# What is the density of NH_3 gas at 435 K and 1.00 atm?

Feb 16, 2017

From the ideal gas equation: $\frac{n}{V} = \frac{P}{R T}$. Agreed? And we assume ideality for ammonia gas (good enuff for a first approx.).
We get $\rho \approx 0.5 \cdot g \cdot {L}^{-} 1$

#### Explanation:

But $n = \text{Mass"/"Molar mass}$.

Thus $\text{Mass"/"Molar mass} = \frac{P V}{R T}$

And on rearrangement, $\text{Mass"/"V"=(P)/(RT)xx"Molar mass}$

But, by definition, $\text{density, "rho="Mass"/"Volume"=(P)/(RT)xx"Molar mass}$

$= \frac{1.00 \cdot \cancel{a t m} \times 17.03 \cdot g \cdot \cancel{m o {l}^{-} 1}}{0.0821 \cdot L \cdot \cancel{a t m} \cdot \cancel{{K}^{-} 1} \cdot \cancel{m o {l}^{-} 1} \times 435 \cdot \cancel{K}} =$

??g*L^-1

So this expression gives us an answer in $g \cdot {L}^{-} 1$ as required for a density.