# Question 38860

Mar 3, 2017

The answer is B) $1$ mole of silver

#### Explanation:

The idea here is that you need to convert everything to grams.

You already know that one of the samples contains $2$ gram atoms of nitrogen. Now, a gram atom is used to denote the mass of a substance that contains $6.02 \cdot {10}^{23}$ atoms.

Note that $6.02 \cdot {10}^{23}$, known as Avogadro's constant, represents the definition of a mole.

Simply put, a gram atom is the mass of a substance that contains $1$ mole of atoms. In this case, $2$ gram atoms of nitrogen will be equivalent to $2$ moles of elemental nitrogen.

This means that the mass of the first sample will be

2 color(red)(cancel(color(black)("moles N"))) * "14 g"/(1color(red)(cancel(color(black)("mole N")))) = "28 g"

Keep in mind that the relative atomic mass is actually equivalent to its molar mass. So if nitrogen is said to have a relative atomic mass of $14$, its molar mass will be equal to ${\text{14 g mol}}^{- 1}$.

The relative atomic mass of silver is said to be equal to $108$. This is equivalent to saying that $1$ mole of silver atoms has a mass of $\text{108 g}$.

Now, a sample of any ideal gas that is being kept at a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$ contains exactly $1$ mole of gas and occupies $\text{22.4 L}$.

This implies that you're dealing with $1$ mole of oxygen gas, ${\text{O}}_{2}$. Elemental oxygen has a molar mass of ${\text{16 g mol}}^{- 1}$, which means that diatomic oxygen will have a molar mass of

M_ ("M O"_2) = 2 xx "16 g mol"^(-1) = "32 g mol"^(-1)#

You can thus say that the sample of oxygen gas has a mass of $\text{32 g}$.

Finally, $6.02 \cdot {10}^{23}$ atoms of carbon are needed in order to have $1$ mole of carbon.

This means that the last sample will contain $1$ mole of carbon and have a mass of $\text{12 g}$ since carbon has a molar mass of ${\text{12 g mol}}^{- 1}$.

Therefore, you will have

$\text{108 g Ag" > "32 g O"_2 > "28 g N" > "12 g C}$