Answer:
The number of moles of N₂ gas in the container is approximately 2.02 moles
Explanation:
We re told that;
Volume of container = 45.2 L
Container Content is N₂, nitrogen gas at STP, Standard Temperature and Pressure
Standard Temperature = 273.15 K
Standard Pressure = 1 atmosphere
We can find the number of moles from the universal gas equation as follows;
Universal gas equation: P·V = n·R·T
Therefore;
[tex]n = \frac{P \times V}{R \times T}[/tex]
Where:
n = Number of moles
P = Pressure = 1 atmosphere
V = Volume = 45.2 L
T = Temperature = 273.15 K
R = Universal Gas Constant = 0.08205 L·atm/(mol·K)
Plugging in the values gives;
[tex]n = \frac{1 \times 45.2}{0.08205 \times 273.15 } = 2.01678 \ moles[/tex]
Therefore, the number of moles of N₂ gas in the container = 2.01678 moles or ≈ 2.02 moles.
Considering the definition of STP conditions, 2.02 moles of N₂ gas are in the container.
The STP conditions refer to the standard temperature and pressure. Pressure values at 1 atmosphere and temperature at 0 ° C are used and are reference values for gases. And in these conditions 1 mole of any gas occupies an approximate volume of 22.4 liters.
You can apply the following rule of three: if by definition of STP conditions 1 mole of N₂ occupies a volume of 22.4 liters, how many moles of N₂ occupy a volume of 45.2 L?
[tex]amount of moles=\frac{45.2 Lx1 mole}{22.4 L} [/tex]
amount of moles= 2.02 moles
Finally, 2.02 moles of N₂ gas are in the container.
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