Respuesta :
Answer:The final volume of nitrogen gas will be 13 L. Nitrogen gas was collected in the plastic bag.
Explanation:
Volume of the storage cylinder:
Volume of the cylinder = [tex]\pi r^2h[/tex]
Diameter of the cylinder (d)= 6.6 cm
So, radius of the cylinder [tex]=\frac{d}{2}=\frac{6.6}{2}=3.3cm[/tex]
Height of the cylinder = 26 cm
Volume of the cylinder=[tex]=V_1=\pi r^2h=3.14\times (3.3cm)^2\times 26cm=889.05 cm^3=889.05\times 10{-3} L(1cm^3=10^{-3}L)[/tex]
Pressure of the [tex]N_2[/tex] gas in a cylinder =[tex]P_1= 14.9 atm[/tex]
The cylinder is opened and the gas allowed to escape into a large empty plastic bag. So, now the value of the pressure[tex]P_2[/tex] will become equal to atmospheric pressure that 1 atm .
Volume of [tex]N_2[/tex] gas in plastic bag [tex]V_2[/tex] will be given by the expression of Boyle's law
[tex]P_1V_1=P_2V_2[/tex]
On substituting the values:
[tex]14.9\times 889.05\times 10^{-3} L= 1atm \times V_2=[/tex]
[tex]V_2=13.24 L[/tex]
The final volume of nitrogen gas will be 13.24 L when rounded of to two significant figures will be 13 L. Nitrogen gas was collected in the plastic bag.
According to Boyle's law, the total volume occupied after exiting the
cylinder is directly proportional to the new pressure of the gas.
The volume occupied by the gas after leaving the cylinder is approximately
13.25 liters.
Reasons:
The volume of the cylinder, V₁ = π ×(6.6/2 cm)² × 26 cm = 283.14·π cm³
Pressure of the gas, P₁ = 14.9 atm.
Pressure after escape, P₂ = Atmospheric pressure = 1 atm.
Required:
Volume occupied by the gas after expansion
Solution:
The expansion of the gas at constant temperature process and the
volume of the gas after expansion is given by Boyles law as follows;
P₁·V₁ = P₂·V₂
Therefore;
[tex]V_2 = \dfrac{P_1 \cdot V_1}{P_2}[/tex]
Which gives;
[tex]V_2 = \dfrac{14.9 \ atm.\times 283.14 \cdot \pi \ cm^3}{1 \ atm} = 4,218.786 \cdot \pi \ cm^3[/tex]
1 cm³ = 0.001 L
∴ 4,218.786·π cm³ = 4.218786·π L ≈ 13.25 L
The volume occupied by the gas after leaving the cylinder, V₁ ≈ 13.25 L.
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