# Question 8c9fd

Jul 5, 2017

It could be ${\text{O}}_{2}$

#### Explanation:

We're asked to identify the gas based on some gas measurements and it's mass.

What we can do is find the molar mass $M$ of the gas, using the equation

$M = \frac{\mathrm{dR} T}{P}$

where

• $d$ is the density of the gas, in $\text{g/L}$. We're given that $4$ $\text{g}$ occupies $2.8$ $\text{L}$, so the density is

$\left(4 \textcolor{w h i t e}{l} \text{g")/(2.8color(white)(l)"L}\right) = 1.43$ $\text{g/L}$

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"•"atm")/("mol"•"K}\right)$

• $T$ is the absolute temperature of the gas, in $\text{K}$. Standard temperature is defined as $273.15$ $\text{K}$

• $P$ is the pressure of the gas, in $\text{atm}$. Standard pressure is usually for these types of problems defined as $1$ $\text{atm}$

Plugging in known values, we have

$M = \left(\left(1.43 \text{g"/(cancel("L")))(0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(273.15cancel("K")))/(1cancel("atm}\right)\right)$

= color(red)(32.0 color(red)("g/mol"

To me, sfcolor(red)("oxygen gas"# seems pretty close to this value, so it could be ${\text{O}}_{2}$.