Problem 16 - Chemistry: An Atoms-Focused Approach

Question

In a balanced chemical equation for the complete combustion of a hydrocarbon, what is the ratio of atoms of C in the hydrocarbon to molecules of \(\mathrm{CO}_{2}\) produced?

Step-by-Step Solution

Answer

Answer: The ratio of carbon atoms in a hydrocarbon to the molecules of carbon dioxide produced during complete combustion is 1:1.

Step 1: Write the general reaction for complete combustion of a hydrocarbon

A hydrocarbon can be represented as \(C_{x}H_{y}\), where x and y are integers representing the number of carbon and hydrogen atoms, respectively. The complete combustion reaction can be represented as: $$C_{x}H_{y} + O_{2} \rightarrow CO_{2} + H_{2}O$$

Step 2: Balance the equation

To balance the chemical equation, we need to make sure that there are equal numbers of each atom on both sides of the equation. We can do this by adjusting the coefficients: $$C_{x}H_{y} + \frac{y}{2}O_{2} \rightarrow xCO_{2} + \frac{y}{2}H_{2}O$$

Step 3: Identify the ratio of carbon atoms in hydrocarbon to CO2 molecules

From the balanced chemical equation, we can see that there are x carbon atoms in the hydrocarbon, and x molecules of CO2 are produced as a result of the complete combustion. Therefore, the ratio of carbon atoms in the hydrocarbon (C) to molecules of CO2 produced is: $$\frac{x\text{ (carbon atoms in hydrocarbon)}}{x\text{ (molecules of }CO_{2}\text{ produced)}}$$

Step 4: Simplify the ratio

The ratio can be simplified as follows: $$\frac{x}{x} = 1$$ This means that for every carbon atom in the hydrocarbon, one molecule of carbon dioxide (CO2) is produced during complete combustion. Therefore, the ratio of carbon atoms in the hydrocarbon to molecules of CO2 produced is 1:1.

Key Concepts

Combustion

Combustion is an exothermic reaction where a substance combines with oxygen to produce heat and light. In the case of hydrocarbons, this reaction typically involves burning these compounds in the presence of excess oxygen. Let's break it down:

• A hydrocarbon is a compound made up of carbon (C) and hydrogen (H) atoms.
• During combustion, the carbon atoms in the hydrocarbon react with oxygen (\(O_{2}\)) to form carbon dioxide (\(CO_{2}\)).
• Hydrogen atoms react to form water (\(H_{2}O\)).

The general word equation for combustion is: hydrocarbon + oxygen → carbon dioxide + water.

This process is vital because it releases energy that is used for various applications, such as heating homes and driving engines. In essence, combustion plays a critical role in energy production from chemical reactions.

Balancing Chemical Equations

Balancing chemical equations is crucial in chemistry because it ensures the law of conservation of mass is upheld. This law states that matter cannot be created or destroyed in an isolated system.

• A balanced chemical equation has equal numbers of each type of atom on both the reactant and product sides.
• To achieve balance, coefficients are adjusted in front of the chemical formulas involved in the reaction.

For instance, the complete combustion of a hydrocarbon (\(C_{x}H_{y} + O_{2} \rightarrow CO_{2} + H_{2}O\)) begins with identifying the number of carbon and hydrogen atoms in the hydrocarbon.

By adjusting the coefficients, you can balance the equation so that:

• The number of carbon atoms in the hydrocarbon equals the number of CO2 molecules.
• The number of hydrogen atoms in the hydrocarbon equals two times the number of H2O molecules.

Balancing ensures precision in chemical reactions and is fundamental in predicting the outcomes of chemical processes.

Chemical Stoichiometry

Chemical stoichiometry involves the calculation of reactants and products in chemical reactions. It is the bridge between the balanced chemical equation and the actual quantities of substances involved. Let's explore its components:

• Stoichiometry uses molarity, coefficients, and the mole concept to determine quantities needed or produced.
• By knowing the balanced reaction (\(C_{x}H_{y} + \frac{y}{2}O_{2} \rightarrow xCO_{2} + \frac{y}{2}H_{2}O\)), stoichiometry helps calculate the number of moles of oxygen required or moles of water and CO2 produced.

For example, to find the ratio of carbon atoms to CO2 molecules in combustion, stoichiometry illustrates that for each mole of carbon in the hydrocarbon, one mole of CO2 is produced.

This is crucial in chemical manufacturing and laboratories, where stoichiometric calculations provide the foundation for formulating materials, optimizing yields, and minimizing wastage.