A 22.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.40 105 Pa and temperature of 22.0°C.

Question

(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: 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

Answer 1

(a) To convert the temperature from Celsius to Kelvin, add 273.15:

T(K) = T(°C) + 273.15
T(K) = 22.0 + 273.15
T(K) = 295.15 K

(b) Use the ideal gas law:
PV = nRT

Rearrange for n:
n = PV/(RT)

Given values are:
P = 9.40 * 10^5 Pa
V = 22.0 L = 0.022 m^3 (convert L to m^3 by multiplying with 0.001)
T = 295.15 K
R = 8.314 J/(mol*K) (gas constant)

n = (9.40 * 10^5 * 0.022) / (8.314 * 295.15)
n = 9.66 mol

(c) The molecular weight of carbon dioxide (CO2) is the sum of the atomic weights of carbon and oxygen:

CO2 = C + 2O
M(CO2) = 12.01 + 2 * 16.00
M(CO2) = 12.01 + 32.00
M(CO2) = 44.01 g/mol

(d) To obtain the number of grams, multiply the molecular weight by the number of moles:

mass = M(CO2) * n
mass = 44.01 * 9.66
mass = 425.05 g

(e) First, calculate the new temperature:

Tf = Ti + 224.0
Tf = 295.15 + 224.0
Tf = 519.15 K

To find the new number of moles, subtract the leaked gas in grams (82.0 g) from the initial mass (425.05 g) and divide by the molecular weight:

initial mass = 425.05 g
leaked gas = 82.0 g
remaining mass = 425.05 - 82.0 = 343.05 g

nf = remaining mass / M(CO2)
nf = 343.05 / 44.01
nf = 7.79 mol

(f) According to the ideal gas law and considering constant volume:

Pf/niTi = nfTf/Pi

Rearrange for Pf:
Pf = nfTfTi / (niTi)

(g) Calculate the final pressure:

Pf = (7.79 * 519.15) / (9.66 * 295.15)
Pf = 4028178.85 / 2852.764
Pf = 1412590.41 Pa