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Chapter 3: Problem 91

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 \(\mathrm{O}\). Its molar mass is \(176 \mathrm{~g} / \mathrm{mol}\). Determine its molecular formula.

Short Answer

Expert verified
The molecular formula for serotonin is \(C_{10}H_{12}N_{2}O\).

Step by step solution

01

Calculate Moles of Each Element

Given the mass percentages and assuming a 100g sample, we can calculate the mass of each element in the sample. Then, we'll use their molar masses to convert these values to moles: For Carbon (C): Mass of C = 68.2 g Molar Mass of C = 12.01 g/mol Moles of C = (Mass of C)/(Molar Mass of C) = 68.2/12.01 For Hydrogen (H): Mass of H = 6.86 g Molar Mass of H = 1.008 g/mol Moles of H = (Mass of H)/(Molar Mass of H) = 6.86/1.008 For Nitrogen (N): Mass of N = 15.9 g Molar Mass of N = 14.01 g/mol Moles of N = (Mass of N)/(Molar Mass of N) = 15.9/14.01 For Oxygen (O): Mass of O = 9.08 g Molar Mass of O = 16.00 g/mol Moles of O = (Mass of O)/(Molar Mass of O) = 9.08/16.00
02

Find the Simplest Ratio

Next, we'll find the simplest whole-number ratio of the moles. To do this, divide all the calculated moles by the smallest number of moles: moles of C: 68.2/12.01 = 5.68 moles of H: 6.86/1.008 = 6.81 moles of N: 15.9/14.01 = 1.14 moles of O: 9.08/16.00 = 0.568 Divide each mole value by 0.568 (the smallest value) to get the simplest ratio: moles of C: 5.68/0.568 = 10.0 moles of H: 6.81/0.568 = 12.0 moles of N: 1.14/0.568 = 2.00 moles of O: 1.00 The simplest whole-number ratio is C: 10, H: 12, N: 2, O: 1.
03

Calculate the Empirical Formula Molar Mass

Now we will calculate the molar mass of the empirical formula (simplest whole-number ratio): Empirical formula molar mass (EFMM) = (Moles of C)(Molar Mass of C) + (Moles of H)(Molar Mass of H) + (Moles of N)(Molar Mass of N) + (Moles of O)(Molar Mass of O) EFMM = (10)(12.01) + (12)(1.008) + (2)(14.01) + (1)(16.00)
04

Determine the Molecular Formula

To get the molecular formula, we'll divide the given molar mass by the empirical formula molar mass and multiply the whole-number ratio of elements by this factor: Molecular formula multiplier = (Given molar mass)/(Empirical formula molar mass) Molecular formula multiplier = 176/EFMM Multiply the empirical formula by the molecular formula multiplier: C: (10)(molecular formula multiplier) H: (12)(molecular formula multiplier) N: (2)(molecular formula multiplier) O: (1)(molecular formula multiplier) Calculating the values and rounding to the nearest whole number, we'll get the molecular formula for serotonin.

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Most popular questions from this chapter

Determine the formula weights of each of the following com- pounds: (a) nitric acid, \(\mathrm{HNO}_{3} ;\) (b) \(\mathrm{KMnO}_{4} ;\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} ;\) (d) quartz, \(\mathrm{SiO}_{2} ;\) (e) gallium sulfide, (f) chromium(III) sulfate, (g) phosphorus trichloride.

The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), the main component of gasoline, proceeds as follows: \(2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g)\) (a) How many moles of \(\mathrm{O}_{2}\) are needed to burn \(1.50 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18} ?\) (b) How many grams of \(\mathrm{O}_{2}\) are needed to burn \(10.0 \mathrm{~g}\) of \(\mathrm{C}_{8} \mathrm{H}_{18} ?\) (c) Octane has a density of \(0.692 \mathrm{~g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). How many grams of \(\mathrm{O}_{2}\) are required to burn \(15.0 \mathrm{gal}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) (the capacity of an average fuel tank)? (d) How many grams of \(\mathrm{CO}_{2}\) are produced when 15.0 gal of \(\mathrm{C}_{8} \mathrm{H}_{18}\) are combusted?

A bottling plant has 126,515 bottles with a capacity of \(355 \mathrm{~mL}\), 108,500 caps, and \(48,775 \mathrm{~L}\) of beverage. (a) How many bottles can be filled and capped? (b) How much of each item is left over? (c) Which component limits the production?

(a) What is the mass, in grams, of \(1.223 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{\circ}\) ) if 0.05570 mol has a mass of \(15.86 \mathrm{~g}\) ?

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{PbCO}_{3}(s) \longrightarrow \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)\) (d) \(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (e) \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\)
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