Adilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 l of solution. the resulting solution has an osmotic pressure of 0.605 atm at25∘cassuming that the organic compound is a nonelectrolyte, what is its molar mass?

Explanation:

1) Osmotic pressure is a colligative property, which means that it depends on the number of particles of solute present in the solvent.

2) The mathematical expression that relates osmotic pressure with the concentration of solute is:

Where:

3) Here:

4) Calculate M

             = 0.605 atm / (1 × 0.08206 L atm mol⁻¹ K⁻¹ × 298.15 K) =

             = 0.0247 atm (three significant figures)

5) Calculate number of moles, from molarity definition:

            ⇒ n = M × V (in liters) = 0.0247 M × 0.250 liter =

                    = 0.00618 moles

6) Calculate molar mass:

                             = 2.35 g / 0.00618 moles

                             = 380 g/mol ← answer

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

the number of valence electrons for each molecule or ion is shown beneath the structure. remember hydrogen will not have more than two electrons. this hydrogen is part of a covalent bond (sharing two electrons). a double bond here would cause hydrogen to share four electrons with phosphorus.