# A sample of N_2O gas has a density of 2.85 g/L at 298 K. What must be the pressure of the gas (in mmHg)?

Jun 2, 2017

1.58 Atm

#### Explanation:

From Ideal Gas Law (PV = nRT)

$P = \left(n R \frac{T}{V}\right) = \left(R \left(\text{mass"/"f.wt}\right) \left(\frac{T}{V}\right)\right)$

$P = R \left(\text{mass"/"Volume")(T/"f.wt.}\right)$= $R \left(\text{Density")(T/"f.wt.}\right)$

Given:
$R = 0.08206 \left(\text{L-Atm"/"mol-K}\right)$
$\text{Density} = 2.85 \left(\frac{g}{L}\right)$
$T = 298 K$
$f . w t . = 44 \left(\frac{g}{\text{mol}}\right)$

$P = {\left(0.08206 \text{L-Atm"/"mol-K")(2.85g/L)(298K)(44g/"mol}\right)}^{-} 1 = 1.58 A t m$