxide from silicon and its subsequent mass calculation is directly dependent on its molar mass: \[\text{Grams of CO} = \left(2 \times \frac{44.99 \text{ g}}{28.09 \text{ g/mol}}\right) \times 28.01 \text{ g/mol}\].

Without the correct molar mass, it would be impossible to accurately convert between mass and moles, which is essential for stoichiometric calculations in chemical reactions.