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This is an incomplete question, here is a complete question.
Students at the University of North Texas and the University of Washington built a car propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored in a 200.0 L tank. What volume of N₂ is released at 0.930 atm of pressure and 25.0 degrees Celsius from a tank full of liquid N₂ (d = 0.808 g/mL)?
Answer : The volume of N₂ released is, [tex]1.52\times 10^5L[/tex]
Explanation :
First we have to calculate the density of N₂ in 200.0 L volume.
Conversion used : (1 L = 1000 mL or, 1 mL = 0.001 L)
As, density of N₂ in 1 mL = 0.808 g
So, density of N₂ in 1000 mL = 1000 × 0.808 = 808 g/L
Now we have to calculate the mass of N₂
[tex]\text{Mass of }N_2=\text{Density of }N_2\times \text{Volume of }N_2[/tex]
[tex]\text{Mass of }N_2=808g/L\times 200.0L=161600g[/tex]
Now we have to calculate the volume of N₂ released.
Using ideal gas equation:
[tex]PV=nRT\\\\PV=\frac{w}{M}RT[/tex]
where,
P = pressure of gas = 0.930 atm
V = volume of gas = ?
T = temperature of gas = [tex]25.0^oC=273+25.0=298.0K[/tex]
R = gas constant = 0.0821 L.atm/mole.K
w = mass of gas = 161600 g
M = molar mass of N₂ gas = 28 g/mole
Now put all the given values in the ideal gas equation, we get:
[tex](0.930atm)\times V=\frac{161600g}{28g/mole}\times (0.0821L.atm/mole.K)\times (298.0K)[/tex]
[tex]V=151830.77L=1.52\times 10^5L[/tex]
Therefore, the volume of N₂ released is, [tex]1.52\times 10^5L[/tex]
The volume of the N₂ released from the tank is 151830.81 L
Determination of the mass of N₂ in the tank
We'll begin by calculating the mass of N₂ in the tank.
•Density = 0.808 g/mL
•Volume = 200 L = 200 ×1000 = 200000 mL
•Mass of N₂ =?
Mass = Density × Volume
Mass of N₂ = 0.808 × 200000
Mass of N₂ = 161600 g
Determination of the mole of 161600 g of N₂
•Mass of N₂ = 161600 g
•Molar mass of N₂ = 14 × 2 = 28 g/mol
•Mole of N₂ = 161600 g
Mole = mass / molar mass
Mole of N₂ = 161600 / 28
Mole of N₂ = 5771.43 moles
Determination of the volume of N₂ released from the tank
•Mole of N₂ (n) = 5771.43 moles
•Temperature (T) = 25 °C = 25 + 273 = 298 K
•Pressure (P) = 0.930 atm
•Gas constant (R) = 0.0821 atm.L/Kmol
•Volume of N₂ (V) =?
The volume of the N₂ released from the tank can be obtained by using the ideal gas equation as illustrated below:
PV = nRT
Divide both side by P
V = nRT / P
V = (5771.43 × 0.0821 × 298) / 0.930
V = 151830.81 L
Thus, the volume of the N₂ released from the tank is 151830.81 L
Complete question:
Students at the University of North Texas and the University of Washington built a car propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored in a 200.0 L tank. What volume of N₂ is released at 0.930 atm of pressure and 25.0 degrees Celsius from a tank full of liquid N₂ (d = 0.808 g/mL)
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