/*! 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 99 The mass of an organic compound ... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 99

The mass of an organic compound was found to be \(58.07746\) by mass spectrometry. Is the sample \(\mathrm{C}_{4} \mathrm{H}_{10}, \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\), or \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{~N}_{2} ?\) Exact masses of elements are \(1.007825\) \(\left({ }^{1} \mathrm{H}\right) ; 12.00000\left({ }^{12} \mathrm{C}\right) ; 14.003074\left({ }^{14} \mathrm{~N}\right) ;\) and \(15.994915\left({ }^{16} \mathrm{O}\right)\)

Short Answer

Expert verified
The sample is likely C鈧凥鈧佲個, as its calculated mass is closest to the measured value.

Step by step solution

01

Calculate Mass of C鈧凥鈧佲個

For C鈧凥鈧佲個, calculate the molecular mass using the formula: \[ \text{mass} = 4(\text{mass of C}) + 10(\text{mass of H}) \]Substitute the given values: \[ \text{mass} = 4(12.00000) + 10(1.007825) = 48.00000 + 10.07825 = 58.07825 \]
02

Calculate Mass of C鈧僅鈧哋

For C鈧僅鈧哋, calculate the molecular mass using the formula: \[ \text{mass} = 3(\text{mass of C}) + 6(\text{mass of H}) + 1(\text{mass of O}) \]Substitute the given values: \[ \text{mass} = 3(12.00000) + 6(1.007825) + 15.994915 = 36.00000 + 6.04695 + 15.994915 = 58.041865 \]
03

Calculate Mass of C鈧侶鈧哊鈧�

For C鈧侶鈧哊鈧�, calculate the molecular mass using the formula: \[ \text{mass} = 2(\text{mass of C}) + 6(\text{mass of H}) + 2(\text{mass of N}) \]Substitute the given values: \[ \text{mass} = 2(12.00000) + 6(1.007825) + 2(14.003074) = 24.00000 + 6.04695 + 28.006148 = 58.053098 \]
04

Compare Results to Mass Spectrometry

Compare the calculated masses to the mass measured by spectrometry (58.07746). The molecular mass closest to the spectrometry result helps identify the compound. - Mass of C鈧凥鈧佲個: 58.07825 - Mass of C鈧僅鈧哋: 58.041865 - Mass of C鈧侶鈧哊鈧�: 58.053098 From these values, C鈧凥鈧佲個 (58.07825) is the closest to the measured 58.07746.

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Key Concepts

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

Molecular Mass Calculation
Calculating the molecular mass of a compound is about adding up the exact masses of all the atoms within its molecular formula. This process is fundamental in chemistry, allowing researchers to identify unknown substances and verify the purity of known ones. For example, when we have a formula such as \(\text{C}_4\text{H}_{10}\), we need to determine the contribution of each element to the total mass.

Here's how you do it:
  • Find the number of each type of atom in the compound鈥檚 formula. For \(\text{C}_4\text{H}_{10}\), there are 4 carbon atoms and 10 hydrogen atoms.
  • Multiply the number of each type of atom by its exact mass. For carbon (\(C\)), it鈥檚 12.00000, and for hydrogen (\(H\)), it's 1.007825.
  • Add up all these values to get the molecular mass.

    For \(\text{C}_4\text{H}_{10}\), you will calculate: \(4 \times 12.00000 + 10 \times 1.007825\)
    = \(48.00000 + 10.07825 = 58.07825\)
Molecular mass calculations are crucial to many fields of study and industry, ensuring that compounds are correctly identified and used appropriately.
Organic Compounds
Organic compounds are a vital category in chemistry, primarily made up of carbon atoms paired with elements like hydrogen, oxygen, nitrogen, and more. At its core, organic chemistry studies these compounds鈥� structures, properties, compositions, reactions, and preparations.

