3.2: Background

Background

There are two parts to this experiment.  In the first part, you will make two different aqueous solutions of sodium chloride and express their concentration in different ways.  Then you will place the solutions in a calorimeter containing dry ice and solidify around 20% of the water in the salt water solution and then measure the temperature at which the last bit of ice melts, and record this as the freezing point of the ice solution

The first part of this experiment is routine and the "work" is in the write up, where you need to express your solutions in multiple units.  The second part is far more challenging, but if you do your work carefully you can get real good data with the equipment we are using.  But, you can also get real bad data if you are not careful.

Part 1: Solutions

In this part of the experiment you will make two solutions of sodium chloride and report their concentrations in different units (sec. 13.1). You will add some solid salt to a 25 mL volumetric flask and dilute to volume (add water until the meniscus aligns with the calibration mark). A common mistake is to make that measurement while there is still solid (undissolved) salt in the flask.  If you can not dissolve all the salt you have a saturated solution and you have no idea what the concentration is, because you do not know how much is at the bottom (think about experiment 2). But even if you can dissolve it all, you need to double check the volume after mixing as there if often a contraction in volume upon mixing, especially if you are dissolving ionic compounds in water. 

This is because the ion-dipole forces (sec. 11.2) of the solute-solvent interactions are often stronger than the dipole/hydrogen bonding forces between water molecules, so the water is pulled in closer to the ions than it is pulled to itself, resulting in a contraction in the total volume upon mixing.  So you add the salt to the volumetric flask, fill it half way and try and mix it so all the solid dissolves.  Then you dilute it to volume.  But no matter what, make sure all the solute is dissolved before you make your final volumetric measurement.

You will save these solutions for the second part of the lab.

Part 2: Freezing Point Depression

Colligative properties (sections 3.4.3-3.4.6 ) are properties of a solvent that a solute affects, like the freezing or boiling point of the solvent.  In this lab we will measure the freezing point of the two solutions created in the first part of the lab and compare them to pure water.  You should observe that as the salt concentration increases the freezing decreases, and this can be explained by the following equation:

\[\begin{align} \Delta T & =-ik_{f}m  \\ &\text{where} \nonumber \\ i & = \text{Van't Hoff Factor} \nonumber \\ k_{f} & = \text{cryoscopic (melting point depression) constant} \nonumber \\ m & = \text{molality} \left ( \frac{mole_{solute}}{kg_{solvent}} \right ) \nonumber  \\ & and \nonumber   \\ \nonumber \Delta T & = T_{fp}\text{(solution)}-T_{fp}\text{(pure solvent)} \nonumber \end{align}\]

The value of k_f for various solvents can be obtained from table 13.4.2.

For a non-electrolyte i=1 and the Van't Hoff equation is expressed as: 

\[\Delta T  =-k_{f}m \]

Note

If the value of k_f from a thermodynamic table is negative, remove the negative sign from the above equation (use  \(\Delta T =ik_{f}m\) if k_f is a negative). That is, the freezing point is always depressed, and some table report these as positive values and others as negative values.  So be alert!

What is confusing for many people is that the Van't Hoff factor (i) is itself a function of the molality (section 13.4.5).  The Van't Hoff factor (i) takes into account the dissociation of ionic compounds upon dissolution and is the number of ions in an ionic formula for an "ideal solution." This value is approached for dilute solutions, but as the solute becomes more concentrated the solute particles interact with each other and the observed value of i is less than the number of particles the ionic compound breaks into.  The value of i can be experimentally determined by comparing the observed \(\Delta T\) with the predicted  \(\Delta T\) if the ionic compound was considered to be a nonelectrolyte (i=1).

given

\[\begin{align} & \Delta T_{real} =ik_{f}m \nonumber \\   & \;\;\;\;\;\;\;\; and \nonumber \\  &\Delta T_{\text{i=1, nonelectrolyte}}  =-k_{f}m\end{align}\]

where the second term is not taking into account the ions the solute breaks into.  If we divide the first by the second we get:

\[\frac{\Delta T_{real}}{\Delta T_{i=1}}=\frac{ik_fm}{k_fm}\]

so

\[i=\frac{\Delta T_{real}}{\Delta T_{i=1}}\]

That is, we simply divide the observed temperature depression by that which we would get if we did not take into account the dissociation of the ionic compound.

There are two major problems with measuring the freezing point of a salt water mixture.  First, is freezing the substance and second, is that the moment some of the water freezes the concentration of the salt in the liquid phase goes up, and so the freezing point goes down.  The video in section 13.4.4 shows how the freezing point depression results from the solute interfering with the growth of the crystal, which are essentially pure water (although salt particles do get trapped in the crystal, most likely in the interstitial regions). A consequence is that pure water has a constant temperature as it goes from pure liquid to pure solid, while salt water does not.  So if you froze a container of pure water the temperature would be the same if it was 90% water/10% ice or 10% water/90% ice. In contrast a salt water mixture water would be warmer when it was 90% salt water/10% ice and colder when it was 10% salt water/90% ice.  An interested biological effect of this is that there are lateral bands in polar sea ice of brine (salt water) channels that support a subzero ecosystem complete with brown photosynthetic algae that migrate vertically up and down the ice pack due to seasonal temperature variations (figure \(\PageIndex{1}\), NOAA PMEL Artic Zone).

 

 

Figure \(\PageIndex{1}\): Band of brown sea ice algae living in salt water (brine) channels in Artic sea ice. Near the surface the temperature can get down to -35^oC while deeper down it warms up, and living organisms can live in the brine channels when the temperatures are above -5^oC. The salinity of the channels changes as the temperature changes and so there are bands that the brown photosynthetic organisms can live in, and these migrate up and down the ice pack due to seasonal temperature changes.  It is estimated that sea ice algae are responsible for up to 57% of the primary photosynthetic production in the artic and the brown pigments are due to spectral changes of the light as it passes through the ice pack (see PMEL Artic Zone) (Copyright; Artic Zone, Pacific Marine Environmental Laboratory, NOAA)

It would be nice if we had a sub-zero freezer with a watch glass that allowed us to control and observe the temperature at which the salt solution freezes, but we do not have one.  So we are going to use an endothermic reaction to cool the solution down, the sublimation of solid carbon dioxide.  We will place the salt water in an 8 in test tube and then put the test tube in thermal contact with dry ice. The problem is that at 1 atm dry ice sublimes at -78.5^oC and so will very quickly the salt water.  You will place a digital thermometer into the salt water solution and then place in an open calorimeter that has some dry ice shavings.  The temperature will cool very rapidly until the solution starts to freeze, and you want to freeze about 10% of the solution, and then pull it out of the cold calorimeter and place in an Erlenmeyer flask. Initially the ice will be at the bottom of the test tube, where it was in contact with the dry ice, and that part of the test tube will be colder than the rest. You need to stir the solution and make sure the ice floats to the top before it melts and record the temperature when the last piece of ice melts.  You can only know the molality when the last bit of ice melts and you need to be sure you have a constant temperature throughout the solution when you record that measurement, so it is imperative that you stir the solution while you are melting the ice.  If done with care, you can get very accurate data, but it is tricky.