units of mole formula [closed]








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I am a high school student.I am currently studying "moles" chapter in my textbook.I think my book is misleading me in regards with units of a formula.
The formula is,


NO.of moles= (Given mass of an element)/(Molar mass of element).


so,the units used here are,(Given mass of an element)=gram,g AND (Molar mass 
of element)=**g/mol**


I think that the denominator of the formula is incorrect.The therm "Molar mass of element" should be replaced with "Gram Atomic Mass of the element". The thing which forces me to think so is the "Derivation of this formula".
The formula is derived in this way-
The mass of an atom of carbon 12, call it mC12,
 so,mC12=12 amu/atom


mC12=12 g/mol


thus, => 12 amu/atom = 12 g/mol


=> 1 amu/atom= 1 g/mol


=> (1 amu /atom) \* 1 mol = 1 g


let,1 mol = k (constant)


thus, 1 amu is directly proportional to 1 g


now let an element has atomic mass "x" amu.


thus, an element of mass "x" amu must have its gram atomic mass as x g (keeping k= 1 mol constant).


now, (x amu/atom) \* 1 mol = x g


now, keeping q= x amu/atom constant,


we have,


1 mol is directly proportional to x g.


so,x g is directly proportional to 1 mol.


Now,by using the unitary method we have, 
1 g = 1mol/x
now,let the given mass of an element is y g.


thus, y\* 1 g= y \* 1mol / x


y g= y/x mol


here, x= gram atomic mass of the given element.
 y=given mass of the element.


thus,the formula is.


No. of moles= (Given mass of the element)\*1 mol/(gram atomic mass)
the units here are, (Given mass of the element)= gram


(gram atomic mass)= gram


So,i arrived at a result in which the denominator is "gram atomic mass"(g) not "molar mass"(g/mol).


Do you think my book is wrong?




Gram atomic mass is the molar mass multiplied by one mole. All you've done is replace $$\frac{\ce{g}}{\ce{mol}}$$ in the formula by $$\ce{mol}\cdot\frac{\ce{g}}{\ce{mol}}\cdot\frac{1}{\ce{mol}}$$
which can be done far quicker without the algebra contortion.


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