Physics HL
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To what extent does temperature (275, 285, 295, 305 and 315 K) affect pressure in light ideal gases at a constant volume of 1x10-6 m3?

Introduction and Background

The scientific term "ideal gas" describes a scientific notion in which a specific gas is made up of molecules that adhere to one major principal: that no attraction or repellence exists between its molecules. The only possible way molecules of an ideal gas would be able to interact with one another would be through elastic collisions; when they collide with one another or the container’s walls. Other conditions a gas must fulfill in order to be considered “ideal” are that the gas particles must have negligible volume, the particles must be of equal size and they must follow Newton’s 3 laws of motion (Tenny & Cooper, 2021). A law was thus derived in order to coherently predict these gases’ behaviour. Émile Clapeyron introduced the rule in 1834. The ideal gas law can thus be seen as a combination of Charles' law, Avogadro's law, Boyle's law and Gay-Lussac's law. In spite of the fact that no gas has these exact characteristics, the ideal gas law can rather accurately predict how real gases behave at enough low pressures and high temperatures , when very huge distances between molecules and their fast speeds preclude any contact. But when the gas in question is close to its condensation point, or the temperature at which it liquefies, it deviates from obedience to the equation.

This topic peaked my interest since I had already studied it in the Chemistry SL IB course and thus I wondered if its applications might be different in the physics course as both sciences revolve around two different domains. Another reason I was enticed to commence this exploration is the fact that I am a car enthusiast. Not long ago I was surfing the internet when I found a very interesting article that explains how a car’s airbags are deployed during an accident. Airbags were one of the few components in a car which I had no idea on how they operated. Turns out that the ideal gas law governs how these airbags function. The numerous sorts of gases swiftly fill the airbags upon installation, inflating them. An interaction between potassium nitrate and sodium azide results in the nitrogen gas filling the airbags. (Vedantu Content Team, 2022)

The aim of this exploration it thus to investigate how temperature affects pressure in light ideal gases and at a constant volume. To do so, I will be using a computer simulation that models the relationship between the variables in the ideal gas law.

Theory and Hypothesis

The general gas equation also known as the ideal gas law is essentially a rule that links pressure, volume, temperature, number of moles and the gas constant. Although the law describes an ideal (hypothetical ) gas's behaviour, in many circumstances it closely resembles the behaviour of real gases. ("Ideal gas | Definition, equation, properties, & facts," n.d.)

The equation for ideal gas law is: pv = nrt Equation 1 Where -

p - pressure in pascals ( Pa )

v - volume in ( m3 )

n - quantity of particles in ( mol )

R - ideal gas constant

$$( 8.31446261815324 ≈ 8.31\frac{ J} {K.mol} )$$

t - temperature in Kelvin ( K )

This equation suggests that grapphing temperature on the X-axis as an independent variable and pressure on the Y-axis as a dependent variable should result in a linear correlation. It can thus be deduced that pressure and temperature share a relationship of proportionality and that the graph would have a gradient of $$\frac{ Nr}{ v} .$$

In order to properly study the connection between temperature and pressure, all other variables present in the equation must be kept constant. Since most real life applications involve “light gases”, this is the option that will be chosen during this simulation.

Because the procedure followed was performed using a computerized simulation, the environmental ramifications of this exploration are practically non-existent. This also applies to the ethical consequences as the usage of this computerized simulation rendered them unsubstantial; no real materials were used and therefore there was no waste and no material loss. Following a simulated procedure also helped in the reduction of random errors as most of the calculations were done by an artifical intelligence system and not by a human.

Variables

Figure 1 - Table On

Diagram

Figure 2 -
• The top right section entitled “Hold Constant” is to choose which variables should be kept unchanged throughout the whole simulation
• The section right under it entitled “Particles” serves as a means to choose the number of particles that will be interacting in the simulation
• The bucket labelled “Heat & Cold” serves as a means to manipulate the temperature
• The pump present on the right of the bucket serves as a means to choose which kind of particles will be interacting in the simulation
• The thermometer and barometer serve as a means to measure temperature and pressure respectively

Apparatus

Method

• Open Phet colorado ideal gas simulation and choose option labelled “ideal”
• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!

Video Course

• Figure 3 -
• Click on “width” to display the value and adjust it so it’s 10 nm
Figure 4 -
• Select “Volume” as the variable that will be held constant during the simulation
Figure 5 -
• Select Kelvin as the unit for measuring temperature
• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!

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• Figure 6 -
• Select kPa as the unit for measuring pressure
Figure 7 -
• Select light particles in this section ( as light gases are the most used in real life applications relating to the ideal gas law )
Figure 8 -
• Add particles till there are 602 light particles and adjust temperature from the bucket labelled “Heat & Cold” till it’s 275 K.
• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!

