Question

- Calculate the molar mass of a gas that has a density of 1.55g/L.

Answer 1

Answer: 39.86 g/mol

Explanation:

Assuming this gas is at a pressure of $0.99 atm$ and a temperature of $37 \°C+273.15=310.15 K$, we can solve this problem with the Ideal Gas Law equation:

$P.V=n.R.T$  (1)

Where:  

$P=0.99 atm$ is the pressure of the gas  

$V$ is the volume of the gas  

$n$ the number of moles of gas  

$R=0.0821 \frac{atm.L}{mol.K}$ is the gas constant  

$T=310.15 K$ is the absolute temperature of the gas in Kelvin

On the other hand, we know the density $\rho=1.55 g/L$ is given by a relation between the mass $m$ and the volume $V$:

$\rho=\frac{m}{V}$ (2)

Then, the mass is:

$m=\rho V$ (3)

Another important fact here is that the molar mass $M_{mass}$ of an element is given by a relation between the mass of that element and the number of moles $n$ it contains:

$M_{mass}=\frac{m}{n}$ (4)

Isolating $n$:

$n=\frac{m}{M_{mass}}$ (5)

Substituting (5) in (1):

$P.V=\frac{m}{M_{mass}}.R.T$  (6)

Substituting (3) in (6):

$P.V=\frac{\rho V}{M_{mass}}.R.T$  (7)

Isolating $M_{mass}$:

$M_{mass}=\frac{\rho V}{PV}RT$ (8)

Simplifying:

$M_{mass}=\frac{\rho}{P}RT$ (9)

Solving with the given data:

$M_{mass}=\frac{1.55 g/L}{0.99 atm}(0.0821 \frac{atm.L}{mol.K})(310.15 K)$ (10)

Finally:

$M_{mass}=39.86 g/mol$ This is the molar mass of the gas