Derive the formula:
d=M[1/m+MB/1000]
where d=density of solution
M=Molarity of solution
m=molality of solution
MB=molar mass of solute
Answers
Answer:
The atomic weight scale defines the masses of atoms relative to the mass of an atom of carbon (C). The mass of one carbon atom exactly 12.000 atomic mass units (amu).
Why? The number 12 is chosen so that the least massive atom, hydrogen, has a mass of about 1 on the same scale!
Next, the gram atomic weight scale was defined, so that atoms could be be expressed in terms of well known units like ‘grams’, and was in correspondence to the atomic mass unit.
Generally, any element E with an atomic mass N, 1 atom of D weighs N a.m.u and 1 atomic-weight of D is N g. Thus, for element C (carbon) with atomic mass 12, 1 atom of C weighs 12 a.m.u and 1 gram atomic-weight of C is 12 g.
It was estimated that for 1 gram atomic-weight of carbon or 12 g or carbon, there are 6.022 x 10^23 atoms (remember, 1 atom of C weighs 12 a.m.u) of C. This number is called a mole or Avogadro’s number, denoted by Na. Mole is a unit of number. Just like a dozen refers to 12 units, a mole refers to 6.022 x10^23 units! One can also say that 12g is the weight one mole of C atoms.
For any element like carbon, or any molecule, we can relate this number Na to its atomic-weight in g by the equation,
Na atoms/mole x 12 amu /atom = (Na x 12 amu) /mole = 12g/mol
(Total number of atoms per mole) multiplied by the (weight of each atom) = Weight per mole.
This weight is referred to as the ‘formula mass’ of an element/molecule.
Molarity: It is defined as the moles of a substance/solute in 1 liter of a solution.
Say you’ve dissolved 100g of NaCl (table salt, with formula mass: 58.44 g/mol) in 4 liters of water, what’s the molarity? First we find the number of moles. Since 58.44 g gives 1 mole of NaCl molecules, 100g gives 1.71 moles of NaCl. Thus, the molarity would be 1.71/4 = 0.43 moles/L.
Molality: It is defined as the moles of a substance/solute in 1 kg of a solvent.
If 300 g of sugar(molar mass: 342 g/mol) is dissolved in 1500 g of water, the molality would be number of moles (342/300=0.87 moles) divided by 1500/1000 = 1.5 kg of solvent. Thus molality will be 0.87/1.5 = 0.58 moles/kg
The preparation of a solution of a given molality involves weighing both solute and solvent and getting their masses. But in the case of molarity, the volume of the solution is measured, which leaves room for variations in density as a result of the ambient condition of temperature and pressure.
Mole fraction: Mole fraction is another way of expressing the concentration of a solution or mixture. It is equal to the moles of one component divided by the total moles in the solution or mixture.
For example, if 3.47 moles of water and 8.54 moles of acetone are mixed together, the mole fraction of water will be 3.47 divided by the total moles (which is 12.01), and is therefore 0.289