I need some help with these excercises Thousands of buses run on compressed natu
ID: 869678 • Letter: I
Question
I need some help with these excercises
Thousands of buses run on compressed natural gas (CNG) to reduce pollution and to save on fuel costs. CNG, which is mostly methane, is stored on the roofs of the buses in large tanks under high pressure. If the density of CH4 in a tank at 25 degreeC is 153g/L, use the van der Waals equation and the ideal gas equation to calculate the methane gas pressure. Automobile air bags inflate during a crash or sudden stop by the rapid generation of nitrogen gas from sodium azide, according to the reaction: 2 NaN3(s) rightarrow 2 Na(s) + 3 N2(g) How many grams of sodium azide are needed to provide sufficient nitrogen gas to fill a 45.0 times 45.0 times 25.0 cm bag to a pressure of 1.10 atm at 22degreeC?Explanation / Answer
1.
(a)
(P + n2a / V2)(V- nb) = nRT
The a value for methane = 2.300 bar L^2 /mol^2
In order to convert that to atm we multiply that with 0.986 .
Thus, a = 2.2678 atm L^2 / mol^2
The b value for methane = 0.04301 L/mol
Plugging in the values,
[P + (9.56)^2(2.2678) / (1)^2)] + [(1 - (9.56)(0.04301)] = (0.956)(0.0821)(298)
[P + (9.56)^2(2.2678) / (1)^2)] = 237.305
P = 30.04 atm
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(b) Ideal gas equation is PV = nRT
P = ?
V = 1 L
n = Mass / Molar mass = 153 / 16 = 9.56 mol
R = 0.0821 L atm / mol. K
T = 25 oC = 298 K
P = (9.56) (0.0821) (298) / (1) = 233.89 atm
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Given, volume = 45.0 x 45.0 x 25.0 = 50625 cm^3 = 50625 mL = 50.625 L = V
P = 1.10 atm
n = ?
R = 0.0821
T = 22 oC = 295 K
PV = nRT
n = (1.10)(50.625) / (0.0821)(295)
n = 2.299 mol of N2 gas.
2 mol of NaN3 produces 2 mol of N2 gas.
So, 2.299 mol of NaN3 produces 2.299 mol of N2 gas.
So, moles of NaN3 = 2.299 mol
Mass = Moles x Molar mass = 2.299 x 65 = 149.45 g