# Consider three 1-gram samples of matter: A, carbon-12; B, carbon-13; C, uranium-238. How do you rank them in terms of having the greatest number of atoms, from least to most?

Mar 8, 2017

#### Answer:

From least to most.........${\text{^238U, ""^13C, }}^{12} C \ldots \ldots \ldots . .$

#### Explanation:

How do you know? Well, consider the molar masses of each element. To find the number of moles we multiply thru by the ATOMIC mass of each isotope:

$\text{Moles of}$ ""^12C=(1*cancelg)/(12*cancelg*mol^-1)=1/12*mol

$\text{Moles of}$ ""^13C=(1*cancelg)/(13*cancelg*mol^-1)=1/13*mol

$\text{Moles of}$ ""^238U=(1*cancelg)/(238*cancelg*mol^-1)=1/238*mol

So how does this calculation help us answer the question? Well, $\text{1 mole}$ is just another number, just like a $\text{dozen,}$ or  "score", or $\text{century}$, or $\text{gross}$. Admittedly, the $\text{mole}$ is a very large number; $1 \cdot m o l$ of stuff specifies $6.022 \times {10}^{23}$ individual items of that stuff. And thus, CLEARLY, the GREATEST MOLAR QUANTITY corresponds to the greatest number of particles.

And here, the greatest number of particles necessarily occurred with the element with the LEAST atomic mass, i.e. ""^12C. Capisce?

Can you work out the actual numbers of atoms in each of the individual quantities?