Question

A. Calculate the density of oxygen: 1) at T.P.N 2) at 20°C and 740 mmHg 3•) The density of a gas, at 152 kPa and 27°C, is 1950g/cm3 . Calculate the molar mass of this gas.

Answer 1

Density is defined as mass divided by volume. To find these parameters we will use the ideal gas equation that tells us:

`\begin{gathered} PV=nRT \\ (n)/(V)=(P)/(RT) \end{gathered}`

where,

n is the moles of the gas

V is the volume

P is the pressure of the gas

T is the temperature

R is a constant = 0.08206 (atm.L)/(mol.K)

We see that we will have the molar density of oxygen as a result, to obtain the density we use the molar mass of oxygen, so we will have:

`\begin{gathered} Density=(n)/(V)*(MolarMass,gO_2)/(1molO_2) \\ Density=(n)/(V)*(32gO_2)/(1molO_2) \end{gathered}`

Now let's substitute the data we get:

1)TPN conditions are equal to

T=20°C=293.15K

P=1atm

`(n)/(V)=(1atm)/(293.15K*0.08206(atm.L)/(mol.K))=0.042(mol)/(L)`

Density will be:

`Density=0.042(mol)/(L)*(32g)/(1mol)=1.3g/L`

2) T=20°C=293.15K

P=760mmHg=0.97atm

`(n)/(V)=(0.97atm)/(293.15K*0.08206(atm.L)/(mol.K))=0.040*(mol)/(L)`
`Density=0.040(mol)/(L)*(32g)/(1mol)=1.3g/L`