Answer:
Explanation:
1) Data:
a) T = 25°C = 25 + 273.15K = 298.15 K
b) P = 1 atm
c) assumption: ideal gas
2) Formulae and principles
a) Ideal gas equation: p V = n R T, where:
b) Molar volume: ν = V / n, where:
3) Solution:
= 0.0821 atm-liter / mol-K × 298.15 K / 1 atm
= 24.5 liter / mol
Considering the definition of molar volume and ideal gas law, the molar volume of an ideal gas at 25∘C and 1 atm pressure is 24.436 [tex]\frac{L}{mole}[/tex].
An ideal gas is a theoretical gas that is considered to be composed of point particles that move randomly and do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.
An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T).
The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:
P×V = n× R× T
On the other hand, molar volume is a property that indicates how much space a mole of a certain substance or compound occupies.
The expression to calculate the molar volume is:
[tex]Molar Volume=\frac{V}{n}[/tex]
where V is the volume it occupies, and n is the amount of the species in moles.
Then, rearranging the expression for the ideal gas law, you obtain:
[tex]\frac{V}{n} =\frac{RxT}{P}[/tex]
[tex]MolarVolume =\frac{RxT}{P}[/tex]
In this case, you know:
Replacing:
[tex]MolarVolume =\frac{0.082\frac{atmL}{molK} x298 K}{1 atm}[/tex]
Solving:
MolarVolume= 24.436 [tex]\frac{L}{mole}[/tex]
In summary, the molar volume of an ideal gas at 25∘C and 1 atm pressure is 24.436 [tex]\frac{L}{mole}[/tex].
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