Experiment: Diffusion Coefficient of NaCl in water

Introduction

The purpose of this experiment is to determine the diffusion coefficient of NaCl in distilled water. Diffusion is an important property of many materials. Its importance is more significant than ever, where the transfer and distribution of materials is involved and quantitative values are needed to be determined.

Results

Measurement taken every 30 seconds, conductivity @ time 0 = 0.294mS

Temperature (°C)	TIME (Minutes)	Conductivity (S)	Temperature (°C)	TIME (Minutes)	Conductivity (S)
31.9	0.5	0.287	32	8	0.375
31.9	1	0.273	32	8.5	0.374
31.9	1.5	0.272	32.1	9	0.372
31.9	2	0.289	32.1	9.5	0.379
31.9	2.5	0.407	32.2	10	0.374
31.9	3	0.383	32.2	10.5	0.388
31.9	3.5	0.384	32.2	11	0.387
31.9	4	0.381	32.2	11.5	0.383
31.9	4.5	0.374	32.2	12	0.389
31.9	5	0.374	32.2	12.5	0.39
31.9	5.5	0.38	32.3	13	0.388
32	6	0.371	32.3	13.5	0.394
32	6.5	0.371	32.3	14	0.396
32	7	0.371	32.3	14.5	0.389
32	7.5	0.371	32.3	15	0.388

Temperature (°C)	TIME (Minutes)	Conductivity (S)
32.4	16	0.41
32.4	17	0.418
32.5	18	0.42
32.5	19	0.432
32.6	20	0.441
32.6	21	0.446
32.7	22	0.447
32.7	23	0.449
32.7	24	0.447
32.8	25	0.445
32.8	26	0.456
32.9	27	0.465
32.9	28	0.467
33	29	0.467
33	30	0.463

Conductivity measurements taken every 1 minute.

The results of the conductivity measured were then plotted against time on the following graph.

The equation of a line is included as well as the coefficient of determination value. A trendline is fitted to the as a line of best fit as the data points are not exactly in linear form.

Calculations

Calculating the diffusivity of NaCl in water. The following equation will be used to calculate this, specifically it is the calculation of which is the diffusivity of A in B.

)

dCa/dt is the diffusion coefficient and this value is the slope of conductivity Vs. time graph above.

A = the area through which mass transfer occurs

D_AB = diffusion coefficient of A in B

C_A1 = the concentration of the saline solution inside the diffusion cell.

C_A2 = the concentration of salt in the bulk solution within the diffusion tank.

Z = diffusion path length = 5 mm

V= Diffusion tank volume

The following calculation is of the total area of the pores in the diffusion cell where the NaCl will transfer into the water.

A = Area of Diffusion Cell

D = pore diameter = 1mm

N = number of pores = 317                   

A = 2.489 -10^-4m²

Water was added to the diffusion tank to height of 170mm. This value along with the tanks cross sectional area (14.4 10^-3 m² were used to calculate the volume of the diffusion tank.

Calculation of diffusion tank volume= 14.4 10^-3 m²0.170m

= 2.448m³

3 values were chosen for the conductivity (concentration of salt in the water in the diffusion tank) from the graph for the calculation of D_AB.

1. 0.374 S/cm
2. 0.410 S/cm
3. 0.456 S/cm

)

From the slope of the graph:

A= 2.489 -10^-4m²

mS

mS

Z = diffusion path length = 5 mm

V= 2.448m³

Substituting each of the values into the above equation gives:

1. 

Rearranging for :            

2. 

3. 

Average value of diffusivity of NaCl in water.

Average

Average =

Questions

To determine the accuracy of the measured value achieved in the experiment, a reference value is required. The reference value for the diffusivity of NaCl in water is 1.9910^-9 m²/s  @ 37°C.(1)

Taking the temperatures of the 3 conductivity readings that were used in the calculation of    they were averaged to adjust against the reference value.

1. 0.374= 32.2°C

2.0.410=32.4°C

3. 0.456 =32.8°C

Average temp =32.5°C

Reference value temperature = 37°C

An approximate temperature coefficient value of 2%/°C can be used to adjust the conductivity value of the measured value relative to the conductivity of the reference value.

