Question

If the concentration of the fluid inside a tree is about 0.15 M greater than the groundwater that bathes the roots, how high will a column of fluid rise in the tree at 19°C? Assume that the density of the fluid is 1.1 . (The density of mercury is 13.6 .) m

Answer 1

The fluid column will rise a height of 3720.96 cm

Step-by-step explanation:

The osmotic pressure is equal:

`P_(osm) =MRT`

Where

M = 0.15 M

T = 19ºC = 292 K

Replacing:

`P_(osm) =0.15*0.0821*292=3.6atm=273.6cmHg`

The height is:

`h=P_(osm) \rho`

Where

ρ = 13.6 g/cm³

Replacing:

`h=273.6*13.6=3720.96cm`

Answer 2

The height is
`h =37.17m`

Step-by-step explanation:

From the question we are told that

The concentration inside a is tree
`M= 0.15M`

The temperature condition is
`T = 19^oC = 19+ 273 = 292K`

The density of the fluid is
`\rho = 1.1 g/cm^3`

The density of mercury is
`\rho__(Hg) = 13.6 g/cm^3`

Generally osmotic pressure experience is mathematically represented as

`P_o =MRT`

Where R is the universal gas constant with a value of R = 00821 L.atm/K/mol

`P_o = 0.15 * 0,0821* 292`

`=3.59598 atm`

Converting to cm of Mercury

`P_o = 3.59598 * 76 cm of Hg`

`= 273.29 \ cm \ of \ Hg`

Generally pressure is mathematically represented as

`P = (Height )/(Density )`

Now making height the subject

`Height = pressure * Density`

Where pressure is
`= 273.29 \ cm \ of \ Hg`

and Density is
`\rho__(Hg) = 13.6 g/cm^3`

So we have

`Height (h) = 273.29 * 13.6`

`= 3716.8 cm`

In meters h
`= (3716.8)/(100) = 37.17m`

`h =37.17m`