How Many Electrons Are in Aluminum Spheres?

[sckeen1988]

Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters.

How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 grams per mole, and its atomic number is 13.)

The attempt at a solution
I said that there are 6.02*10^23 atoms in a mole, and noted that after converting the mass into grams each sphere has .9265 moles. If the Aluminum spheres are uncharged there are 13 electrons per atom. I multiplied all three together to get 7.25*10^24 total electrons, but this comes up as the wrong answer.

Any guidance as to what I'm doing wrong will be highly appreciated, thanks

 

[Dickfore]

What's the right answer?

 

[sckeen1988]

It was on a mastering physics quiz, viewing the right answer was blocked.

 

[Dickfore]

So, how are you supposed to enter your answer?

 

[asteriatic]

!

Your approach is correct, but there is a small error in your calculation. The mass of each sphere is 0.0250 kilograms, which is equivalent to 25 grams. So, the number of moles in each sphere is 25/26.982 = 0.9265 moles, as you correctly calculated. However, when you multiplied this by 6.02*10^23 atoms per mole, you should get 5.57*10^23 atoms, not 7.25*10^24. This means that each sphere contains 13*5.57*10^23 = 7.24*10^24 electrons. Therefore, the correct answer is that each sphere contains approximately 7.24*10^24 electrons.

 

[asteriatic]

.Your approach is correct, but there are a few things to consider in your calculation.

Firstly, the atomic mass of aluminum is given in grams per mole, not kilograms per mole. So when you convert the mass of the spheres from kilograms to grams, you need to divide by 1000. This will give you a mass of 25 grams for each sphere, and 0.05 moles.

Secondly, you need to multiply the number of moles by Avogadro's number, 6.02 x 10^23, to get the total number of atoms. So for each sphere, there are 3.01 x 10^22 atoms.

Finally, as you mentioned, each aluminum atom has 13 electrons. So for each sphere, there are 3.91 x 10^23 electrons.

Therefore, for two spheres, there are a total of 7.82 x 10^23 electrons. This is slightly different from your calculated answer, which may have been due to rounding errors.

I hope this helps clarify your calculation. Keep up the good work in your scientific endeavors!