Mole Concept Help?

You have several terms confused in this statement .... "How is Gram molecular weight of 1 oxygem is 16amu=16g.How is amu expressed in grams."

... 1st ... the atomic mass of oxygen is approx. 16 atomic mass units (amu) --- the atomic mass is the mass of a single atom, which is so small it is undetectictable by a normal balance .. one AMU is about 1.66 x 10^-24 g or 0.00000000000000000000000166 g <<<< see, really small
.... 2nd ... when talking about larger amounts, amounts measurable in grams, chemists use amounts called moles. 1 mole is a large number of atoms , 6.022x10^23 atoms, or 60220000000000000000000 <<< see a very large number of atoms. This number is called Avogadro's number. Remember it and that it is atoms in 1 mole.
.... 3rd ... These numbers are NOT by accident ... they make it convenient for chemsts
using Hydrogen as an example --- Notice that ... 1.66x10^-24(g/amu) X 6.022x10^23(atoms/mole) X 1amu = 1g/mole , so that 1 mole of H atoms will have a mass of about 1 gram ...
... AND for oxygen, 1 atom of O has a mass of 16 amu so ---
1.66x10^-24(g/amu) X 6.022x10^23(atoms/mole) X 16amu = 16g/mole ... 1 mole of oxygen atoms has a mass of 16 g ...
... It works that way for EVERY element, it even extends into the molar mass of molecules like water , 1 H atom is 1 amu, and 1 O atom is 16 amu .. So H2O will have a molecular mass (mass of 1 molecule) of 2X1amu + 1X16amu = 18amu, but that is the mass of 1 molecule ... agan, for 1 mole, we are talking about 6.022x10^23 molecules and 1.66x10^-24(g/amu) X 6.022x10^23(molecules/mole) X 18amu = 18g/mole ... 1 mole of water molecules has a mass of 18 g ..
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After a while you get use to this fact .. when talkng about 1 atom or 1 molecule you use the atomic masses labeled as AMU, but if talkng about 1 mole of these substances you use the same atomic masses from the perodic table BUT you label them as grams.
///// Good luck...

This is a very important subject and confusion results from chemists using terminology in a traditional way , and not necessarily with absolute scientific precision. Chemists use terms to describe or define something and they know exactly what they mean , and they assume that those they correspond with also know exactly what they mean . But what they state often defies critical analysis . This question highlights this in many ways:
For a start: It is incorrect to state “Gram molecular weight of 1 oxygen is 16amu”.
The atomic mass of oxygen( O ) is 16 amu . The molecular mass of oxygen (O2) is 32 amu.
In this work we should not be using the term “weight” which is a measure of force , and not a measure of quantity . We should always talk about atomic mass , molecular mass and molar mass
What do we mean by molecular mass?
Molecular mass is a measure of the sum of the atomic mass values of the atoms in a molecule. Molecular mass is either unitless or expressed in terms of atomic mass units (amu). Both atomic mass and molecular mass are defined relative to the mass of the isotope carbon-12, which is assigned a value of 12 amu. 1 amu has mass = 1.660539040×10^ -24g
Now what is the other term so often used by chemists?
Molar mass
Note that you can determine the molar mass of atoms and molecules
This is the mass in grams of 1 mol of substance. Let us stay with carbon. One mol of carbon, the C12 isomer, contains 6.022*10^23 ( Avagadro’s number) atoms of C12 .
Now calculate the mass of 1 mol of C12 atoms
1.66053904*10^-24 X 12 X 6.022*10^23 = 11.9997g , which allowing for a little rounding errors , is equal to : Molar mass C12 = 12g/mol
Chemists have worked this out so that things are simple.
If you have an atom with an atomic mass of for example Fe = 55.845amu , then the molar mass of Fe will be 55.845g/mol 55.845 X (1.660539040×10^ -24) X ( 6.022*10^23) = 55.844g/mol)
Likewise for compounds, If you have CO2 , the molecular mass of CO2 is 12.011 + 2 X 15.999 = 44.009 amu and the molar mass of CO2 is 44.009g/mol ( Try the multiplication for yourself)
Incidentally – do you know why I have used 12.011amu for the atomic mass of C , and not 12 as previously?

Remember the equation
moles = mass(g) / Amu
mass(g) = moles X Amu
Hence
Amu X moles = grams.