Question

at the boiling - point, the density of the liquid is 809 g/l and that of the gas is 4.56 g/l. how many liters of liquid nitrogen are produced when 988.0 l of nitrogen gas is liquefied at 77.36 k? be sure your answer has the correct number of significant figures.

Explanation:

Step1: Recall density - volume - mass relationship

The formula is $m =
ho V$, where $m$ is mass, $
ho$ is density and $V$ is volume. When converting from gas to liquid, the mass remains the same. First, find the mass of the gas. Given the density of the gas $
ho_{gas}=4.56\frac{g}{L}$ and volume of the gas $V_{gas} = 989.0\ L$. So, $m=
ho_{gas}V_{gas}$.
$m = 4.56\frac{g}{L}\times989.0\ L$
$m=4.56\times989.0\ g=4519.84\ g$

Step2: Calculate volume of liquid

Now, use the mass of the gas (which is equal to the mass of the liquid) and the density of the liquid $
ho_{liquid}=809\frac{g}{L}$ to find the volume of the liquid $V_{liquid}$. Rearranging the formula $V=\frac{m}{
ho}$, we get $V_{liquid}=\frac{m}{
ho_{liquid}}$.
$V_{liquid}=\frac{4519.84\ g}{809\frac{g}{L}}$
$V_{liquid}=\frac{4519.84}{809}\ L\approx5.59\ L$

Answer:

$5.59\ L$