Chapter 15, Problem 1TC

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

To determine

The most to least rank number of atoms in 1-gram samples of matter: A, carbon-12; B, carbon-13’ C, uranium-238.

Answer to Problem 1TC

Uranium-238 ($U$) has the least number of atoms and, then carbon-13($C$), and then carbon-12( $C$) has the most number of atoms.

Explanation of Solution

The mole is a measuring quantity that measures the number of atoms that an element contains. One mole contains $6.022\times {10}^{23}$ atoms in the element.

From the given sample, the molar mass of carbon-12 is $12\text{g}/\text{mol}$, molar mass of carbon-13 is $13\text{g}/\text{mol}$, and uranium-238 has $238\text{g}/\text{mol}$.

The moles of matter can be calculated by dividing 1g with their molar mass.

The number of moles of a sample is calculated by dividing the given mass to its the molar mass.

Write the expression for the number of moles.

$\text{Number of moles }=\frac{\text{Given mass}}{\text{ Molar mass}}\mathrm{........}\left(\text{i}\right)$

Substitute the values in the above equation to get the number of moles of Carbon-12.

$\begin{array}{l}C=\frac{1\times g}{12\times g\times {\text{mol}}^{\text{-1}}}\\ C=0.083\text{moles}\end{array}$

Substitute the given values of Carbon-13 in the equation (i) to get the number of moles of Carbon-13.

$\begin{array}{l}C=\frac{1\times g}{13\times g\times {\text{mol}}^{\text{-1}}}\\ C=0.076\text{moles}\end{array}$

Substitute the values in the above equation to get the number of moles of Uranium-238.

$\begin{array}{l}U=\frac{1\times g}{238\times g\times {\text{mol}}^{\text{-1}}}\\ U=0.004\text{moles}\end{array}$

The moles of the matter in given sample is calculated, the matter with more number of moles will have more number of atoms in it. So, $C$ has most number of atoms, then $C$ (carbon-13), and then uranium-238 $U$ h has the least number of atoms in descending order.

Conclusion:

Therefore, Uranium-238 ($U$) has the least number of atoms and is arranged at first from least to most order, then carbon-13($C$), and then carbon-12( $C$) as it has the most number of atoms and is arranged at the last in the order.