# How do I convert  9.0x10^23 atoms of barium to grams? Also, How do the opposite? (Meaning grams to atoms) I am having trouble understanding my teacher while he is doing the problems and no matter...

How do I convert  9.0x10^23 atoms of barium to grams?

Also, How do the opposite? (Meaning grams to atoms)

I am having trouble understanding my teacher while he is doing the problems and no matter how many times I ask for help, he just doesn't seem to help me understand it more clearly.

llltkl | Student

Assembly of a huge number of microscopic or subatomic particles like atoms, molecules, ions, electrons etc. constitute macroscopic objects that we see in our surroundings.  Dealing with and referencing such huge numbers every time one talk about these particles is quite inconvenient. That is the reason a large quantity, 6.02214 × 10˄23, called the Avogadro’s number, has been accepted as unit in atomic (or subatomic) scale for describing the amount of substance. This unit of substance is called a mole.In other words, 1 mole of molecules has a mass equal to the molecular mass (or atomic mass) in grams.

For Barium, the atomic mass is 137.33. That means 137.33 grams of barium contains 6.02214 × 10˄23 number of barium atoms. So, 9.0 x 10^23 number of atoms of barium would weigh `137.33/(6.02214*10^23) * (9.0 * 10^23)=205.24` grams. Following similar arguments one can convert mass in grams into number of atoms. For compounds like water, 18 grams of it contain 6.02214 × 10˄23 numbers of molecules and so on.

pranitingale | Student

ATOMS OF BARIUM TO GRAMS

♦GIVEN :- mass of the substance (m)= ?

no. of particles (N) = 9.0 x 10^23

molar mass (M) = 137.34 g

avagadro's no.(Na) = 6.022 x 10^23

♦SOLUTION :- m = M x N / Na

m = 137.34 x 9 x 10^23 / 6.022 X 10^23

m = 137.34 x 9 / 6.022

m = 137.34 x 1.49

m = 204.63 g

◘◘◘ FORMULA FOR YOUR NEXT QUESTION =

NO. OF PARTICLES (N) = MASS OF THE SUBSTANCE(m) / MOLAR MASS(M) x AVAGADRO'S NUMBER (Na)