Critical solution temperature-Molar Volume of a Gas, Chemistry tutorial


Two components system

When 2 liquids are mixed together, one of the following cases may arise:

(a) The 2 liquids are completely miscible at all proportions yielding one homogeneous liquid phase, for example alcohol and water.

(b) The two liquids are moderately miscible yielding either one or two liquid phases, depending on the conditions, for instance phenol and water.

(c) The two liquids are practically immiscible yielding always 2 distinct phases under ordinary situations, for instance carbon disulphide and water.


The dangerous solution temperature is the temperature at which a mixture of two liquids, immiscible at ordinary temperatures, ceases to divide into 2 phases. The upper critical solution temperature (UCST) is the critical temperature above which the components of a mixture are miscible in all proportions. The word upper specifies that the UCST is an upper bound to a temperature range of partial miscibility, or miscibility for definite compositions only.  The lower critical solution temperature (LCST) is the critical temperature below that the components of a mixture are miscible for all compositions. The word lower specifies that the LCST is a lower bound to a temperature interval of partial miscibility, or miscibility for definite compositions only.

The mutual solubility of partially miscible liquids generally enhances through temperature. In this case, the solubility curve exhibits a maximum at the critical solution temperature above which the 2 liquids become entirely miscible at all proportions. For several liquid pairs these as ether and water, though, the mutual  solubility reduces by temperature, and the solubility curve illustrates a minimum at the critical solution temperature below that the 2 liquids become entirely miscible at all proportions.

Composition-temperature diagrams

The temperature-composition diagram of the water-phenol system as following in the figure. Outside the area bounded via the curve ABC, there take places one unsaturated homogeneous liquid phase. Within that area, 2 liquid phases in equilibrium through each other coexist; one is water saturated through phenol and the other phenol saturated by water. Any point on the curve symbolizes one saturated homogeneous phase; the existence of the saturating phase should be assumed. As the solubility curve is scarcely affected via pressure, the system might be treated as a condensed one of 2 components. For condensed systems the phase rule might be expressed as

F = C - P + 1

Where F is the number of degrees of freedom, C the number of components and P the number of phases. Outside the area surrounded via the curve, since P = 1, consequently the number of degrees of freedom F is 2, that means that the temperature and concentration, as variants, might be transformed separately. For any point on the curve, P = 2, hence F is 1, meaning that concentration must transform by temperature. For the points enclosed inside the curve, the situation is the similar for any particular layer as for any point on the curve. 

As we know that Phase is described as any homogeneous and physically distinct part of a system that is divided from other parts of the system via definite bounding surfaces.

The number of Components in a system in equilibrium is the smallest number of separately variable constituents via means of which the composition of each phase present can be conveyed either directly, or in the form of a chemical equation.

The no of degrees of freedom or variance is the number of variable factors, these as temperature, pressure and concentration, which require to be fixed in order to entirely define the conditions of a system in equilibrium.


1. In a clean dry test tube (phenol tube) weigh accurately about 1 g phenol.

2. From a burette, add 0.5 ml of distilled water. Cover the tube through a cork stopper carrying a thermometer and a stirrer, and then place in a beaker enclosing water to serve as bath.

3. Heat (or cool) gradually while the mixture is continually stirred until the 2 layers disappear forming one homogeneous layer. The 2 temperatures (t1 and t2), at which this occurs on passing from a lower (t1) to a higher (t2) temperature and the reverse, are recorded. These two temperatures should be nearly the same, and their mean gives the miscibility temperature of the mixture utilized.

4. To the similar mixture add the needed volumes of water (0.5, 1, 1.5,...) and heat steadily, and then verify the miscibility temperature of the new mixture as explained above.


1. Record the volume of water used for each composition.

2. Plot miscibility temperature against percentage water or phenol for the various mixtures.

3. From the curve attained find out the critical solution temperature and the corresponding composition.

Description measuring the molar volume:

In this experiment, we will find out the volume that is occupied by one mole of gas. We will utilize the reaction of magnesium by hydrochloric acid to produce hydrogen according to the equation:

Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)

Knowing the volume (V) of one mole (n = 1) at a temperature (T) and pressure (P) permits the computation of the general gas constant (R) in the ideal gas equation of state, generally recognized as the ideal gas law:

PV = nRT

The value of R will differ depending on the units used for pressure and volume. When P is in atmospheres and V is in liters, the value of R is 0.08206 (L atm) / (mol K). 

This equation is helpful since it permits one to compute the pressure, volume, temperature or number of moles of a gas basically via knowing the other three variables and doing a little algebra. 

Experiment summary

About 10 mL of hydrogen can be produced via the reaction of approximately 9 mg (0.009 g) of magnesium by excess hydrochloric acid. It is not possible through the balances available in our lab to weigh such a small quantity to the three figure (±0.00001 g) accuracy that would be a reasonable target for this experiment. Instead, the length of magnesium ribbon taken can be utilized to compute the mass by sufficient accuracy - see the pre-lab question. The hydrogen gas will be gathered via downward displacement of water in a measuring cylinder. The temperature and pressure at that the experiment will be executed are constant (room temperature and atmospheric pressure) and will be computed. 


