Question

The hallucinogenic drug LSD has the molecular formula \(\mathrm{C}_{20} \mathrm{H}_{25} \mathrm{~N}_{3} \mathrm{O} .\) One suspected sample contained \(74.07 \% \mathrm{C},\) \(7.95 \% \mathrm{H},\) and \(9.99 \% \mathrm{~N}\) (a) What is the percentage of \(\mathrm{O}\) in the sample? (b) Are these data consistent for \(L S D ?\)

Short answer

The percentage of \text{O} in the sample is 8.99\text{%}. The data are consistent for LSD because the percentages of C, H, N, and O closely match the expected percentages derived from the molecular formula of LSD.

Step-by-step solution

Calculate the percentage of oxygen

To find the percentage of oxygen in the sample, add the given percentages of carbon, hydrogen, and nitrogen, and subtract this sum from 100%.

Compare the theoretical and experimental percentages

Check the consistency of the data by comparing the calculated percentage of oxygen with the theoretical percentage of oxygen in the molecular formula of LSD.

Analysis of the results

Determine if the calculated percentages of the elements in the sample match closely enough with the percentages that would be expected from the molecular formula of LSD.

Key concepts

Molecular Formula

Understanding the molecular formula of a substance is crucial for analyzing its chemical composition. A molecular formula indicates the type and number of atoms in a single molecule of a compound. For example, the molecular formula for LSD is \(\mathrm{C}_{20}\mathrm{H}_{25} \mathrm{N}_{3} \mathrm{O}\). Each letter represents a different element from the periodic table: carbon (C), hydrogen (H), nitrogen (N), and oxygen (O). The numbers, called subscripts, show how many atoms of each element are present in a molecule of the compound.

For educational purposes, let's simplify: visualize the molecular formula as the 'recipe' for a molecule. Just as a recipe dictates the exact amount of each ingredient needed to bake a cake, the molecular formula tells us how many atoms of each element are needed to form a molecule of a specific compound. By knowing the formula, scientists and students can delve deeper into the compound's properties and reactions.

Percent Composition by Mass

Percent composition by mass refers to the percentage ratio of each element's mass to the total mass of the compound. To calculate this for a particular element, use the formula: \[ \text{Percent Composition} = \frac{\text{Mass of element in one mole of the compound}}{\text{Mass of one mole of the compound}} \times 100\% \]

As an illustration, consider a cake you're making, where you're interested in knowing what percentage of the cake's weight comes from sugar. If you have the weight of sugar used and the total cake weight, you could find the sugar's percent composition. Similarly, chemists calculate the mass percentages of elements in compounds to understand their makeup and to help identify substances based on experimental data, which links directly to stoichiometry and the chemical's identity. This concept is foundational in exercises such as the one analyzing LSD's composition.

Hallucinogenic Drugs Chemistry

Hallucinogenic drugs like LSD work by affecting the neurotransmitter systems in the brain, leading to profound changes in perception, mood, and thought. The chemistry behind these drugs is fascinating and complex, involving interaction with specific receptors in the brain. The molecular structure, which can be represented by the molecular formula, plays a significant role in the drug's effects and potency.

To further simplify, think of a lock and key, where the hallucinogenic drug is the key, and the receptor in your brain is the lock. The molecular formula tells us the shape of the key, which needs to precisely fit the lock to unleash the drug's effects. This is why understanding the molecular formula and the correct composition of a hallucinogenic drug is not only crucial for pharmacology but also for ensuring safe and controlled use.

Stoichiometry

Stoichiometry is essentially the math behind chemistry, dealing with the quantitative relationships that govern the mixing of elements and compounds in chemical reactions. It uses the mole concept, molar masses, and balanced chemical equations to calculate the amounts of reactants and products involved in a chemical reaction.

Imagine you're a chef trying to scale a recipe, you'll need to know precisely how much of each ingredient to use to keep the flavors balanced. In a similar sense, stoichiometry helps chemists balance chemical recipes, ensuring that atoms are neither wasted nor left over. A good understanding of stoichiometry is necessary when comparing theoretical data and experimental data, like analyzing whether the suspected LSD sample's composition matches its known molecular formula.