Question

A mixture is made equal volume of \(\mathrm{CO}\) and air. A spark passed through so that all the oxygen is converted to carbon dioxide. What will be fractional decrease in the total volume of system assuming pressure and temperature remain constant? Air contains \(20 \%\) oxygen by volume. (a) \(0.1\) (b) \(0.2\) (c) \(0.15\) (d) \(0.3\)

Short answer

The fractional decrease in the total volume of the system is 0.1.

Step-by-step solution

Understand the Reaction

Write down the chemical reaction that occurs when a spark is passed through the mixture of CO and air. All the oxygen is used up to convert CO to CO2: 2CO + O2 -> 2CO2. This reaction shows that two volumes of CO react with one volume of O2 to produce two volumes of CO2.

Determine Volume of Oxygen in Air

Since air contains 20% oxygen by volume, calculate the volume of oxygen that would be present in the original mixture. If V is the total volume of air, then the volume of oxygen, VO2, is 0.2V.

Calculate the Decrease in Volume

According to the reaction, one volume of O2 reacts with two volumes of CO to form two volumes of CO2. Therefore, for one volume of O2, one volume of CO will be left unreacted. Since only 0.2V of the air is oxygen, the decrease in volume is 0.2V due to CO consumption.

Find the Fractional Decrease in Total Volume

To find the fractional decrease, divide the decrease in volume (0.2V, due to the oxygen reacting) by the initial total volume of the system, which is volume of CO (V) plus volume of air (V), making it 2V. Fractional decrease in volume = (0.2V) / (2V) = 0.1.

Key concepts

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry is pivotal for solving problems where reactants are converted into products. It refers to the quantitative relationship between reactants and products in a chemical reaction, often represented in the form of balanced chemical equations.

In our exercise, the stoichiometric equation is given by 2CO + O2 -> 2CO2. This indicates that two moles of carbon monoxide (CO) react with one mole of oxygen (O2) to produce two moles of carbon dioxide (CO2). To approach problems like these, start by balancing the reaction, ensuring the number of atoms of each element is the same on both sides. Then, use the coefficients to establish molar ratios that help determine how much of one substance reacts or forms from another.

For instance, in the given equation, the ratio of CO to O2 is 2:1, which means that for every two volumes of CO consumed, one volume of O2 is required. A clear grasp of stoichiometry enables students to predict the amounts of reactants used and products formed, which is essential in this exercise to calculate the resultant volume change.

Gas Laws

Gas laws are a set of general principles that describe how gases behave under various conditions of pressure, volume, and temperature. They are the foundation for understanding the physical behavior of gases in chemical reactions and everyday life.

In this scenario, we rely on the assumption that pressure and temperature remain constant, which relates to Boyle's Law (at constant temperature, pressure and volume are inversely proportional) and Charles's Law (at constant pressure, volume is directly proportional to temperature). However, the most directly relevant is Avogadro's law for this exercise, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules.

By applying Avogadro's principle, we can infer that the volume of gas before and after the reaction – when considering ideal behavior – should remain constant if the number of moles of gas does not change. This allows us to initially approach the problem by focusing purely on volume relationships without worrying about pressure and temperature changes.

Volume Relationships in Reactions

Volume relationships in chemical reactions involving gases can be understood through the lens of stoichiometry and Avogadro's law. When dealing with gas reactions at constant temperature and pressure, the volume ratios of the reactants and products are directly proportional to the ratios of their coefficients in the balanced chemical equation.

In our example, the stoichiometry of the balanced equation shows that one volume of O2 reacts with two volumes of CO to yield two volumes of CO2, which initially suggests no overall change in volume. However, since air is only 20% oxygen, the volume of pure oxygen reacting is less than the total volume of air. Following the reaction, the remaining unreacted components of air do not affect the total volume of gas left, resulting in a decrease equivalent to the volume of O2 consumed.

It's crucial to recognize that not all reactions between gases lead to an increase or decrease in volume. Some reactions may retain the same volume despite the number of reactants being different from the number of products, which is dictated by the unique stoichiometric ratios and the types of gases involved.