Question

1. ammonium nitrate, a substance commonly used as a fertilizer, can decompose explosively under the right conditions. this happened in beirut, lebanon in august 2020, when approximately 2700 metric tons (2.7 x 10^6 kg) of ammonium nitrate exploded, leveling much of the nearby neighborhood, killings hundreds. this explosive process produced about 1.2 x 10^6 kg of water vapor, in addition to a mixture of nitrogen and oxygen gases. if this mixture had a density of 1.1 g/l, how many liters of it was released in the explosion? you need to be careful with units in this problem.

Explanation:

Step1: Convert mass to grams

We know that $1$ kg = $1000$ g. Given the mass of ammonium nitrate is $2.7\times 10^{6}$ kg. So the mass in grams is $m=(2.7\times 10^{6})\times1000 = 2.7\times 10^{9}$ g.

Step2: Use density - volume formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We are given $
ho = 1.1$ g/L. Rearranging the formula for volume gives $V=\frac{m}{
ho}$.
Substituting $m = 2.7\times 10^{9}$ g and $
ho=1.1$ g/L into the formula, we get $V=\frac{2.7\times 10^{9}}{1.1}\approx2.45\times 10^{9}$ L.

Answer:

$2.45\times 10^{9}$ L