Consider a few important aspects of organic compounds:
  • Organic compounds are often described by their molecular formulas, like \(\text{C}_3\text{H}_6\text{O}\) or \(\text{C}_2\text{H}_6\text{N}_2\), which indicate the number and types of atoms present.
  • They are predominantly found in living organisms but are also synthesized for various industrial applications. Compounds such as butane (\(\text{C}_4\text{H}_{10}\)), acetone (\(\text{C}_3\text{H}_6\text{O}\)), and hydrazine (\(\text{C}_2\text{H}_6\text{N}_2\)) all serve different roles, from fuel gases to solvents and rocket propellants.
Understanding organic compounds involves recognizing their molecular structures and how these structures affect their interactions with other substances. Knowing their molecular formulas is just the beginning of delving into the rich chemistry of organic compounds.
Exact Mass of Elements
In molecular chemistry, the precise mass of elements within a compound is essential for molecular identification and analysis. The exact mass refers to the true atomic weight of each isotope of an element. It is slightly different from the standard atomic weight found on periodic tables because it accounts for isotopes' presence.

Key points to remember:
  • The exact mass is important for calculations in mass spectrometry, a technique that measures the mass-to-charge ratio of ions to identify the composition of a sample.
  • For hydrogen \((^1\text{H})\), the exact mass is 1.007825; for carbon \((^{12}\text{C})\), it is exactly 12.00000; nitrogen \((^{14}\text{N})\) is 14.003074; and oxygen \((^{16}\text{O})\) is 15.994915.
In calculations, these precise values contribute to achieving accurate and reliable results, which are crucial when identifying compounds鈥� structures or confirming the purity of a sample. The exact mass serves as the foundation upon which more complex analyses can be accurately conducted.

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Most popular questions from this chapter

An alternative method for producing hydriodic acid is the reaction of iodine with hydrogen sulfide: $$ \mathrm{H}_{2} \mathrm{~S}+\mathrm{I}_{2} \longrightarrow 2 \mathrm{HI}+\mathrm{S} $$ (a) How many grams of \(\mathrm{I}_{2}\) are needed to react with \(49.2 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{~S} ?\) (b) How many grams of HI are produced from the reaction of \(95.4 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{~S}\) with excess \(\mathrm{I}_{2} ?\)

What are the empirical formulas of each of the following substances? (a) Ibuprofen, a headache remedy: \(75.69 \% \mathrm{C}, 15.51 \% \mathrm{O}, 8.80 \% \mathrm{H}\) (b) Magnetite, a naturally occurring magnetic mineral: \(72.36 \%\) Fe, \(27.64 \%\) O (c) Zircon, a mineral from which cubic zirconia is made: \(34.91 \%\) \(\mathrm{O}, 15.32 \% \mathrm{Si}, 49.77 \% \mathrm{Zr}\)

Sodium azide \(\left(\mathrm{NaN}_{3}\right)\) yields \(\mathrm{N}_{2}\) gas when heated to \(300{ }^{\circ} \mathrm{C}\), a reaction used in automobile air bags. If \(1.00 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) has a volume of \(47.0 \mathrm{~L}\) under the reaction conditions, how many liters of gas can be formed by heating \(38.5 \mathrm{~g}\) of \(\mathrm{NaN}_{3} ?\) The reaction is $$ 2 \mathrm{NaN}_{3}(s) \longrightarrow 3 \mathrm{~N}_{2}(g)+2 \mathrm{Na}(s) $$

How many grams of the dry-cleaning solvent 1,2 -dichloroethane (also called ethylene chloride), \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\), can be prepared by reaction of \(15.4 \mathrm{~g}\) of ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}\), with \(3.74 \mathrm{~g}\) of \(\mathrm{Cl}_{2}\) ? $$ \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{Cl}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2} $$

An unidentified metal M reacts with an unidentified halogen \(\mathrm{X}\) to form a compound \(\mathrm{MX}_{2}\). When heated, the compound decomposes by the reaction: $$ 2 \mathrm{MX}_{2}(s) \longrightarrow 2 \mathrm{MX}(s)+\mathrm{X}_{2}(g) $$ When \(1.12 \mathrm{~g}\) of \(\mathrm{MX}_{2}\) is heated, \(0.720 \mathrm{~g}\) of \(\mathrm{MX}\) is obtained, along with \(56.0 \mathrm{~mL}\) of \(\mathrm{X}_{2}\) gas. Under the conditions used, \(1.00 \mathrm{~mol}\) of the gas has a volume of \(22.41 \mathrm{~L}\). (a) What is the atomic weight and identity of the halogen \(\mathrm{X} ?\) (b) What is the atomic weight and identity of the metal M?
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