Question

how many molecules of sulfuric acid are in a spherical raindrop of diameter 6.0 mm if the acid rain has a concentration of 4.4 * 10^-4

Answer 1

Answer:

The number of moles =

$Moles=4.97\times 10^{-8}$

The number of molecules =

$Molecules = 2.99\times 10^{16}$

Explanation:

Volume of the sphere is given by :

$V=\frac{4}{3}\pi r^{3}$

here, r = radius of the sphere

$radius=\frac{diameter}{2}$

$radius=\frac{6.0}{2}$

Radius = 3 mm

r = 3 mm

1 mm = 0.01 dm (1 millimeter = 0.001 decimeter)

3 mm = 3 x 0.01 dm = 0.03 dm

r = 0.03 dm

("volume must be in dm^3 , this is the reason radius is changed into dm"

"this is done because 1 dm^3 = 1 liter and concentration is always measured in liters")

$V=\frac{4}{3}\pi 0.03^{3}$

$V=\frac{4}{3}\pi 2.7\times 10^{-5}$

$V=1.13\times 10^{-4}dm^{3}$

$V=1.13\times 10^{-4}L$   (1 L = 1 dm3)

Now, concentration "C"=

$C=4.4\times 10^{-4}moles/liter$  

The concentration is given by the formula :

$C=\frac{moles}{Volume(L)}$

This is also written as,

$Moles = C\times Volume$

$Moles=1.13\times 10^{-4}\times 4.4\times 10^{-4}$

$Moles=4.97\times 10^{-8}$moles

One mole of the substance contain "Na"(= Avogadro number of molecules)

So, "n"  mole of substance contain =( n x Na )

$N_{a}=6.022\times 10^{23}$

Molecules =

$Molecule=4.97\times 10^{-8}\times 6.022\times 10^{23}$

$Molecules = 2.99\times 10^{16}$ molecules