Question

A sample of gas has a volume of 0.05 m3 at a pressure of 2 atmospheres and a temperature of 20 0C. How many moles of gas are in the sample?

Answer 1

We can use,ideal gas equation to solve this,

i.e `PV=nRT` (where, `P` is the pressure of `n` moles of a gas of volume `V` at temperature `T` and `R` is the universal gas constant)

given, `P=2 atm` , `V=0.05*1000=50 L` , `T=273+20=293K` and `R=0.0821` `L` `atm` `K^-1` `mol ^-1`

so, `n= (PV)/(RT) =4.16` moles

Answer 2

I get `4.16` moles.

Explanation:

We need to use the ideal gas law here, which states that

`PV=nRT`

Rearranging for `n`, we get

`n=(PV)/(RT)`

We got: `P=2 \ "atm", V=0.05 \ "m"^3=50 \ "L", T=20^@C=293 \ "K"`

Given those conditions, we can use `R=0.082 \ "L" \ "atm" \ "K"^-1 \ "mol"^-1`.

Plugging in the values, we get

`n=(2color(red)cancelcolor(black)"atm"*50color(red)cancelcolor(black)"L")/(0.082color(red)cancelcolor(black)"L"color(red)cancelcolor(black)"atm"color(red)cancelcolor(black)("K"^-1)"mol"^-1*293color(red)cancelcolor(black)"K"`

`n=100/(24.026 \ "mol"^-1`

`n~~4.16 \ "mol"`

So, there will be approximately `4.16` moles of the gas.