Question

Challenge All you know about two unknown compounds is that they have the same percent by mass of carbon. With only this information, can you be sure the two compounds are the same? Explain.

Short answer

No, having the same percent by mass of carbon is not enough to be sure that the two compounds are the same. The example of Ethanol (C2H5OH) and Dimethyl Ether (CH3OCH3) demonstrates that different compounds can have the same percent by mass of carbon (52.17% in this case). Hence, more information is needed to determine if the two compounds are the same.

Step-by-step solution

Define percent by mass of carbon for a compound

Percent by mass of carbon in a compound refers to the ratio of the mass of carbon atoms present in the compound when compared to the total mass of the compound. It is expressed as a percentage. Formula to find the percent by mass of carbon in a compound: \[%\text{ by mass of C} = \frac{\text{mass of C atoms}}{\text{total mass of the compound}} \times 100\]

Analyze Example 1: Ethanol (C2H5OH) and Dimethyl Ether (CH3OCH3)

In this example, we will analyze the percent by mass of carbon in two different compounds: Ethanol (C2H5OH) and Dimethyl Ether (CH3OCH3). 1. Ethanol (C2H5OH): - Mass of carbon atoms: \(2 \times 12 = 24\text{g/mol}\) - Total mass of the compound: \(24\text{g/mol (C)} + 6 \times 1\text{g/mol (H)} + 1 \times 16\text{g/mol (O)} = 46\text{g/mol}\) - % by mass of C: \(\frac{24\text{g/mol}}{46\text{g/mol}} \times 100 = 52.17\%\) 2. Dimethyl Ether (CH3OCH3): - Mass of carbon atoms: \(2 \times 12 = 24\text{g/mol}\) - Total mass of the compound: \(24\text{g/mol (C)} + 6 \times 1\text{g/mol (H)} + 1 \times 16\text{g/mol (O)} = 46\text{g/mol}\) - % by mass of C: \(\frac{24\text{g/mol}}{46\text{g/mol}} \times 100 = 52.17\%\) We can see that the percent by mass of carbon is the same for ethanol and dimethyl ether, and yet they are different compounds.

Conclusion

Based on the analysis done in the example, it is evident that two different compounds can have the same percent by mass of carbon. Therefore, we cannot be sure that the two given compounds are the same just based on the same percent by mass of carbon.

Key concepts

Chemical Composition

When discussing chemical composition, we're essentially referring to what a substance is made up of at the atomic or molecular level. This composition can be qualitative, telling us which elements are present, or quantitative, revealing the proportion of each element within the compound.

For example, water (H₂O) has a chemical composition of two hydrogen atoms for every oxygen atom. Knowing the percentage by mass of an element within a compound is a crucial part of understanding its chemical composition. It's like having a recipe for a cake; the ingredients list doesn't just tell you what's in it but also how much of each component you'll need.

Calculating the percent by mass is straightforward, as shown in the exercise solution. The key takeaway is that knowing the percent by mass of carbon, or any other element, gives us vital information about the composition of a compound, but it isn't enough to uniquely identify the compound, as compounds can share the same percentage by mass of an element but have different structures or chemical properties.

Molecular Formula

Diving into molecular formulas, they are the notations used to represent the number and type of atoms present in a molecule of a compound. They provide a direct insight into the chemical composition of the compound. Let's decode this concept with an example.

The molecular formula of Ethanol is C₂H₅OH, indicating that each molecule consists of two carbon atoms, six hydrogen atoms, and one oxygen atom. What's interesting here is the power of molecular formulas to describe the actual number of atoms in one molecule of the substance.

Yet, the key detail to remember is that different compounds can share the same molecular formula or even have the same ratios of elements (as in isomers) but differ in structure. This difference in structure can mean entirely different physical and chemical properties. Therefore, while the molecular formula is a critical component of a compound's identity, it doesn't always give the full picture of a compound’s characteristics.

Stoichiometry

Stoichiometry is all about the math behind chemistry. Think of it as the accountancy of chemistry — it deals with the quantitative relationships that govern the combination of substances as they react to form products.

This branch of chemistry involves using balanced chemical equations to calculate the masses, volumes, and concentrations of reactants and products in a chemical reaction. For instance, the balanced equation for the combustion of Ethanol is: C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O. It tells us that one molecule of Ethanol reacts with three molecules of Oxygen to form two molecules of Carbon Dioxide and three molecules of Water.

Stoichiometry is not only about counting molecules but also fundamentally understanding how compounds interact with one another. It informs us how much product you can expect from certain amounts of reactants, and vice versa. Effectively, if you know the percentages by mass of different elements in the reactants, you can predict the composition of the products formed. However, as demonstrated in the exercise, stoichiometry assumes that reactions go to completion and that you're dealing with pure substances, which isn't always the case in the real-world applications.