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Chapter 3: Problem 86

Serotonin is a compound that conducts nerve impulses in the brain. It contains \(68.2\) mass percent \(C\), \(6.86\) mass percent \(\mathrm{H}, 15.9\) mass percent \(\mathrm{N}\), and \(9.08\) mass percent O. Its molar mass is \(176 \mathrm{~g} / \mathrm{mol}\). Determine its molecular formula.

Short Answer

Expert verified
The molecular formula of serotonin is C10H12N2O.

Step by step solution

01

Find the moles of each element

By assuming a 100 g sample, we can use the mass percentages to calculate the mass of each element in the sample. Then, we'll divide the mass of each element by its molar mass to find the number of moles. For Carbon (C): mass = 68.2 g (mass percent = 68.2%) moles of C = mass / molar mass = 68.2 g / (12.01 g/mol) = 5.68 mol For Hydrogen (H): mass = 6.86 g (mass percent = 6.86%) moles of H = mass / molar mass = 6.86 g / (1.01 g/mol) = 6.79 mol For Nitrogen (N): mass = 15.9 g (mass percent = 15.9%) moles of N = mass / molar mass = 15.9 g / (14.01 g/mol) = 1.13 mol For Oxygen (O): mass = 9.08 g (mass percent = 9.08%) moles of O = mass / molar mass = 9.08 g / (16.00 g/mol) = 0.568 mol
02

Find the lowest mole ratio

Now, we'll divide all the calculated moles by the smallest mole value to find the ratio of the elements in the molecule. The lowest mole value is 0.568 (for Oxygen). Ratio of C = 5.68 / 0.568 = 10.00 (approximately) Ratio of H = 6.79 / 0.568 = 11.96 (approximately 12) Ratio of N = 1.13 / 0.568 = 1.99 (approximately 2) Ratio of O = 0.568 / 0.568 = 1.00 (approximately 1)
03

Determine the molecular formula

Based on the simplified ratios from Step 2, the molecular formula of serotonin is: C10H12N2O1 or C10H12N2O So, the molecular formula of serotonin is C10H12N2O.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Serotonin: A Brief Introduction
Serotonin is a key neurotransmitter in the brain. It helps transmit messages between nerve cells. It plays a significant role in mood, emotion, and overall brain function. Additionally, serotonin impacts sleep patterns, appetite, and digestion. When we understand serotonin at a chemical level, it assists us in comprehending its role in neurobiology. Knowing the exact makeup of serotonin can aid in the development of medications and treatments for various disorders related to serotonin levels. This makes the study of its molecular formula crucial.
Understanding Mass Percent Composition
Mass percent composition tells us how much of each element makes up a compound. It is expressed as a percentage of each element's mass relative to the total mass of the compound. To find it, take the mass of the element in one mole, divide it by the molar mass of the entire compound, and multiply by 100. For serotonin, the given mass percentages are:
  • Carbon ( C ercentage): 68.2%
  • Hydrogen ( H ercentage): 6.86%
  • Nitrogen ( N ercentage): 15.9%
  • Oxygen ( O ercentage): 9.08%
These values provide insight into the proportion of each element within serotonin, ultimately helping us identify its empirical formula.
Steps for Empirical Formula Calculation
The empirical formula represents the simplest whole-number ratio of elements in a compound. To find it:
  • Assume a 100 g sample of the compound, making calculations straightforward, as each percentage is equal to the mass in grams.
  • Convert these masses to moles by dividing each by its respective atomic molar mass.
  • From our example: Carbon (C): 68.2 g = 5.68 mol, Hydrogen (H): 6.86 g = 6.79 mol, Nitrogen (N): 15.9 g = 1.13 mol, and Oxygen (O): 9.08 g = 0.568 mol.
  • Divide each mole value by the smallest number obtained (0.568), giving us a ratio.
  • The simplest ratio forms the empirical formula: C 10H12N2O.
This empirical formula provides the backbone for deriving the molecular formula.
Molar Mass and its Application in Molecular Formulas
Molar mass is the mass of one mole of a substance. Measured in grams per mole (g/mol), it is derived by summing the atomic masses of all atoms in a molecule. For serotonin, the molar mass provided is 176 g/mol. Knowing the molar mass allows us to determine the molecular formula from the empirical formula. To do this:
  • Calculate the empirical formula mass by adding the atomic masses based on the empirical formula ( C 10H12N2O).
  • The empirical formula mass for serotonin is: (10 × 12.01 for C) + (12 × 1.01 for H) + (2 × 14.01 for N) + (16.00 for O) = 176 g/mol, which matches the molecular molar mass.
  • The empirical and molecular formulas are the same, since their masses coincide: C 10H12N2O.
This showcases the link between empirical formulas, molar mass, and molecular formulas, highlighting their importance in chemistry.

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Most popular questions from this chapter

Determine the formula weights of each of the following compounds: (a) nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\), known as laughing gas and used as an anesthetic in dentistry; (b) benzoic acid, \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\), a substance used as a food preservative; (c) \(\mathrm{Mg}(\mathrm{OH})_{2}\), the active ingredient in milk of magnesia; (d) urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\), a compound used as a nitrogen fertilizer; (e) isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\), responsible for the odor of bananas.

(a) When the metallic element sodium combines with the nonmetallic element bromine, \(\mathrm{Br}_{2}(l)\), how can you determine the chemical formula of the product? How do you know whether the product is a solid, liquid, or gas at room temperature? Write the balanced chemical equation for the reaction. (b) When a hydrocarbon burns in air, what reactant besides the hydrocarbon is involved in the reaction? What products are formed? Write a balanced chemical equation for the combustion of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\), in air.

Balance the following equations: (a) \(\mathrm{L}_{\mathrm{L}(s)}+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Li}_{3} \mathrm{~N}(s)\) (b) \(\mathrm{La}_{2} \mathrm{O}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{La}(\mathrm{OH})_{3}(a q)\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{Ca}_{3} \mathrm{P}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{PH}_{3}(g)\) (e) \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q)\) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (f) \(\mathrm{AgNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \overrightarrow{\mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+\mathrm{NaNO}_{3}(a q)}\) (g) \(\mathrm{CH}_{3} \mathrm{NH}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \longrightarrow\) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)\)

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, which are principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%)\). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NOx" gases. In 2004, the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{\mathrm{x}}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane, and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of 500 grams of octane.

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\), \(8.80 \% \mathrm{H}\), and \(15.51 \%\) O by mass, and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H}\), and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\). (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \% \mathrm{C}, 7.1 \% \mathrm{H}, 26.2 \% \mathrm{O}\), and \(7.7 \% \mathrm{~N}\) by mass; its \(\mathrm{MW}\) is about \(180 \mathrm{amu}\).
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