A 22.0-L tank of carbon dioxide gas (CO 2 ) is at a pressure of 9.90 ? 10 5 Pa a

Question

A 22.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.90 ? 105 Pa and temperature of 18.0°C.

(a) Calculate the temperature of the gas in Kelvin.
_______ K

(b) Use the ideal gas law to calculate the number of moles of gas in the tank.
mol

(c) Use the periodic table to compute the molecular weight of carbon dioxide, expressing it in grams per mole.
______ g/mol

(d) Obtain the number of grams of carbon dioxide in the tank.
______ g

(e) A fire breaks out, raising the ambient temperature by 224.0 K while 82.0 g of gas leak out of the tank. Calculate the new temperature and the number of moles of gas remaining in the tank.

(f) Using the ideal gas law, find a symbolic expression for the final pressure, neglecting the change in volume of the tank. (Use the following as necessary: ni, the initial number of moles; nf,the final number of moles; Ti, the initial temperature; Tf, the final temperature; and Pi, the initial pressure.)
Pf = _____

  


(g) Calculate the final pressure in the tank as a result of the fire and leakage.
____Pa

Explanation / Answer

a)
0 degrees corresponds to 273 K
so 18 degrees corresponds to 273 + 18 = 291 K

b)
According to ideal gas law, PV = nRT
Number of moles, n = PV/RT
Where P is the pressure, V is the volume, R is gas constant and T is temperature.
P = 9.9 x 105 Pa
V = 22 L = 22 x 10-3 m3.
R = 8.314 J/ mol.K
T = 291 K

Substituting,
n = [(9.9 x 105) x (22 x 10-3)] / [8.314 x 291]
= 9 mol

c)
Molar mass of CO2 = 44 g/mol

d)
1 mol contains 44 g of CO2,
So 9 moles contain 9 x 44 = 396 g

e)
Initial temperature = 291 K
Temperature rise by 241 K
Final temperature = 291 + 241 = 532 K

Initial mass of CO2 = 396 g
Final mass of CO2 = 396 - 82 = 314 g
Number of moles = 314/44
= 7.14 mol

f)
Using ideal gas law,
Pf x Vf = nf R Tf
Pf = nf RTf / Vf

g)
Pf = [7.14 x 8.314 x 532] / [22 x 10-3]
= 14.347 x 105 Pa

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