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The average mass, in grams, of one mole of carbon atoms is equal to (A) the average mass of a single carbon atom, measured in amus (B) the ratio of the number of carbon atoms to the mass of a single carbon atom (C) the number of carbon atoms in one amu of carbon (D) the mass, in grams, of the most abundant isotope of carbon

Short Answer

Expert verified
The correct answer is (A) the average mass of a single carbon atom, measured in AMU.

Step by step solution

01

Detail on the concept of mole and AMU

In chemistry, a mole is quantity that contains Avogadro's number (6.022 x 10^23) of atoms or molecules. On the other hand, the atomic mass unit (AMU) is a unit of mass used to express atomic and molecular weights, such that the mass of one mole of a substance expressed in grams is numerically equal to the atomic or molecular weight of that substance expressed in atomic mass units (AMU). Hence, for carbon atoms, one mole has a mass of about 12 grams, which is also equivalent to the mass of a single carbon atom, 12 AMU.
02

Analyzing the options

Looking at option A, it says the mass of a mole of carbon atoms is equal to the mass of a single carbon atom in Atomic Mass Units (AMU), which aligns with the above explanation. However, option B doesn't make sense because we don't determine the mass of a mole based on a ratio of number of atoms to the mass of a single atom. Option C is incorrect, because the AMU is defined such that a carbon-12 atom has a mass of exactly 12 amu and a mole of carbon has a mass of about 12 grams, not amu as suggested. Option D is incorrect because the mass of a mole is determined by the number of atoms/molecules in a mole (Avogadro's number), rather than being based on the mass of any particular isotope.
03

Choosing the correct option

From the analysis, the correct answer is option A, because the mass of a mole of carbon atoms is numerically equivalent to the mass of a single carbon atom, when measured in Atomic Mass Units (AMU).

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Key Concepts

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

Understanding Atomic Mass Unit (AMU)
The atomic mass unit (AMU) is a fundamental unit of mass used in the field of chemistry to express atomic and molecular weights. Imagine if you had to weigh individual atoms—these particles are so tiny that ordinary units like grams or kilograms would not be practical. That's where AMU comes into play. It serves as a convenient way to express atomic masses and molecular weights in a much more manageable form.
A single atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom. This makes the value of 1 AMU approximately equal to 1.66 x 10^-24 grams.
  • This definition was chosen based on the carbon-12 isotope because it is a standard, universally agreed upon reference point.
  • An important aspect of the AMU is that it allows scientists to express the masses of different atoms relative to each other, simplifying the work in fields like chemistry and physics.
A carbon atom, for example, has an atomic mass of about 12 AMU. In practical terms, this means that if you have a sample containing one mole of carbon atoms, it will weigh approximately 12 grams. This is due to the numerical equivalence, where the atomic mass in AMU matches the molar mass in grams.
Significance of Avogadro's Number
Avogadro's number is crucial when working in chemistry because it bridges the macroscopic and microscopic worlds. Simply put, it helps scientists count extraordinarily small particles using large, manageable numbers. Avogadro's number, which is 6.022 x 10^23, represents the number of atoms or molecules present in a single mole of a substance.
Picture a mole as a bridge between the atomic scale and the gram scale: this is what Avogadro's number essentially provides.
  • It allows chemists to convert from the microscopic scale of atoms and molecules to the macroscopic world we interact with daily, like grams or liters.
  • For example, if you have one mole of carbon atoms, that is 6.022 x 10^23 individual atoms of carbon.
This number is extraordinarily large because atoms and molecules themselves are extraordinarily small. Thus, Avogadro's number offers a method by which these small particles can be quantified in bulk, making chemistry a practical and scalable science.
An Insight into Carbon Isotopes
Carbon isotopes are variations of the carbon element that have different numbers of neutrons in their nuclei, but the same number of protons. The most prevalent carbon isotope is carbon-12 (C-12), which constitutes 98.9% of naturally occurring carbon.
Carbon-12 has 6 protons and 6 neutrons in its nucleus. Due to its abundance and stability, it was chosen as the standard for assigning the atomic mass unit.
  • Other isotopes of carbon include carbon-13, which has 6 protons and 7 neutrons, and carbon-14, which has 6 protons and 8 neutrons.
  • Carbon isotopes can be used to study various phenomena, from radiocarbon dating in archaeology to tracing the pathways of carbon in metabolic processes.
  • The mass of carbon-12 being precisely 12 AMUs makes it instrumental as a reference in chemistry and helps in calculating the molecular weights of other atoms.
The existence of carbon isotopes highlights the diversity and complexity of elements beyond their basic definitions, offering valuable tools for scientific inquiry across disciplines.