Video Course

• Figure 9 -
• Set a timer for 15 seconds on an external device (stop-watch) and write down the value of the pressure that has been yielded
Figure 10 -
• Repeat steps 1 to 8 for each of these different temperatures (275 K, 285 K, 295 K, 305 K and 315 K) (each time adding 10 K)
• Repeat steps 1 to 8 three times for each of the temperatures chosen

Raw data

Temperature ( K )
Pressure 1 st trial ( kPa )
Pressure 2 nd trial ( kPa )
Pressure 3 rd trial ( kPa )
275
6565
6520
6565
285
6776
6795
6750
295
7010
6985
7010
305
7239
7247
7236
315
7514
7487
7490
Figure 11 - Table On

Processed data

Temperature ( K )
Pressure 1 st trial ( kPa
Pressure 2 nd trial ( kPa )
Pressure 3 rd trial ( kPa )
Pressure Average
Pressure Uncertainty
275
6565
6520
6565
6550
20
285
6776
6795
6750
6770
20
295
7010
6985
7010
7.00 x 103
10
305
7239
7247
7236
7240
6
315
7514
7487
7490
7490
20
Figure 12 - Table On

N.B Pressure will be kept in kPa for ease and versatiltiy but for calculations in the “analysis and conclusion” section it will be converted to Pa.

Calculation examples -

• Pressure Average ( for 285 K ) -

$$\frac{pressure\,1+\,pressure\,2+\,pressure}{3}=\frac{6776+6795+6750}{3}=6773.66666≈ 6770 (3sf)$$

the average pressure was rounded to three significant figures corresponding to the lowest number of significant fiugures in a variable ( temperature )

• Pressure uncertainty$$( for 275 K) - \frac{max-man}{2}=\frac{6565-6520}{2}=22.5≈ 20 (2sf)$$

Graph

Figure 13 -

Best Fit Line Gradient - 23.543

Maximum Fit Line Gradient - 24.59

Minimum Fit Line Gradient - 22.592

• Slope uncertainty -

$$\frac{max-min}{2}=\frac{24.592-22.592}{2}=1 (1sf)$$

• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!

• Analysis and conclusion

Althought the results seem valid and coherent with the original hypothesis, there is a way to further fortify their reliability. Before starting, it must be noted that the volume of the container was constant throughout the experiment and is equal to 1x10-6 m3 . (the container was square shaped and its width was 10 nm which in turn means that its volume must equate to 10x10x10 = 1000 nm3 = 1x10-6 m3 ) The slope of the graph “Pressure vs Temperature” gives a slope that is equal to$${\frac nr }{v}$$ and thus if we equate it to the slope value that’s been obtained, we can calculate the number of moles -

$$\frac{nr}{v}=23.543$$

$$\frac{nx8.31}{1x10^{-6}}=23.543$$

n = 2.833092659 x 10-6 ≈ 2.83 x 10-6

n = ( 2.83 x 10-6 ) x 103 = 2.83 x 10-3

Since this slope was calculated with pressure being in kPa instead of Pa then the value obtained for the number of moles must be multiplied by 103 (since 1 kPa is equal to 1000 Pa)

Now that we have this generalized number of moles we can use the original ideal gas equation to check if the same value will be obtained from the data that has been procured from the simulation.

N.B All values of pressure must be converted to Pa (1 kPa is equal to 1000 Pa) Example 1 (for temperature of 275 K)

$$pv=nrt$$

(6550 x103 ) x 1x10−6 = n x 8.31 x 275

$$n=\frac{(6550x10^3)\,x\,1x10^{-6}}{8.31x275}=2866207198\,x\,10^{-3}≈ 2.87 \,x \,10^{-3}$$

Example 2 (for temperature of 315 K)

pv = nrt

(7490 x103 ) x 1x10−6 = n x 8.31 x 315

$$n=\frac{(7490x10^3x1x10^{-6})}{8.31x315}=2.8613451x10^{-3}x 1≈ 2.86 x 10^{-3}$$

The values are practically identical with those obtained from the slope calculation which thus reinforces the validity of my procured results and its coherence and consistency with the ideal gas law. The original hypothesis has consequently been proven right which consolidates the replicability and universality of the ideal gas law.

Evaluation

Figure 14 - Table On

References

Gas Properties. (n.d.). PhET: Free online physics, chemistry, biology, earth science and math simulations. https://phet.colorado.edu/sims/html/gas-properties/latest/gas- properties_en.html

“Ideal Gas.” (n.d). Encyclopædia Britannica, Inc., https://www.britannica.com/science/ideal-gas

Tenny KM, Cooper JS. Ideal Gas Behavior. (2022, Nov 28). In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing: https://www.ncbi.nlm.nih.gov/books/NBK441936/

Vedantu Content Team. (2022, August 18). What is the reallife example of ideal gas law class 11 chemistry CBSE. Vedantu: Online Courses - Best LIVE Classes For CBSE, ICSE, JEE & NEET. https://www.vedantu.com/question-answer/reallife-example-of-ideal-gas-law-class-11- chemistry-cbse-60da8d2a48f07e606c1f6f4d

• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!

Video Course

• David McKay

Ivy league graduate, 4+ yrs of experience, vetted IB Examiner!