  • Vernier caliper
  • 400 mL beaker
  • 10.0 mL graduated cylinder
  • 1-hole stopper to fit the cylinder
  • 10 - 15 cm of 22-gauge copper wire
  • Wash-bottle (with water)

Reagents and Materials

  • Magnesium ribbon (0.9 - 1.0 cm) cut carefully so that the ends are "square"
  • 3 M hydrochloric acid
  • Sodium hydrogen carbonate (to neutralize the hydrochloric acid)


We will be working by tiny quantities of quite concentrated hydrochloric acid. Be watchful not to get any on our skin, eyes or clothing. Wipe up small spills instantly-consult our demonstrator in the case of a serious spill. It is robustly recommended us wear latex gloves, particularly at steps (6) and (8). Replicate the experiment 3 times. 

1. Almost fill a 400 mL beaker by tap water. The water should be close to room temperature, if possible, via the time we start the reactions.

2. Attain a short (0.9 - 1.0 cm) length of magnesium ribbon. Calculate the length of the ribbon as accurately as possible by a ruler. (Ideally this should be done by a vernier caliper.) [The ends should be cut as squarely as possible - the length measurement will be utilized to compute the mass of the magnesium and requires being as accurate as possible.]

3. Wind one end of the copper wire around the magnesium ribbon and then bend them mutually so that the ribbon can't slip out. Hydrochloric acid doesn't react by copper, so copper wire can be utilized to hold the magnesium in place. Pass the free end of the wire through the rubber stopper so that the magnesium is positioned 2 to 3 cm from the narrow end of the stopper and bend it over the wide end to hold it insecurely in place. (See the picture below.)

4. Wash the 10 mL cylinder by detergent so that it isn't greasy and drains cleanly. Then pour into it about 3 mL of 3M hydrochloric acid.

5. Using a plastic wash-bottle, extremely carefully add water gradually down the side of the cylinder so that the denser acid in the bottom does not mix significantly with the water as we add it -we are trying to float the water on top! Fill the cylinder to the brim. Carefully insert the stopper through the magnesium ribbon. Several water should come through the hole in the stopper. Make sure that the hole is full of water when the stopper is firmly in place. [If we see any sign that the ribbon is reacting at this point, the acid was stirred up too much as we added the water - we should get to the next step as rapidly as possible!

6. Use our index finger to close the hole in the stopper, invert the cylinder and lower it into the beaker of water. As soon as the stopper is below the water surface we can eliminate our finger. Clamp the reversed cylinder in a vertical position. The denser hydrochloric acid should mix with the water in the cylinder and begin to react with the magnesium. We should see bubbles of hydrogen rising to fill the base end of the cylinder. Wait for all the magnesium to dissolve and then wait 2 or 3 minutes more. Tap the sides of the cylinder to dislodge bubbles from time to time.

7. Adjust the height of the cylinder so that the water levels, and the pressures, inside and outside are the similar (that is atmospheric pressure). Our demonstrator will tell we what this pressure is; it will have been computed on a barometer elsewhere in the department. Record the volume of hydrogen evolved via reading the water level on the scale on the cylinder as precisely as possible (± 0.02 mL).

8. Clean-up: Eliminate the cylinder and turn it the right way up. Pour the water out of the beaker into the sink and then empty the cylinder into the beaker. Add sodium hydrogen carbonate to the acidic solution until the evolution of carbon dioxide stops. Then flush the mixture down the sink through plenty of water. Rinse the pieces of apparatus and repeat the experiment twice more.

Data and Calculations

Complete the data table below. The following notes refer to the entries in the Data column: 

i. Our demonstrator will probably give you the value of atmospheric pressure read from the barometer in the  lab in mm Hg (torr).Convert it to atmospheres using 1 atm = 760 mm Hg.

ii. Refer to the small table below to find out the vapour pressure of water at the temperature we are reporting. Exchange it to atmospheres.

 Vapour Pressure of Water at Various Temperatures

Temperature (oC) 15       16       17    18     19      20     21     22     23     24     25    26    27      28     29 30

Pressure (mm Hg) 12.8   13.6 14.5 15.5 16.5 17.5 18.6 19.8 21.1 22.4 23.8 25.2 26.7 28.3 30.  31.8

iii. The actual hydrogen pressure will be the current atmospheric pressure (i) minus the vapour pressure of water from (ii).

Experimental Data            Run 1     Run 2   Run 3

i .Water temperature (oC)

ii. Water temperature (K)

iii. Atmospheric pressure (atm)

iv. Vapour pressure of water (atm)

v. Corrected pressure of hydrogen (atm)

vi. Volume of gas collected (L)

vii. Length of magnesium ribbon used (mm)

viii. Mass of magnesium used (g)

ix. Moles of magnesium used

x. Theoretical moles of hydrogen produced

xi. Volume hydrogen/moles hydrogen (L/mol)

xii. Gas constant R

Average value of the gas constant R (with units!): _

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