2 4.5= 9

Adjusting the measured value to the same temperature of the reference value will give us

=

Adjusted Diffusivity Value

Difference between 2 values = 1.675  10^-6

A much higher rate of diffusion was achieved on this occasion compared the reference value of the rate of diffusion of NaCl in water.

Discussion

It is well known that a change in the temperature of a solution will result in the change of conductivity. An increase in temperature results in an increase in conductivity. The increase that is observed is as a result of a number of factors. Firstly, the increase in temperature can cause ionic compounds to split resulting in an increasing number of ions in the solution. So in this experiment the diffusivity of NaCl in H₂O, the NaCl compound will break apart resulting in Na and Cl ions surrounded by H₂O molecules. As the NaCl (in water it is classed as an electrolyte) dissolves (diffuses) charged ions (Na and Cl) are formed that can carry charge.

Secondly, the increasing temperature of a solution can result in a lower viscosity. This in turn increases ion mobility throughout the H₂O, which further increases the ability of the ions to carry the charge throughout the solution and therefore increases conductivity. These two factors highlight the significance that temperature plays in the diffusivity of a compound in a solution. Not including the variation of temperature would certainly have affected the final value. The conductivity of the stock solution was given as 189.6 mS at 22°C. This value wasn’t adjusted to a more accurate temperature at which the experiment was performed at which was approximately between 32-33°C. The measured value from the calculation of may not be completely accurate.

The majority of substances that dissolve in a solvent such as NaCl in water already have diffusion coefficients predetermined which allows one to compare the accuracy of the measurement against. Diffusion coefficients are measured at specific temperatures because of the fact that there value is temperature dependent. If the experiment was not carried out at the reference diffusion coefficients temperature then a temperature compensation method may be used, which was the case in this experiment, where the measured value was adjusted to the reference value. Compensation methods include both linear and non-linear methods to adjust the conductivity value attained with a %/°C value.

However these methods are not completely accurate and it is preferable that a conductivity measurement be taken at the same temperature as the reference value. This is particularly true where highly accurate measurements are required. In this experiment no variation in temperature was assumed. To incorporate a variation in temperature one could use a temperature compensation method but as I’ve mentioned this isn’t entirely accurate. These factors are only likely to have relatively minor inaccuracies.

Comparing the two values there are several orders of magnitude of a difference. Several factors have influenced this including errors in the actual apparatus for measuring the conductivity in the diffusion cell as well as the errors that occurred during the experiment. It can be seen from the early measurements of conductivity that something went wrong with one or more of the apparatuses as erroneous results were produced.  From the 4^th to the 5^th measurement there is a large jump in conductivity. This large sudden variation in conductivity was caused by an air bubble blocking the conductivity meter. The air bubble present in the diffusion cell gave the false conductivity measurement. This resulted in an outlier in the conductivity versus time graph. A trendline was fitted to the graph to allow the slope to be calculated as the outliers present result in a non-linear graph. Despite this trendline this large variation certainly affected the final measured value.

From the point of view of the apparatus it does certainly have some limitations.  The heating element is at one end of the device and so it doesn’t give a consistent dispersion throughout the tank as the side of the tank nearest the element would be of a slightly higher temperature than the rest of the tank. It is difficult to say how much this would affect the diffusivity but it is something to consider.

Conclusion

A quantitative value for the diffusivity of NaCl in water was determined. The calculated measured value attained was compared against a reference value and a large discrepancy was observed between the two values. The reasons for the discrepancy from an experimental and theoretical point of view have being outlined in the discussion.

References:

1. Barron, J. and Ashton, C. (2008) ‘The Effect of Temperature on Conductivity Measurement’, County Clare, Ireland.
2. Lide, D.R. and Staff, L.D.R. (2007) CRC handbook of chemistry and physics, 88th edition (Crc handbook of chemistry and physics). 88th edn. Boca Raton, FL: CRC Press.