Question

where would you find the most particles: in the sahara desert at a depth of two meters, 18 ml of water or an iron bolt with a mass of 56 g? by particles i mean, sand grains, water molecules and iron atoms. click the view image button to view the three pictures. a) in the iron bolt! it is quite heavy, and iron atoms are very small b) there are roughly the same amount of particles on each picture c) in the sahara desert! the desert is huge, and sand grains are small d) in the water glass! a shot of water isnt very large, but water molecules are super

Explanation:

Step1: Calculate number of particles in water

The molar mass of water ($H_2O$) is $M=(2\times1 + 16)\text{ g/mol}=18\text{ g/mol}$. The density of water is $
ho = 1\text{ g/ml}$, so for $V = 18\text{ ml}$ of water, the mass $m=
ho V=18\text{ g}$. The number of moles $n=\frac{m}{M}=\frac{18\text{ g}}{18\text{ g/mol}} = 1\text{ mol}$. According to Avogadro's number $N_A=6.022\times 10^{23}\text{ mol}^{-1}$, the number of water - molecules $N_{water}=n\times N_A=6.022\times 10^{23}$.

Step2: Calculate number of particles in iron

The molar mass of iron ($Fe$) is $M_{Fe}=55.85\text{ g/mol}$. For a mass $m_{Fe}=56\text{ g}$ of iron, the number of moles $n_{Fe}=\frac{m_{Fe}}{M_{Fe}}=\frac{56\text{ g}}{55.85\text{ g/mol}}\approx1\text{ mol}$. The number of iron - atoms $N_{Fe}=n_{Fe}\times N_A\approx6.022\times 10^{23}$.

Step3: Estimate number of sand - grains in Sahara desert

The Sahara desert has a vast volume, but sand grains are much larger than atoms or molecules. Even at a depth of 2 meters, the number of sand - grains is much less than the number of atoms or molecules in 1 mole of a substance.

Answer:

B. There are roughly the same amount of particles on each picture