So you want to calculate a change for a solution compared to a pure solvent? You need the formula for the colligative property. There are three things to remember about such calculations.
1. They assume what matters is the total concentration of "stuff" in the solution (not what that stuff is). This is what we mean by colligative property. What matters is the concentration and the solvent.
2. The above statement is an approximation, so don't expect these answers will be exact in the real world.
3. The formulas all have different historical derivations. As such, they tend to use different concentration units. The concept is always the same. In the details of the calculations, be sure to pay attention to the units.
Boiling Point elevation
\[ \Delta T = iK_b \; m\]
\(K_b\) is a constant that depends on the solvent and m is the total solute concentration in molality. The little "i" is the van't Hoff factor for how many ions an electrolyte breaks up into. If you have a mixture of many solutes. You need to remember the concentration that matters is the total concentration of solute "particles". So in this case you have to add up i times the molality for each solute. This also assumes that the solute is non-volatile (that is the vapor pressure of the solute itself is approximately zero). Therefore this will work well for solutions like salt in water since NaCl is non-volatile. It won't work well for solutions like ethyl alcohol in water since the alcohol itself also has a vapor pressure.
Freezing Point depression
\[ \Delta T = -iK_f \; m\]
Again \(K_f\) is a constant that depends on the solvent and m is the total solute concentration in molality. Sometimes this formula doesn't have the negative sign and you simply need to remember that freezing point goes down.
Vapor Pressure
There are two formulas for vapor pressure of a solution. They are really exactly the same. One is written in term of the concentration of the solute and the other in the concentration of the solvent. The solvent formula is the following
\[P_{\rm solution} = \chi _{solvent} \; P^{\circ}\]
Where \(P^{\circ}\) is the vapor pressure of the pure solvent. This relationship is known as Raout's Law. The formula can be re-written as a change in vapor pressure as
\[\Delta P = -\chi _{solute} \; P^{\circ}\]
Because this formula is written in terms of mole fraction, it is not easy to include the i for the van't Hoff factor in this formula since uses mole fraction to measure the concentration (and the moles of solute will appear in both the numerator and denominator of the fraction). You still need to include the fact that you have multiple ions for an ionic solute. For example if you have a 1m solution of NaCl in water. This is 1 mole of NaCl in 1 kg of water. 1 mole of NaCl will lead to 2 moles of solute (1 mole of Na+ and 1 mole of Cl-). 1kg of water is 55.55 moles of water. Therefore the mole fraction of solute is 0.035 [(2)/(2+55.55)]. Note: this is very close to what you get if you just look at the ratio of moles of solute to moles of solvent 0.036 (2/55.55).
Osmotic Pressure
The osmotic pressure for a solution is found from the concentration in molarity and is the same regardless of the solvent. It is
\[ \Pi = iMRT\]
where the osmotic pressure is Π, i is the van't Hoff factor, M is the molarity of the solute, R is the ideal gas constant (typically in units of L-atm K-1 mol-1, and T is the temperature in the Kelvin. Note the units of the gas constant will determine the pressure units.
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