Answer:
C. 12.8 liters.
Explanation:
The Standard Temperature and Pressure (STP) of a gas are 273.15 K and 100 kilopascals. From Avogadro's Law, a mole of carbon dioxide contains [tex]6.022 \times 10^{23}[/tex] molecules. If we suppose that carbon dioxide behaves ideally, then the equation of state for ideal gas is:
[tex]P\cdot V = n\cdot R_{u}\cdot T[/tex] (1)
[tex]P\cdot V = \frac{r\cdot R_{u}\cdot T}{N_{A}}[/tex] (1b)
Where:
[tex]P[/tex] - Pressure, measured in pascals.
[tex]V[/tex] - Volume, measured in liters.
[tex]r[/tex] - Amount of molecules, no unit.
[tex]N_{A}[/tex] - Avogadro's number, no unit.
[tex]R_{u}[/tex] - Ideal gas constant, measured in pascal-liters per mole-Kelvin.
[tex]T[/tex] - Temperature, measured in Kelvin.
If we know that [tex]P = 100000\,Pa[/tex], [tex]r = 3.44\times 10^{23}[/tex], [tex]N_{A} = 6.022\times 10^{23}[/tex], [tex]T = 273.15\,K[/tex] and [tex]R_{u} = 8.314\times 10^{3}\,\frac{L\cdot Pa}{mol\cdot K}[/tex], then the volume of carbon dioxide at STP is:
[tex]V = \frac{r\cdot R_{u}\cdot T}{N_{A}\cdot P}[/tex]
[tex]V = \frac{(3.44\times 10^{23})\cdot \left(8.314\times 10^{3}\,\frac{L\cdot Pa}{mol\cdot K} \right)\cdot (273.15\,K)}{(6.022\times 10^{23})\cdot (100000\,Pa)}[/tex]
[tex]V = 12.972\,L[/tex]
Therefore, the correct answer is C.
