# Which sample of gas contains the FEWEST molecules?

## $1.$ $\text{A 4.4 g mass of carbon dioxide.}$ $2.$ $\text{A 3.4 g mass of ammonia.}$ $3.$ $\text{A 1.6 g mass of methane.}$ $4.$ $\text{A 3.2 g mass of sulfur dioxide.}$

May 24, 2017

$\text{Sample 4}$, $\text{sulfur dioxide.}$

#### Explanation:

All we need to do is to calculate the molar quantity of each gas, and we know that $1 \cdot m o l$ of any substance constitutes $6.022 \times {10}^{23}$ individual particles of that substance.........

$\text{Moles of}$ $C {O}_{2} = \frac{4.4 \cdot g}{44.01 \cdot g \cdot m o {l}^{-} 1} = 0.1 \cdot m o l$.

$\text{Moles of}$ $N {H}_{3} = \frac{3.4 \cdot g}{17.01 \cdot g \cdot m o {l}^{-} 1} = 0.2 \cdot m o l$.

$\text{Moles of}$ $C {H}_{4} = \frac{1.6 \cdot g}{16.04 \cdot g \cdot m o {l}^{-} 1} = 0.1 \cdot m o l$.

$\text{Moles of}$ $S {O}_{2} = \frac{3.2 \cdot g}{64.1 \cdot g \cdot m o {l}^{-} 1} = 0.05 \cdot m o l$.

Since the molar quantity represents an actual number, ${N}_{A} = 6.022 \times {10}^{23} \cdot m o {l}^{-} 1$, clearly, there are FEWER $\text{sulfur dioxide}$ molecules than the number of molecules of any other gas. In other words, since $S {O}_{2} \left(g\right)$ is the heaviest, the given mass contains the least number of molecules.