What do I mean by "dimensionally"?
Suppose we have a 1.00*g mass of water. Now we know that "Avogadro's number of water molecules" has a mass of 18.01*g, and we would typically write this as......
"Molar mass of water"=18.01*g*mol^-1
And if I wanted to work out the MOLAR quantity, I would perform the division by leaving the UNITS in......i.e.
"Moles of water"=(1.00*g)/(18.01*g*mol^-1), and of course we can do some cancellation of units.....
"Moles of water"=(1.00*cancelg)/(18.01*cancelg*mol^-1)
=0.0555*1/(mol^-1)=0.0555*1/(1/(mol)) because x^-1-=1/x, and
=0.0555*1/(mol^-1)=0.0555*1/(1/(mol))=0.0555*mol.
And as for volumes, we need a "density", rho, the which for chemists is typically quoted as g*mL^-1-=g*cm^-3.
By definition, rho="Mass"/"Volume" i.e. mass per unit volume.
Here rho_(H_2O)=("Molar quantity"xx"Molar mass")/(1*mL)
=(0.0555*cancel(mol)xx18.01*g*cancel(mol^-1))/(1*mL)
1*g*mL; dimensionally consistent as required. Of course, the "density" needs to be measured......
If this does not help you will have to refine your question.
