Question

A gaseous organic compound containing only carbon, hydrogen, and nitrogen is burned in oxygen gas, and the volume of each reactant and product is measured under the same conditions of temperature and pressure. Reaction of four volumes of the compound produces 4 volumes of \(\mathrm{CO}_{2}, 2\) volumes of \(\mathrm{N}_{2},\) and 10 volumes of water vapor. (a) How many volumes of \(\mathrm{O}_{2}\) were required? (b) What is the empirical formula of the compound?

Short answer

The volumes needed are 18 volumes of \( \text{O}_2 \), and the compound formula is \( \text{CH}_2 \text{N} \)

Step-by-step solution

Determine Moles from Volumes

Given all gases are measured under the same conditions of temperature and pressure, we know that the volume ratios are equivalent to mole ratios.

Write the Balanced Chemical Equation

The chemical equation can be written based on the volumes given. Let the compound be represented as \( \text{C}_x \text{H}_y \text{N}_z \). The reaction can be written as: \( 4 \text{C}_x \text{H}_y \text{N}_z + \text{O}_2 \rightarrow 4 \text{CO}_2 + 2 \text{N}_2 +10 \text{H}_2 \text{O} \)

Find Oxygen Needed for Complete Combustion

From the balanced equation, note each volume of product requires certain volumes of \( \text{O}_2 \). Burning 1 vol of compound:

Calculate Oxygen for Each Product

To produce 4 volumes of \( \text{CO}_2 \): \( x\text{ volumes}\), for 2 volumes of \( \text{N}_2 \): no \( \text{O}_2 \) consumed, and for 10 volumes of \( \text{H}_2 \text{O} \): \( 5\text{ volumes} \).The total volume \( \text{O}_2 \)

Calculate Total Volume

Adding the required volumes for the complete combustion:\( 4(4 + 5) \), thus 18 volumes of \( \text{O}_2\).

Determine Empirical Formula

Using mole ratios resulted from products. For \( \text{C} \) and \( \text{H} \). Therefore\( \text{C}_1 \text{H}_2 \text{N}_1 \)

Key concepts

Gas Stoichiometry

Gas stoichiometry involves the calculation of reactants and products in a chemical reaction involving gases. To simplify, if gases are measured under the same conditions of temperature and pressure, the volumes of gases can be directly related to their mole quantities. For example, suppose we have 4 volumes of a gaseous organic compound. When this compound reacts with oxygen gas (combustion reaction), we can determine the volumes of products formed and the volumes of reactants consumed. This means that our calculations can be translated into easy volume-to-volume relationships without delving into mole conversions! This method is particularly helpful for understanding gas reactions involving combustion reactions and determining volumes of products like \(\text{CO}_2\), \(\text{H}_2\text{O}\) vapor, and other gases.

Combustion Reactions

Combustion reactions occur when a substance reacts with oxygen gas to produce energy, often releasing light and heat. In our particular exercise, we burn a compound containing carbon, hydrogen, and nitrogen. The general form of a combustion reaction with a hydrocarbon is:
\[\text{C}_x \text{H}_y + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}\]\
Involving a nitrogenous compound in our exercise, we extend to include nitrogen gas as a product too:
\[ \text{C}_x \text{H}_y \text{N}_z + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{N}_2\]\
During the reaction, carbon and hydrogen in the compound oxidize to form carbon dioxide and water, respectively, while nitrogen is released as nitrogen gas. Key points in combustion reactions include identifying the reactants, ensuring the reaction with sufficient oxygen, and accurately measuring the formed products. This exercise demonstrates how analyzing the volumes of products can furnish necessary details for understanding the combustion of complex organic molecules.

Chemical Equations Balancing

Balancing chemical equations is fundamental in chemistry to satisfy the Law of Conservation of Mass, which states that matter must neither be created nor destroyed. Each side of the equation must have an equal number of atoms for each element involved in the reaction. For instance, the initial step of solving our exercise requires writing and balancing the chemical equation:
\[4 \text{C}_x \text{H}_y \text{N}_z + \text{O}_2 \rightarrow 4 \text{CO}_2 + 2 \text{N}_2 + 10 \text{H}_2\text{O} \]\
Here’s a simple way to balance:

• Count the number of atoms for each element on both sides of the equation
• Adjust coefficients (numbers in front of molecules) to balance the atoms
• Ensure the balanced equation reflects the simplest whole number ratio

After balancing, we use the mole or volume ratios to find out how many volumes of oxygen are required for the complete burning process. We discovered that the compound requires 18 volumes of \(\text{O}_2\) to combust fully. Mastering this step-by-step technique is crucial for accurately interpreting and solving chemical reactions, paving the way for understanding more intricate topics in chemistry.