At `0^(@)C,` the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Explanation

The density `(rho)` of a gas `= PM//RT`
Here R and T are the constants for the gases
For nitrogen, `P = 5 "bar", M = 28 g mol^(-1)`
`:. rho_(N_(2)) = (PM)/(RT) = ((5 "bar") xx (28 g mol^(-1)))/(R xx T)`
For gaseous oxide, `P = 2 "bar" , M = ?`
`:. rho_("oxide") = (PM)/(RT) = ((2 "bar") xx M)/(R xx T)`
According to available data , `rho_(N_(2)) = rho _("oxide")`
or `(5 "bar") xx (28 g mol^(-1)) = (2 "bar") xx M`
`:. M = ((5 "bar") xx (28 g mol^(-1)))/((2 "bar")) = 70 g mol^(-1)`.