Question

Osmosis is the process responsible for carrying nutrients and water from groundwater supplies to the upper parts of trees. The osmotic pressures required for this process can be as high as 20.1 atm . What would the molar concentration of the tree sap have to be to achieve this pressure on a day when the temperature is 29 ∘C?

Answer 1

Answer:

The molar concentration would have to be 0,81 M.

Explanation:

The osmotic pressure equation is:

                                               $\pi = M R T$

where:

$\pi$: osmotic pressure [atm]

M: molar concentration [M]

R: gas constant 0,08205 [atm.L/mol.°K]

T: absolute temperature [°K]

To solve the problem, we just clear M from the osmotic pressure equation and then replace our data using the appropiate units. Clearing the variable M we have:

$M = \frac{\pi }{RT}$

We have to use temperature as absolute temperature (in kelvins), T=29+273=302 °K. Now we can replace our values in the equation:

$M = \frac{20,1 atm}{0,08205 \frac{atm.L}{mol.K} * 302 K }$

As we can see, all units will be simplified and we'll have the molar concentration in mol/L.

$M = 0,81 \frac{mol}{L} = 0, 81 M$