Dry ice is sometimes used for special effects to form a "fog" as it sublimes from the solid to the gaseous state. If 99.0 grams of dry ice is used to generate this "fog", how many torr of pressure will be exerted by the gaseous carbon dioxide once all of the dry ice sublimes? Assume the volume of the auditorium where the fog is generated is 1.24 x 10^5 m^3 and the temperature is 22ºC. (Enter your answer using either standard or scientific notation. For scientific notation, 6.02 x 10^23 is written as 6.02 x 10^ 23.)

3.34x10^-4 Torr

Explanation:

Step 1:

Data obtained from the question:

Mass of CO2 = 99g

Volume (V) = 1.24x10^5 m^3

Temperature (T) = 22ºC

Pressure = ?

Step 2:

Determination of the number of mole of CO2.

Mass of CO2 = 99g

Molar Mass of CO2 = 12 + (2x16) = 44g/mol

Number of mole = Mass / Molar Mass

Number of mole of CO2 = 99/44

Number of mole of CO2 = 2.25 moles

Step 3:

Conversion to appropriate unit.

For Volume:

1 m^3 = 1000L

Therefore, 1.24x10^5 m^3 = 1.24x10^5 x 1000 = 1.24x10^8 L

For temperature:

T (Kelvin) = T (°C) + 273

T (°C) = 22ºC

T (Kelvin) = 22ºC + 273 = 295K

Step 4:

Determination of the pressure exerted by the gas.

The pressure can be obtained by using the ideal gas equation as follow:

Volume (V) = 1.24x10^8 L

Temperature (T) = 295K

Number of mole (n) = 2.25 moles

Gas constant (R) = 0.082atm. L/Kmol

Pressure = ?

PV = nRT

Divide both side by V

P = nRT / V

P = (2.25 x 0.082 x 295) / 1.24x10^8

P = 4.39x10^-7 atm.

Step 5:

Conversion of 4.39x10^-7 atm to Torr.

This is illustrated below:

1 atm = 760 Torr

Therefore, 4.39x10^-7 = 4.39x10^-7 x 760 = 3.34x10^-4 Torr

Therefore, the pressure exerted by the gass in torr is 3.34x10^-4 Torr