Question

Which law would you use to compare \(CO\) and \(CO_{2} ?\) Explain. Without doing any calculations, determine which of the two compounds has the highest percent by mass of oxygen in the compound.

Short answer

We would use the Law of Definite Proportions to compare CO and CO₂. Observing their fixed ratios of 1 Carbon atom to 1 Oxygen atom (1:1) in CO and 1 Carbon atom to 2 Oxygen atoms (1:2) in CO₂, we can conclude that CO₂ has the highest percent by mass of oxygen in the compound without performing any calculations.

Step-by-step solution

Identify the Law

In this case, we need to use the Law of Definite Proportions (also known as Proust's law). This law states that in a pure chemical compound, the proportions of its constituent elements are always in a fixed ratio by mass, regardless of the source of the compound or the method of preparation.

Applying the Law of Definite Proportions

To apply the Law of Definite Proportions to our problem, we need to find the fixed ratio of the elements in the given compounds, CO and CO₂. For CO: the fixed ratio is 1 Carbon atom to 1 Oxygen atom (1:1) For CO₂: the fixed ratio is 1 Carbon atom to 2 Oxygen atoms (1:2)

Comparing the Percent by Mass of Oxygen

Since we are not allowed to perform any calculations, we can still compare the percent by mass of oxygen in these compounds by observing their fixed ratios. In CO, there is 1 Oxygen atom for every 1 Carbon atom, while in CO₂, there are 2 Oxygen atoms for every 1 Carbon atom. Oxygen atoms have the same mass in both compounds, but there are more Oxygen atoms in CO₂ than in CO. Therefore, without doing any calculations, we can conclude that the compound CO₂ has the highest percent by mass of oxygen in the compound compared to CO.

Key concepts

Percent by Mass

The concept of percent by mass is a valuable way to describe how much of a substance is present in a chemical compound. It tells us how much of the compound's total mass is made up of a particular element. To calculate the percent by mass of an element in a compound, you divide the total mass of the element by the total mass of the compound and multiply by 100. For example, if a compound has 10 grams of oxygen in a total compound mass of 50 grams, then the percent by mass of oxygen is \[ (\frac{10}{50} \times 100) = 20\% \].
When comparing two compounds like carbon monoxide \(CO\) and carbon dioxide \(CO_2\), understanding the fixed ratios of their elements helps us infer their percent by mass. Since \(CO_2\) contains more oxygen atoms than \(CO\), it suggests \(CO_2\) has a higher percent by mass of oxygen. No calculations needed here; just understanding the ratio does the trick. This makes it an insightful way to understand compound compositions without diving into complex math.

Chemical Compounds

Chemical compounds are pure substances that consist of two or more elements that are chemically bonded together. These substances have definite compositions, meaning the ratio of the different elements in them is fixed by mass. This ensures they follow the Law of Definite Proportions, which states that a chemical compound will always have the same proportion of elements by mass, regardless of the sample size or the source of the compound.
Consider water \(H_2O\), a simple yet vital chemical compound. It is made of hydrogen and oxygen in a fixed ratio of 2:1 by atoms. This fixed ratio ensures that the masses of the elements in water are constant throughout any sample. Similarly, carbon monoxide \(CO\) and carbon dioxide \(CO_2\) are both made of carbon and oxygen, yet they follow distinct fixed ratios which define unique properties and behaviors for each compound.

Element Ratios

Element ratios are pivotal in understanding the composition of chemical compounds. These ratios indicate the number of atoms of each element in a compound. For instance, the chemical formula \(CO\) tells us there is one carbon atom for every oxygen atom, representing a 1:1 ratio. On the other hand, \(CO_2\) shows a 1:2 ratio, depicting two oxygen atoms for every carbon atom.
Element ratios are foundational in applying the Law of Definite Proportions. They help chemists predict properties and behaviors of compounds, such as reactivity, stability, and even the percent by mass of elements without needing extensive analysis. By understanding these ratios, we're able to make informed guesses about a compound's nature, such as CO₂ having more oxygen by percent mass than CO, just by noting there are twice as many oxygen atoms relative to carbon in CO₂. This understanding illuminates why the ratios in chemical formulas are so important.