Question

Titan, the largest satellite of Saturn, has a thick nitrogen atmosphere. At its surface, the pressure is 1.5 Earth-atmospheres and the temperature is 94 K. Part APart complete Part B Calculate the surface density in Titan's atmosphere in molecules per cubic meter. Express your answer as a number of molecules per meter cubed.

Answer 1

1.2×1026molecules/m3

Step-by-step explanation:

given

Answer 2

N' = 1.17*10^21 molecules/m^3

Step-by-step explanation:

In order to calculate the surface density in Titan's atmosphere, in molecules per cubic meter, you use the following formula for ideal gases:

`PV=nRT` (1)

P: pressure = 1.5 Earth-atmospheres = 1.5 atm

R: ideal gas constant = 8.205 m^3.atm.mol^-1.K^-1

T: temperature in Titan = 94K

n: number of moles

To obtain the number of moles per cubic meter you write the equation (1) as follow:

`N=(n)/(V)=(P)/(RT)` (2)

N: moles per cubic meter

You use the Avogadro's number for the number of molecules:

`N'=NA=(AP)/(RT)` (3)

A: Avogadro's number = 6.022*109^23 molecules/mol

N': molecules per cubic meter

You replace the values of all parameters in the equation (3):

`N'=((6.022*10^(23)molecules/mol)(1.5atm))/((8.205m^3.atm.K^(-1)mol^(-1))(94K))\\\\N'=1.17*10^(21)(molecules)/(m^3)`

The surface density of molecules in Titan is 1.17*10^21 molecules/m^3