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Most popular questions from this chapter

A stock solution of 0.100 \(\mathrm{M}\) cobalt (II) chloride is used to create several solutions, indicated in the data table below: \(\begin{array}{|c|c|c|}\hline \text { Sample } & {\text { Volume } \mathrm{CoCl}_{2}} & {\text { Volume }} \\ \hline & {(\mathrm{mL})} & {\mathrm{H}_{2} \mathrm{O}(\mathrm{mL})} \\ \hline 1 & {20.00} & {0} \\\ \hline 2 & {15.00} & {5.00} \\ \hline 3 & {10.00} & {10.00} \\ \hline 4 & {5.00} & {15.00} \\ \hline\end{array}\) (a) In order to achieve the degree of accuracy shown in the table above, select which of the following pieces of laboratory equipment could be used when measuring out the CoCl_{2} : \(150-\mathrm{mL}\) beaker \(\quad 400-\mathrm{mL}\) beaker \(\quad 250-\mathrm{mL}\) Erlenmeyer flask \(\begin{array}{ll}{\text { 50-mL buret }} & {\text { 50-mL graduated }} \\ {} & {\text { cylinder }}\end{array} \quad 100\) -mL graduated cylinder (b) Calculate the concentration of the CoCl, in each sample. The solutions are then placed in cuvettes before being inserted into a spectrophotometer calibrated to 560 \(\mathrm{nm}\) and their values are measured, yielding the data below: \(\begin{array}{|c|c|}\hline \text { Sample } & {\text { Absorbance }} \\\ \hline 1 & {0.485} \\ \hline 2 & {0.364} \\ \hline 3 & {0.243} \\ \hline 4 & {0.121} \\ \hline\end{array}\) (c) If gloves are not worn when handling the cuvettes, how might this affect the absorbance values gathered? (d) If the path length of the cuvette is \(1.00 \mathrm{cm},\) what is the molar absorptivity value for \(\mathrm{CoCl}_{2}\) at 560 \(\mathrm{nm}\) ? (e) On the axes on the next page, plot a graph of absorbance vs. concentrrion. The \(y\) -axes scale is set, and be sure to scale the \(x\) -axes appropriately (f) What would the absorbance values be for \(\mathrm{CoCl}_{2}\) , solutions at the following concentrations? (i) 0.067 (ii) 0.180 \(\mathrm{M}\)

Regarding reaction I, how would the addition of a catalyst affect the enthalpy and entropy changes for this reaction? Enthalpy \(\quad\) Entropy (A) Decrease \(\quad\) Decrease (B) Decrease \(\quad\) No Change (C) No Change \(\quad\) Decrease (D) No Change \(\quad\) No Change

Consider the Lewis structures for the following molecules: $$\begin{equation} \mathrm{CO}_{2}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{2}^{-}, \text {and } \mathrm{NO}_{3}^{-} \end{equation}$$ Which molecule would have the shortest bonds? (A) \(\mathrm{CO}_{2}\) (B) \(\mathrm{CO}_{3}^{2-}\) (C) \(\mathrm{NO}_{2}^{-}\) (D) \(\mathrm{NO}_{3}^{-}\)

Most transition metals share a common oxidation state of \(+2 .\) Which of the following best explains why? (A) Transition metals all have a minimum of two unpaired electrons. (B) Transition metals have unstable configurations and are very reactive. (C) Transition metals tend to gain electrons when reacting with other elements. (D) Transition metals will lose their outermost s-block electrons when forming bonds.

Hydrogen fluoride, HF, is a liquid at \(15^{\circ} \mathrm{C}\) . All other hydrogen halides (represented by HX, where \(\mathrm{X}\) is any other halogen) are gases at the same temperature. Why? (A) Fluorine has a very high electronegativity; therefore, the H–F bond is stronger than any other H–X bond. (B) HF is smaller than any other H–X molecule; therefore, it exhibits stronger London dispersion forces. (C) The dipoles in a HF molecule exhibit a particularly strong attraction force to the dipoles in other HF molecules. (D) The H–F bond is the most ionic in character compared to all other hydrogen halides.

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