Question

Question #13daf

Answer 1

Start from the ideal gas law equation, `PV= nRT`, where n is the number of moles.

The number of moles can be written as the ratio between the weight of the gas, i.e. its mass, and its molecular mass.

`n = m/M_M`

This means that you can write

`PV = (m/M_M)RT`

Density is defined as mass per unit of volume

`rho = color(blue)(m/V)`

Therefore, if you rearrange the equation, you obtain

`PV = m/M_M * RT => P * M_M * V = mRT`

`P * M_M = color(blue)(m/V) * RT = rho * RT`

As a result,

`M_M = (rho * RT)/P = (1.43 "g"/cancel("L") * 0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * (273.15 + 23)cancel("K"))/("0.789"cancel("atm")`

`M_M = "44 g/mol"` `->` rounded to two sig figs.

The gas could be carbon dioxide, `CO_2`.