Question

What is the volume at STP of 3.44 x 1023 molecules of CO2

gas?
a 25.1L
b 39.2 L
С
12.8 L
d 15.7 L

Answer 1

C. 12.8 liters.

Step-by-step 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
`6.022 * 10^(23)` molecules. If we suppose that carbon dioxide behaves ideally, then the equation of state for ideal gas is:

`P\cdot V = n\cdot R_(u)\cdot T` (1)

`P\cdot V = (r\cdot R_(u)\cdot T)/(N_(A))` (1b)

Where:

`P` - Pressure, measured in pascals.

`V` - Volume, measured in liters.

`r` - Amount of molecules, no unit.

`N_(A)` - Avogadro's number, no unit.

`R_(u)` - Ideal gas constant, measured in pascal-liters per mole-Kelvin.

`T` - Temperature, measured in Kelvin.

If we know that
`P = 100000\,Pa`,
`r = 3.44* 10^(23)`,
`N_(A) = 6.022* 10^(23)`,
`T = 273.15\,K` and
`R_(u) = 8.314* 10^(3)\,(L\cdot Pa)/(mol\cdot K)`, then the volume of carbon dioxide at STP is:

`V = (r\cdot R_(u)\cdot T)/(N_(A)\cdot P)`

`V = ((3.44* 10^(23))\cdot \left(8.314* 10^(3)\,(L\cdot Pa)/(mol\cdot K) \right)\cdot (273.15\,K))/((6.022* 10^(23))\cdot (100000\,Pa))`

`V = 12.972\,L`

Therefore, the correct answer is C.