Calculating the Mass of C-12 Atom: Homework Solution and Equations

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In summary, the mass of one mole of Carbon-12 atoms is 12 grams, which is equivalent to Avogadro's constant. This means that each Carbon-12 atom has a mass of 12 grams divided by Avogadro's constant, which is equal to approximately 1.9926935*10^-23 grams. This value is also known as the unified atomic mass unit (u). The reason for using Carbon-12 as the standard isotope is because it is the most abundant isotope of carbon found in nature.
  • #1
Physicsissuef
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Homework Statement



Find the 1/12 of the mass of the atom of [tex]\stackrel{12}{6}C[/tex] in kilograms.

Homework Equations



[tex]n=\frac{m}{M}[/tex]

The Attempt at a Solution



How I will do this? I have the answer [tex]\frac{1}{1000N_A}kg[/tex], but don't know where it come from...
 
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  • #2
I might be looking at this problem the wrong way, or you might want a highly specific answer, forgive me if so.

What is the mass of one mole of Carbon 12 atoms?
How many particles are there in one mole?
If X particles have a mass of Y, what is the mass of one particle?
 
  • #3
In one mole have N (Avogadro's number) particles...

The mass of one mole C-12 atoms is:

probably 1mol=[tex]\frac{m}{M}[/tex]

I don't know exactly what is M ([tex]\stackrel{12}{6}C[/tex])

[tex]\frac{X}{Y}=\frac{1}{Z}[/tex]

[tex]Y=XZ[/tex]
 
  • #4
I have no clue what any of those equations mean. The mass of a mole of C-12 is 12 grams, which is equivalent to Avogadro's constant. Find the mass of one atom from this, and then 1/12 of that atom.
 
  • #5
Can you please tell me what do you mean by the mass of a mole of C-12 is 12 grams, which is equivalent to Avogadro's constant? Can you start so I can continue?
 
  • #6
I can't get any simpler by saying that the mass of one mole of C-12 is 12 grams, and that one mole of a substance has Avogadro's number of atoms in it. If you're not unsure of this, I advise you to read your notes or textbook.
 
  • #7
[tex]1mol* 6.022 x 10^2^3mol^-^1=6.022 x 10^2^3=N[/tex]

[tex]1mol=\frac{m}{12g/mol}[/tex]

[tex]m=12g[/tex]

[tex]\frac{1}{12}*6.022 x 10^2^3[/tex] =number of atoms in 1g of C-12

What to do nexT?
 
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  • #8
If you have a number of particles equal to Avogadro's Constant, the mass of said quantity is equal to the relative molecular/formula/atomic mass in grams. 6.023*10^23 Carbon 12 atoms have a mass of 12 grams. 6.023*10^23 Hydrogen atoms have a mass of 1 gram.

So if you know the mass of Avogadro's Constant carbon-12 atoms, what is the mass of one?
 
  • #9
If 6,022x10^23=number of atoms in 12g of C-12, than in one atom will be

[tex]\frac{6,022*10^23}{12g}=\frac{1}{x}[/tex]
the mass of 1 atom will be [tex]\frac{12g}{6,022*10^2^3}=1,9926935*10^-^2^3[/tex]
right? So to get the unified atomic mass unit, I should divide it by 12, so I get
[tex]1u=\frac{1,9926935*10^-^2^3}{12}=1,6605779*10^-^2^4g=1,6605779*10^-^2^7kg[/tex]

and why they use 1/12 of the mass of one atom of C-12? Why not of N-12 or some other element?

right?
 
  • #10
N-12 doesn't exist. C-12 is common.
 
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  • #11
And how many protons and neutrons, the atom of carbon have? The isotope C-12 have 6 protons and 6 neutrons.
 
  • #12
Right.
 
  • #13
Carbon 14 also exists, which has 2 more neutrons. The identity of each element is defined by the amount of protons in it, so a carbon atom will always have 6 protons.

Carbon-12 is used because Carbon 12 is more abundant compared to its isotopes than other elements.
 
  • #14
but why it is called isotope? Istope is called when there is same number of protons and different number of atomic mass number. Isn't there any "standard" carbon atom?
 
  • #15
Zach Smith said:
Carbon 14 also exists, which has 2 more neutrons. The identity of each element is defined by the amount of protons in it, so a carbon atom will always have 6 protons.

Carbon-12 is used because Carbon 12 is more abundant compared to its isotopes than other elements.

I remember in the pase , both H-1 and O-16 were used to define the "relative" mass of other natural isotopes/atoms
 
  • #16
Physicsissuef said:
but why it is called isotope? Istope is called when there is same number of protons and different number of atomic mass number. Isn't there any "standard" carbon atom?

No, all of the carbon found in nature are isotopes of each other. You can't really call anyone of them 'standard' because they all exist. You can call one of them the most common.
 

1. How do you calculate the mass of a C-12 atom?

The mass of a C-12 atom can be calculated using the equation: m = (A)(u), where m is the mass of the atom, A is the atomic mass number (which is 12 for carbon-12), and u is the atomic mass unit (which is approximately equal to the mass of a proton or neutron).

2. What is the atomic mass of C-12?

The atomic mass of C-12 is 12 atomic mass units (u). This is the mass of one atom of carbon-12 in its neutral state.

3. Why is the mass of a C-12 atom important to calculate?

The mass of a C-12 atom is important because it is used as the standard for measuring the masses of other atoms and molecules. It is also essential for determining the molar mass of a substance, which is necessary for many chemical calculations.

4. Can you provide an example of calculating the mass of a C-12 atom?

Yes, for example, if we want to calculate the mass of 3 moles of carbon-12, the equation would be: m = (3 mol)(12 u/mol) = 36 u. This means that 3 moles of carbon-12 would have a mass of 36 atomic mass units.

5. Are there any other methods for calculating the mass of a C-12 atom?

Yes, another method is using the Avogadro's constant (6.022 x 10^23) and the molar mass of C-12 (12 g/mol) to calculate the mass of one mole of carbon-12 atoms, which is equal to 12 grams. This can then be converted to atomic mass units (1 g = 6.022 x 10^23 u).

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