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

The number of moles =

`Moles=4.97* 10^(-8)`

The number of molecules =

`Molecules = 2.99* 10^(16)`

Step-by-step explanation:

Volume of the sphere is given by :

`V=(4)/(3)\pi r^(3)`

here, r = radius of the sphere

`radius=(diameter)/(2)`

`radius=(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=(4)/(3)\pi 0.03^(3)`

`V=(4)/(3)\pi 2.7* 10^(-5)`

`V=1.13* 10^(-4)dm^(3)`

`V=1.13* 10^(-4)L` (1 L = 1 dm3)

Now, concentration "C"=

`C=4.4* 10^(-4)moles/liter`

The concentration is given by the formula :

`C=(moles)/(Volume(L))`

This is also written as,

`Moles = C* Volume`

`Moles=1.13* 10^(-4)* 4.4* 10^(-4)`

`Moles=4.97* 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* 10^(23)`

Molecules =

`Molecule=4.97* 10^(-8)* 6.022* 10^(23)`

`Molecules = 2.99* 10^(16)` molecules