Question

What mass of dioxygen gas exists in a `51.7*L` volume of the gas under conditions of `"STP"`?

Answer 1

Well, `"STP"` specifies an absolute temperature of `273.15*K`, and a pressure of `100*kPa`

Explanation:

And we search for an appropriate gas constant, `R=8.314*L*kPa*K^-1*mol^-1`...and then we solve the Ideal Gas equation....

`PV=nRT="mass"/"molar mass"xxRT`

And so `"mass"=(PVxx"molar mass")/(RT)`

`=(100*cancel(kPa)xx51.7*cancelLxx32.00*g*cancel(mol^-1))/(8.314*cancel(L*kPa*K^-1*mol^-1)xx273.15*cancelK)`

`=??*g`

Answer 2

`=ul?xx32g`

Explanation:

The relationship involved when talking about STP is that "a mole of a gas will occupy a volume of 22.4L. This can be translated as `1mol-=22.4L`; used as conversion factor and this can be computed as:

`eta=51.7cancel(L)xx(1mol)/(22.4cancel(L))`
`eta= ul ? mol`

But, the problem required to find the mass which again calls for another conversion. This case, molar mass of oxygen is needed which is obtainable from the periodic table. Take note that oxygen is a diatomic element; so that the molar mass is
`Mm=2xx(16g)/(mol)`
`Mm=(32g)/(mol)`

Now, find the mass. Multiply the `eta` by the molar mass of `O_2` as shown below.
`m=etaxxMm`
`m=ul?cancel(mol)xx(32g)/(cancel(mol))`
`m=ul?xx32g`