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:

$\begin{gathered} PV=nRT \\ \frac{n}{V}=\frac{P}{RT} \end{gathered}$

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:

$\begin{gathered} Density=\frac{n}{V}\times\frac{MolarMass,gO_2}{1molO_2} \\ Density=\frac{n}{V}\times\frac{32gO_2}{1molO_2} \end{gathered}$

Now let's substitute the data we get:

1)TPN conditions are equal to

T=20°C=293.15K

P=1atm

$\frac{n}{V}=\frac{1atm}{293.15K\times0.08206\frac{atm.L}{mol.K}}=0.042\frac{mol}{L}$

Density will be:

$Density=0.042\frac{mol}{L}\times\frac{32g}{1mol}=1.3g/L$

2) T=20°C=293.15K

P=760mmHg=0.97atm

$\frac{n}{V}=\frac{0.97atm}{293.15K\times0.08206\frac{atm.L}{mol.K}}=0.040\times\frac{mol}{L}$$Density=0.040\frac{mol}{L}\times\frac{32g}{1mol}=1.3g/L$