/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 49 The molar mass of caffeine is \(... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 49

The molar mass of caffeine is \(194.19 \mathrm{~g}\). Is the molecular formula of caffeine \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\) or \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\)

Short Answer

Expert verified
The molecular formula for caffeine is \(C_{8}H_{10}N_{4}O_{2}\)

Step by step solution

01

Find the molar mass for each element of the first formula

For the first formula \(C_{4}H_{5}N_{2}O\), we can calculate the molar mass as follow: 4 * mass of Carbon (C) + 5 * mass of Hydrogen (H) + 2 * mass of Nitrogen (N) + 1 * mass of Oxygen (O) = 4 * 12.01g/mol + 5 * 1.01g/mol + 2 * 14.01g/mol + 1 * 16.00g/mol = 48.04g/mol + 5.05g/mol + 28.02g/mol + 16.00g/mol = 97.11 g/mol.
02

Find the molar mass for each element of the second formula

For the second formula \(C_{8}H_{10}N_{4}O_{2}\), we can calculate the molar mass as follow: 8 * mass of Carbon (C) + 10 * mass of Hydrogen (H) + 4 * mass of Nitrogen (N) + 2 * mass of Oxygen (O) = 8 * 12.01g/mol + 10 * 1.01g/mol + 4 * 14.01g/mol + 2 * 16.00g/mol = 96.08g/mol + 10.1g/mol + 56.04g/mol + 32.00g/mol = 194.22 g/mol.
03

Compare to the Given Molar Mass

Comparing the computed molar masses of the given formulas to the given molar mass of caffeine \(194.19 g/mol\), we see that the molar mass of the second formula \(C_{8}H_{10}N_{4}O_{2}\) closely matches the given molar mass.

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Key Concepts

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

Molar Mass Calculation
Calculating the molar mass of a compound is a key concept when trying to determine its molecular formula. This involves summing up the molar masses of all atoms present within a molecule of the compound. For example, let's determine the molar mass for the empirical formula \(C_4H_5N_2O\):
  • Carbon: 4 atoms \(\times\) 12.01 g/mol = 48.04 g/mol
  • Hydrogen: 5 atoms \(\times\) 1.01 g/mol = 5.05 g/mol
  • Nitrogen: 2 atoms \(\times\) 14.01 g/mol = 28.02 g/mol
  • Oxygen: 1 atom \(\times\) 16.00 g/mol = 16.00 g/mol
Summing these values gives a total molar mass of 97.11 g/mol for \(C_4H_5N_2O\).
Next, if we perform a similar calculation for the formula \(C_8H_{10}N_4O_2\), we get:
  • Carbon: 8 atoms \(\times\) 12.01 g/mol = 96.08 g/mol
  • Hydrogen: 10 atoms \(\times\) 1.01 g/mol = 10.1 g/mol
  • Nitrogen: 4 atoms \(\times\) 14.01 g/mol = 56.04 g/mol
  • Oxygen: 2 atoms \(\times\) 16.00 g/mol = 32.00 g/mol
The sum here is 194.22 g/mol, which very closely matches the given molar mass of caffeine (194.19 g/mol). This indicates that the molecular formula is more likely to be \(C_8H_{10}N_4O_2\).
Caffeine Molecular Structure
Caffeine has an intricate molecular structure that is crucial to understanding its properties and functions. Its chemical structure is represented as \(C_8H_{10}N_4O_2\). This formula provides us with essential information about the arrangement of different atoms within a caffeine molecule. Caffeine belongs to a class of compounds known as alkaloids, which often contain nitrogen and are found in plants.
The structure can be broken down as follows:
  • 8 Carbon atoms form the backbone of the molecule, creating a framework that supports other atoms.
  • 10 Hydrogen atoms are distributed throughout, potentially influencing the molecule's interactions with water and other substances.
  • 4 Nitrogen atoms contribute to caffeine鈥檚 unique chemical properties, including its basicity and ability to interact with biological molecules like DNA.
  • 2 Oxygen atoms play a role in defining the molecule鈥檚 reactivity and solubility characteristics.
The unique arrangement and the specific count of atoms allow caffeine to perform its stimulating effects by acting on the central nervous system.
Elemental Composition Analysis
Elemental composition analysis can be a powerful tool in validating the empirical or molecular formula of a compound, such as caffeine. This analysis revolves around identifying and quantifying the constituent elements within a molecule.
To break this down, the elemental composition of caffeine as \(C_8H_{10}N_4O_2\) comprises carbon, hydrogen, nitrogen, and oxygen:
  • Carbon (C\(_8\)) makes up a sizable portion of the mass, reflecting its role in building the molecular framework.
  • Hydrogen (H\(_{10}\)), while lighter, occurs in larger numbers, affecting molecular weight and geometry.
  • Nitrogen (N\(_4\)) is crucial for defining the compound as an amine, often found in biological contexts.
  • Oxygen (O\(_2\)) is significant due to its electronegativity, contributing to hydrogen bonding and solubility.
By analyzing the proportion and presence of each type of atom, chemists can either confirm the proposed molecular formula or make necessary adjustments. Accurate mass spectrometry or combustion analysis can offer detailed insight, ensuring formulas reflect real molecular structures correctly.

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Most popular questions from this chapter

A compound made up of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{Cl}\) contains 55.0 percent \(\mathrm{Cl}\) by mass. If \(9.00 \mathrm{~g}\) of the compound contain \(4.19 \times 10^{23} \mathrm{H}\) atoms, what is the empirical formula of the compound?

Lysine, an essential amino acid in the human body, contains \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{N} .\) In one experiment, the complete combustion of \(2.175 \mathrm{~g}\) of lysine gave \(3.94 \mathrm{~g}\) \(\mathrm{CO}_{2}\) and \(1.89 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} .\) In a separate experiment, \(1.873 \mathrm{~g}\) of lysine gave \(0.436 \mathrm{~g} \mathrm{NH}_{3}\). (a) Calculate the empirical formula of lysine. (b) The approximate molar mass of lysine is \(150 \mathrm{~g}\). What is the molecular formula of the compound?

Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) can be prepared by heating \(\mathrm{Si}\) in chlorine gas:$$\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(l)$$In one reaction, 0.507 mole of \(\mathrm{SiCl}_{4}\) is produced. How many moles of molecular chlorine were used in the reaction?

A sample of a compound of \(\mathrm{Cl}\) and \(\mathrm{O}\) reacts with an excess of \(\mathrm{H}_{2}\) to give \(0.233 \mathrm{~g}\) of \(\mathrm{HCl}\) and \(0.403 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of the \(\mathrm{com}-\) pound.

The explosive nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) has also been used as a drug to treat heart patients to relieve pain (angina pectoris). We now know that nitroglycerin produces nitric oxide (NO), which causes muscles to relax and allows the arteries to dilate. If each nitroglycerin molecule releases one NO per atom of \(\mathrm{N},\) calculate the mass percent of NO available from nitroglycerin.
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