Question

A 22.0-L tank of carbon dioxide gas (CO_{2}) is at a
pressure of 9.90 ? 10^{5} 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.

temperature _____ | K |

number of moles ______ | mol |

(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: *n*_{i}, the
initial number of moles; *n*_{f},the final
number of moles; *T*_{i}, the initial
temperature; *T*_{f}, the final
temperature; and *P*_{i}, the initial
pressure.)

*P*_{f} = _____

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

____Pa

Answer #1

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 10^{5} Pa

V = 22 L = 22 x 10^{-3} m^{3}.

R = 8.314 J/ mol.K

T = 291 K

Substituting,

n = [(9.9 x 10^{5}) 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 10^{5} Pa

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