Graham’s Law – Diffusion of Gasses PDF

Preview

Summary

Will help with the difficult of physical chemistry lab by showing how to do each calculations....

Description

Graham’s Law – Diffusion of Gasses

Physical Chemistry 3310

Abstract The objective of this experiment was to determine the molar mass of a gas using Graham's law. In a series of two trials, the relative rates of diffusion of two gases (hydrogen chloride and ammonia) will be measured. Gases are made up of continually moving particles. Gases diffuse (travel across space) and completely mix because of this motion. When these two gases mix they will have created a white smoke ring of salt where the gases collide: HCl(g) + 𝑁𝐻3 (g) ->

𝑁𝐻3 CL (s). The expected outcomes are that temperature and diffusion are straightforwardly proportional, and that larger particles diffuse more slowly than smaller molecules. With that, ammonia travel faster than hydrogen chloride. After several calculations, the average molar mass was 30.36g/mol. The percentage error from the experiment was about 16.73%. Some error

during the experiment that could have caused the result to be less than perfect were incorrect measurement, incorrect drops between the two, cross contamination, timing and more.

Introduction Presently, a gas is a condition of matter in which it will expand freely to fill the whole capacity of a container, with no set shape or volume. We can easily measure or detect the activity of the gas. To investigate the activity of the atoms, however, we should use a theoretical model. The Kinetic Theory of Gases model assumes that particles are relatively tiny in comparison to the distance between atoms. The gases are in constant, erratic motion and frequently collide with one another and with the container's wall (elastic collision) (Slabaugh). A gas with these properties is referred to be an ideal or perfect gas. Some assumptions of an ideal gas are that the gas comprises of little particles in which the volume of the particles is negligible compare with the volume of the container. Also, the gas particles are in consistent, arbitrary motion. Must be colliding with one another and have elastic collisions. Lastly, no force are no intermolecular powers in play (Slabaugh). When the kinetic energy of a particle reaches the incomparable zero at temperature, it undergoes diffusion. Graham's law is linked to Kinetic Molecular Theory and is a modified version of the theory. The Graham's Law was created in the mid eighteenth century by Thomas Graham who found it by noticing effusion of gases through a thin plug of mortar of Paris (Mason). Effusion is the interaction of a confined gas getting away through a little opening in its container. Some limitations are the hole should be little to the point that an atom has no choice to collide into one

another (Hawkes). Diffusion is the cycle by which gas atoms blend in with different gas particles without interference. Some limitation is: there must be a diffusing between two gases, the pressing factor should be steady, and the rate should indicate s/mol. (Hawkes). Both effusion and diffusion are identified with the speed of the gas atoms. Gases with low molar masses emit and diffuse at a quicker rate than gasses with higher molar masses. The speed (or rate) at which gas particles move is proportional to the square of the square root of their molecular weights In this experiment, a 60 cm long and measurement of 1.5 cm tube was gotten. Get two clamps into the beam to support the lab bench. Acquire two cotton balls and utilize a glass pipette to soke one in HCl and one in NH3. Utilize a 1-opening plugs that fit in the open closures of the glass tubing. These two gases will diffuse in the glass tube and when they come in touch, they will respond to deliver ammonium chloride, a white strong which will be stored inside the glass tube as confirmed by the presence of a white ring (Ruckstuh). When the ring of ammonium chloride showed up, the distance of the white ring from the tip of the cotton ball at each finish of the end was measured with a ruler. The plugs were then taken out, the cotton balls were taken out. This cycle was then finished 1 additional time. 𝑅

√𝑀

Afterwards we used, ( 1 ) = ( 2) to get the rate of diffusion (Ruckstuhl). Then find the 𝑀1 𝑅 1

average of the determination to find molar mass. The average rate of diffusion was found to be 𝑔

27.39 𝑚𝑜𝑙 𝑎𝑛𝑑 33.32

𝑔

𝑚𝑜𝑙

. This was done by taking the average distance of each determination

from the salt ring to the tip of the end of the cotton ball and dividing them using the equation the Graham’s Law. Then averaging the rate to diffusion to get the Molar mass, 30.36

𝑔

𝑚𝑜𝑙

. The

percentage error was calculated to be 17.63%.

Experimental Method 1. Obtain a clean and dry glass tube with a length of 60 cm in length and diameter of 1.5 cm 2. Grab two utility clamps, a timer, and a ruler. 3. Clamp the tube to the support the beams in the lab bench 4. Obtain two cotton balls and two 1-hole stoppers that fit in the open ends of the glass tubing. 5. Using a glass pipette, add a few drops of concentrated solution of ammonium hydroxide to one of the cotton balls.

