(10 pts.) In a recent experiment conducting during a swimming competition at an indoor swimming pool, the gas-phase concentration of trichloramine (NCl$_3$, molecular weight = 120 g/mole) reached a peak value of 273 ppbv. The experiment was conducted under conditions of a total atmospheric pressure of 1.00 atm and a temperature of 25.0°C.
Express this gas-phase concentration as mass concentration in units of $\mu$g/m$^3$. For context, note that signs of irritation of the human respiratory system become evident at gas-phase NCl$_3$ concentrations of about 500 $\mu$g/m$^3$.
Note the following unit conversions and the value of the gas constant ($R$):
1 $\mu$g = 10$^{-6}$ g
1 m$^3$ = 1000 L
$R$ = 0.08205 $\frac{L \cdot atm}{K \cdot mole}$