Calculate the mass in grams of one mole of each of the...

Calculate the mass in grams of one mole of each of the following (the mass of a single item is given in parentheses): electrons $\left(9.10938 \times 10^{-28} \mathrm{~g}\right),$ protons $\left(1.67262 \times 10^{-24} \mathrm{~g}\right),$ neutrons $\left(1.67493 \times 10^{-24} \mathrm{~g}\right),$ atoms of carbon- $12\left(1.992646 \times 10^{-23} \mathrm{~g}\right)$ and doughnuts $(74 \mathrm{~g})$. Compare the mass of one mole of carbon-12 atoms to the sum of the masses of the particles that it contains. If the doughnut mentioned in this question were made entirely of carbon, how many atoms would it contain?

Calculate the mass in grams of one mole of each of the following (the mass of a single item is given in parentheses): electrons $\left(9.10938 \times 10^{-28} \mathrm{~g}\right),$ protons $\left(1.67262 \times 10^{-24} \mathrm{~g}\right),$ neutrons
$\left(1.67493 \times 10^{-24} \mathrm{~g}\right),$ atoms of carbon- $12\left(1.992646 \times 10^{-23} \mathrm{~g}\right)$
and doughnuts $(74 \mathrm{~g})$. Compare the mass of one mole of carbon-12 atoms to the sum of the masses of the particles that it contains. If the doughnut mentioned in this question were made entirely of carbon, how many atoms would it contain?

Key Concepts

Mass Defect and Binding Energy

The mass defect refers to the difference between the sum of the masses of the individual particles (protons, neutrons, and electrons) and the actual measured mass of an atom. This discrepancy is due to the binding energy that holds the nucleus together, as described by Einstein’s equation E=mc^2, highlighting how energy and mass are interrelated in nuclear physics.

Avogadro's Number

Avogadro's Number, approximately 6.022×10^23, is the fundamental constant that defines the number of units (atoms, molecules, or particles) in one mole of a substance. It is used to convert the mass of a single particle to the molar mass by multiplying the single particle mass by Avogadro’s number, thereby bridging microscopic and macroscopic scales in chemistry.

Mole Concept and Molar Mass

The mole is a standard SI unit for amount of substance, and the molar mass is the mass of one mole of a substance. For atoms, the molar mass is typically given in grams per mole. By using the number of particles in a mole together with the mass of an individual particle, one can calculate the overall mass, which is pivotal in stoichiometric calculations in chemical reactions.

Subatomic Particle Mass

Subatomic particle mass involves the masses of electrons, protons, and neutrons, which are the building blocks of atoms. Understanding their individual masses is crucial for computing the total mass of complex particles like atoms, as well as for analyzing the contributions of each component in the overall structure of matter.

Unit Conversion and Dimensional Analysis

Unit conversion and dimensional analysis involve techniques to ensure that measurements are expressed in consistent units, facilitating accurate calculations. In the context of converting the mass of a single particle to a mole’s mass, it ensures that the multiplication by Avogadro’s number correctly translates mass units (such as from grams per particle to grams per mole) while preserving the mathematical integrity of the calculation.

Transcript

00:05 This item asks us to find the mass of one mole of some subatomic particles, an atom, and some donuts.

00:14 So if we are going to find the mass of a mole of electrons, we need to know the mass of one electron as 9 .10938 times 10 to the negative 28 grams for one electron.

00:33 And then take that times 6 .022 times 10 to the 2030 electrons for one mole of electrons, and that gives us an amount of 5 .486 times 10 to the negative 4th grams for one mole of electrons.

00:52 For protons, we know that the mass of one proton is 1 .67262 times 10 to the negative 24th grams for one proton.

01:03 Take that times avogadro's number of protons for every one mole of protons.

01:11 And that actually gives us something that we could measure, 1 .007 grams for every mole of protons.

01:19 For neutrons, they're just a little bit more massive than the protons.

01:24 1 .67493 times 10 to the negative 24th grams for every one mole of, or for every one neutron.

01:33 And then take a whole mole of those, and that gives us 1 .008 grams for a mole of neutrons.

01:44 So let's actually try an actual atom.

01:51 So a carbon 12 has an individual mass for one atom of 1 .99 -264 -6 times 10 to the negative 23rd grams for one atom of carbon 12.

02:09 And this is kind of how avogadro's number got to find.

02:13 And so hopefully this comes out to get us right back to our 12 grams.

02:19 So if we take 6 .02 times 10 to the 23rd atoms for one mole of carbon 12, sure enough, that gives us 12 moles per gram.

02:28 12 moles for one gram.

02:31 All right.

02:33 Then it goes on...

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