Write a balanced chemical equation for the reaction that occurs when (d) dimethylether, CH3OCH31g2, is combusted in air.

Verified step by step guidance

1. Identify the reactants and products in the combustion reaction. The reactants are dimethyl ether \((\text{CH}_3\text{OCH}_3)\) and oxygen \((\text{O}_2)\). The products of a complete combustion reaction are carbon dioxide \((\text{CO}_2)\) and water \((\text{H}_2\text{O})\).
2. Write the unbalanced chemical equation for the combustion of dimethyl ether: \[ \text{CH}_3\text{OCH}_3(g) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g) \]
3. Balance the carbon atoms first. There are 2 carbon atoms in dimethyl ether, so you need 2 \(\text{CO}_2\) molecules on the product side: \[ \text{CH}_3\text{OCH}_3(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g) + \text{H}_2\text{O}(g) \]
4. Next, balance the hydrogen atoms. There are 6 hydrogen atoms in dimethyl ether, so you need 3 \(\text{H}_2\text{O}\) molecules on the product side: \[ \text{CH}_3\text{OCH}_3(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g) + 3\text{H}_2\text{O}(g) \]
5. Finally, balance the oxygen atoms. There are 4 oxygen atoms in \(2\text{CO}_2\) and 3 oxygen atoms in \(3\text{H}_2\text{O}\), totaling 7 oxygen atoms needed. Therefore, you need \(\frac{7}{2}\) or 3.5 \(\text{O}_2\) molecules. To avoid fractions, multiply the entire equation by 2 to get whole numbers: \[ 2\text{CH}_3\text{OCH}_3(g) + 7\text{O}_2(g) \rightarrow 4\text{CO}_2(g) + 6\text{H}_2\text{O}(g) \]

Key Concepts

Combustion Reactions

Combustion reactions involve the reaction of a substance with oxygen, typically producing heat and light. In organic chemistry, combustion of hydrocarbons or similar compounds results in the formation of carbon dioxide and water. Understanding the general form of combustion reactions is essential for writing balanced equations.

Balancing Chemical Equations

Balancing chemical equations is the process of ensuring that the number of atoms for each element is the same on both sides of the equation. This is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Proper balancing is crucial for accurately representing the stoichiometry of the reaction.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It involves using mole ratios derived from the balanced equation to calculate the amounts of substances consumed and produced. A solid grasp of stoichiometry is necessary for predicting the outcomes of chemical reactions, including combustion.