6. Using a different glass pipette, add a few drops of concentrated hydrochloric acid to the other cotton ball. 7. Place the two saturated cotton balls in the open ends of the glass tubing, immediately insert the two 1-hole stoppers 8. Once in each open end and start the timer. 9. Closely monitor the glass tubing for evidence of the formation of a white ring. 10. Once that the white ring forms, stop the timer and record the elapsed time, t. 11. Using a ruler, measure the distance from each end to the white ring. 12. Remove the stoppers from the ends of the glass tubing and disposed the cotton balls. 13. Rinse the glass tubing with tap water, then rinse with distilled water, and finally rinse with acetone. Allow to dry. 10. Repeat the steps1-13 for a second trail

Results Values found from the experiment:

𝑇𝑖𝑚𝑒 𝑒𝑠𝑐𝑎𝑝𝑒𝑑, 𝑡

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑 𝑏𝑦 𝑁𝐻3 (𝑔), 𝑑𝑁𝐻3

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑 𝑏𝑦 𝐻𝐶𝐿 (𝑔), 𝑑 𝐻𝐶𝐿

1 𝑠𝑡 determination

2𝑛𝑑 determination

260 Sec (4 mins. 20 sec.)

262 Sec (4 mins. 22 sec.)

33 cm

31.5 cm

26 cm

22.5 cm

1 𝑠𝑡 determination

2𝑛𝑑 determination

Rate of diffusion value:

Rate of diffusiuon by 𝑁𝐻3

Rate of diffusiuon by 𝐻𝐶𝐿

0.12692308 𝑐𝑚

0.100 𝑠

𝑐𝑚 𝑠

0.12022901

0.08587786

𝑐𝑚 𝑠 𝑐𝑚 𝑠

Molar mass of HCL: 1 𝑠𝑡 determination Molar mass of HCL:

21.62

2𝑛𝑑 determination

𝑔

23.75

𝑚𝑜𝑙

𝑔

𝑚𝑜𝑙

Average Molar mass of HCL: Average 𝑀𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐻𝐶𝐿, 𝑀𝐻𝑐𝑙

30.36

𝑔

𝑚𝑜𝑙

Percentage error: Average 16.43%

% Error

Appendices Finding the rate of diffusion:

1st determination:

1st determination:

Rate of diffusiuon, cm (𝑁𝐻3 )

Rate of diffusiuon, cm (𝐻𝐶𝐿)

=(

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑒𝑑, 𝑐𝑚 ) 𝑡𝑖𝑚𝑒 𝑒𝑙𝑎𝑝𝑠𝑒𝑑, 𝑠

33𝑐𝑚 Rate of diffusiuon (𝑁𝐻3 ) = ( ) 260 𝑠

Rate of diffusiuon (𝑁𝐻3 ) = 0.12692308

𝑐𝑚 𝑠

=(

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑒𝑑, 𝑐𝑚 ) 𝑡𝑖𝑚𝑒 𝑒𝑙𝑎𝑝𝑠𝑒𝑑, 𝑠

26𝑐𝑚 Rate of diffusiuon (𝐻𝐶𝐿) = ( ) 260 𝑠 𝑐𝑚 Rate of diffusiuon (𝐻𝐶𝐿) = 0.100 𝑠

2nd determination:

2nd determination:

Rate of diffusiuon, cm (𝑁𝐻3 ) =(

Rate of diffusiuon, cm (𝐻𝐶𝐿)

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑒𝑑, 𝑐𝑚 ) 𝑡𝑖𝑚𝑒 𝑒𝑙𝑎𝑝𝑠𝑒𝑑, 𝑠

Rate of diffusiuon (𝑁𝐻3 ) = (

=(

31.5𝑐𝑚 ) 262 𝑠

Rate of diffusiuon (𝑁𝐻3 ) = 0.12022901

Rate of diffusiuon (𝐻𝐶𝐿) = (

𝑐𝑚 𝑠

The Graham Law

M2 M1

Base it on to the experiment (

22.5𝑐𝑚 ) 262 𝑠

Rate of diffusiuon (𝐻𝐶𝐿) = 0.08587786

Calculate the molar mass of HCL:

R1 = R2

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑒𝑑, 𝑐𝑚 ) 𝑡𝑖𝑚𝑒 𝑒𝑙𝑎𝑝𝑠𝑒𝑑, 𝑠

√𝑀𝐻𝑐𝑙 𝑅𝑁𝐻3 )=( ) 𝑅𝐻𝐶𝐿 √𝑀𝑁𝐻3

Rearrange to find 𝑀𝐻𝑐𝑙 (molar mass) of HCL:

𝑅𝑁𝐻3 ∗ √𝑀𝑁𝐻3 = √𝑀𝐻𝑐𝑙 𝑅𝐻𝐶𝐿

𝑅𝑁𝐻3 ∗ √𝑀𝑁𝐻3 = √𝑀𝐻𝑐𝑙 )2 ( 𝑅𝐻𝐶𝐿 𝑀𝐻𝑐𝑙 = 𝑀𝑁𝐻3∗(

𝑅𝑁𝐻3 2 ) 𝑅𝐻𝐶𝐿

𝑐𝑚 𝑠

Plug in the values:

Given 𝑀𝑁𝐻3 = 17.02 g/mol 1st determination: 𝑀𝐻𝑐𝑙 = 𝑀𝑁𝐻3∗( 𝑀𝐻𝑐𝑙 = 17.02

2nd determination:

𝑅𝑁𝐻3 2 ) 𝑅𝐻𝐶𝐿

𝑀𝐻𝑐𝑙 = 𝑀𝑁𝐻3∗ (

𝑔 0.12022901 𝑐𝑚 2 ∗( ) 𝑚𝑜𝑙 0.100 𝑐𝑚

𝑀𝐻𝑐𝑙 = 27.39

𝑀𝐻𝑐𝑙 = 17.02

𝑔

Average molar mass of HCL: 𝑀𝐻𝑐𝑙 = (

Theoretical molar mass of HCL is= 36.46

𝑔 𝑚𝑜𝑙

27.39 + 33.32 ) 2

𝑀𝐻𝑐𝑙 = 30.36

%=(

𝑔 0.12022901 𝑐𝑚 2 ∗( ) 𝑚𝑜𝑙 0.08587786 𝑐𝑚

𝑀𝐻𝑐𝑙 = 33.32

𝑚𝑜𝑙

𝐏𝐞𝐫𝐜𝐞𝐧𝐭 error of HCL:

𝑅𝑁𝐻3 2 ) 𝑅𝐻𝐶𝐿

𝑔

𝑚𝑜𝑙

𝑔

𝑚𝑜𝑙

𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 − 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 ) (100) 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

% error = (

36.46 − 30.36 ) (100) 36.46

% error = 16.73

Discussion: The objective of this lab was to determine the overall relative rate of diffusion for hydrogen

chloride (𝐻𝐶𝐿) and ammonia (𝑁𝐻3 ). This was found by estimating the distances went by the two

gases in a comparable time interval. Because 𝐻𝐶𝐿 is an acid and 𝑁𝐻3 is a base, a balancing

reaction is needed to occur. Larger particles diffuse more slowly than smaller molecules. With that, ammonia travel faster than hydrogen chloride. As a result of this, the development of a ring resulted in the production of a salt, ammonium chloride (where the two gases met). This ring

demonstrated the distance each gas went comparative from the origin point, which was used to address the overall molar mass, which was discovered to be 30.36 g/mol. Thus, we have a

𝑔

16.73% percentage error, because the theoretical molar mass molar mass of 𝐻𝐶𝐿 is 36.46 𝑚𝑜𝑙 . There are a few explanations behind why there is a percentage error. It could be because when measured with the ruler, the value was not the most precise measurement. Regardless of whether the record value was about ±0.5 cm off, this could cause a slight mistake in the

calculations. In addition, poor saturation of the cotton balls with not enough of 𝐻𝐶𝐿 or 𝑁𝐻3 . If one had more liquid than the other one, it could cause an incorrect reaction. Also, if the hole stopper where not secured of the 𝐻𝐶𝐿 or 𝑁𝐻3 , it may have diffused out of the glass tube.

Another one is timing, while putting the cotton balls into the tube would allow for the faster diffusion of one gas versus another. Lastly, if they were to be cross contaminated. Both cotton ball was placed in the same plate, it could have easily gone to the opposite cotton ball. Or when pushing the cotton balls into the glass tube, a portion of the 𝐻𝐶𝐿 or 𝑁𝐻3 would dribble off.

Subsequently, these variables could make the salt line be further aside of the glass tube, bringing about incorrect estimation. All in all, these factors could have caused the percentage error to be high. This lab could be improved by utilizing a more exact strategy for estimation with a smaller inaccuracy, by utilizing an instrument that can quantify precisely how much arrangement is being scattered onto the cotton balls, and by utilizing an instrument that can decide whether the glass tube was level or not.

References Hawkes, J.S. Graham’s Law and Perpetuation of Error.J. Chem. Educ. [online] 1997, vol. 74, no. 9, pp 1069.https://doi.org/10.1021/ed074p1069 (Accessed June 16, 2021). Hawkes, J.S. Misuse of Graham’s law.J. Chem. Educ. [online] 1993, vol. 70, no. 10, pp 836. https://doi.org/10.1021/ed070p836 (Accessed June 16, 2021).

Mason, A.E, and Barbara, K. Graham’s Laws of diffusion and effusion. J. Chem. Educ. [online] 1967, vol. 44, no. 12, pp. 740. https://doi.org/10.1021/ed044p740 (Accessed June 16, 2021).

Ruckstuhl, A. Thomas Graham’s study of the diffusion of gases. J. Chem. Educ. [online]1951. https://doi.org/10.1021/ed028p594 (Accessed June 16, 2021).

Slabaugh, H.W. The kinetic structure of gases. J. Chem. Educ. [Online] 1953. vol 30, no. 2, pp. 68. https://doi.org/10.1021/ed030p68 (Accessed June 16, 2021)...