Lecture 21 - Gases Part III

Thursday, April 4, 2024

11:30 AM

Please review the updated notes from Lecture 20 for answers to the gas law questions Class notes (1-20): https://bricejurban.github.io/CHEM111/ Assignments this week: ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28699/assignments/1014185"HW 12 Chemistry of Gases due next Wednesday Review Answer Key for Midterm 3 Read Chapter 13 Reminders: Midterm 3 is graded and an answer key is posted outside SCNC 336. If you notice any errors in grading, please make a regrade request through Gradescope. My CIC (EDUC 107) Hours: Friday 11AM - 1PM Office Hours (SCNC 314 or Zoom): ﷟HYPERLINK "https://calendly.com/bricejurban/office-hours"By appointment Today (4/4) Applications of Gas Laws Stoichiometry Molecular Masses and Densities Speeds of Gases and Effusion Rates Non-Ideal Gases Next Week Thermochemistry Systems, Surroundings, Work & Heat Enthalpy (H) and Internal Energy (U) Enthalpy Changes (ΔH) of Reactions Hess's Law Standard Molar Enthalpies of Formation Molar Bond Enthalpies Gas Law Equations Summary so Far K=℃ +273.15 °F = 9/5°C + 32 1 𝑎𝑡𝑚= 760 𝑚𝑚𝐻𝑔 =760 𝑡𝑜𝑟𝑟 = 14.7 psi (𝑙𝑏∙﷐𝑖𝑛﷮−2﷯) =1.01325 ×﷐10﷮5﷯ Pa=101.325 𝑘𝑃𝑎 = 29.92 inHg = 1.01325 bar At 273 K, and 1 atm 1 mol = 22.4 L At 273 K, and 1 bar 1 mol = 22.7 L 𝑅=0.08206﷐𝐿⋅𝑎𝑡𝑚﷮𝑚𝑜𝑙⋅𝐾﷯ 𝑅=8.314﷐𝐽﷮𝑚𝑜𝑙⋅𝐾﷯ Untitled picture.png bar atm Torr V 3 L L L mol mol mol mol 8.314472J.m01-l K-l 0.08314472 L.bar.m01-l.K-l 0.0820575 L.atm.m01-l.K-l 62.3637 L.Torr.m01-l.K-l
Untitled picture.png bar atm Torr V 3 L L L mol mol mol mol 8.314472J.m01-l K-l 0.08314472 L.bar.m01-l.K-l 0.0820575 L.atm.m01-l.K-l 62.3637 L.Torr.m01-l.K-l Dalton’s Law of Partial Pressures ﷐𝑃﷮𝐴﷯=﷐﷐𝑛﷮𝐴﷯﷮﷐𝑛﷮𝑡𝑜𝑡𝑎𝑙﷯﷯﷐𝑃﷮𝑡𝑜𝑡𝑎𝑙﷯ ﷐𝑃﷮𝐴﷯+﷐𝑃﷮𝐵﷯+⋯=﷐𝑃﷮𝑡𝑜𝑡𝑎𝑙﷯ Boyles’ Law ﷐𝑃﷮1﷯﷐𝑉﷮1﷯=﷐𝑃﷮2﷯﷐𝑉﷮2﷯ Charles’ Law ﷐﷐𝑉﷮1﷯﷮﷐𝑇﷮1﷯﷯=﷐﷐𝑉﷮2﷯﷮﷐𝑇﷮2﷯﷯ Gay-Lussac’s Law ﷐﷐𝑃﷮1﷯﷮﷐𝑇﷮1﷯﷯=﷐﷐𝑃﷮2﷯﷮﷐𝑇﷮2﷯﷯ Avogadro’s Law ﷐﷐𝑉﷮1﷯﷮﷐𝑛﷮1﷯﷯=﷐﷐𝑉﷮2﷯﷮﷐𝑛﷮2﷯﷯ Combined Gas Law ﷐﷐𝑃﷮1﷯﷐𝑉﷮1﷯﷮﷐𝑇﷮1﷯﷯=﷐﷐𝑃﷮2﷯﷐𝑉﷮2﷯﷮﷐𝑇﷮2﷯﷯ Ideal Gas Law 𝑃𝑉=𝑛𝑅𝑇 Kinetic Molecular Theory Gas particles are in constant, rapid, random, straight-line motion. There are no attractive forces between gas molecules. Collisions between gas particles are completely elastic (no energy is lost) Gas particles occupy negligible volume. The Kelvin temperature is directly related to the average kinetic energy of the gas. Gas Stoichiometry Untitled picture.png Machine generated alternative text: P (atm), V (L), and T (K) of gas A P (atm), V (in L) of gas A at STP + by 22.4 grams of A + by molar mass of A use PV=nRT V (L), or T (K) of gas B use PV=nRT V (in L) of gas B at STP x by 22.4 Coefficient B moles of A CoetT1cent A moles of B x by molar mass of B grams ofB x by 6.022E23 + by 6.022E23 x byM or v +byMorV
Untitled picture.png Machine generated alternative text: P (atm), V (L), and T (K) of gas A P (atm), V (in L) of gas A at STP + by 22.4 grams of A + by molar mass of A use PV=nRT V (L), or T (K) of gas B use PV=nRT V (in L) of gas B at STP x by 22.4 Coefficient B moles of A CoetT1cent A moles of B x by molar mass of B grams ofB x by 6.022E23 + by 6.022E23 x byM or v +byMorV Stoichiometry Problems at Standard Temperature and Pressure (STP) (273 K = 0 °C and 1 atm) Untitled picture.png Machine generated alternative text: V (in L) of gas A at STP V (inL)0fgasBatSTP grams of A + by 22.4 + by molar mass of A Coefficient B moles of A Coefficent A moles of B x by 22.4 x by molar mass of B grams ofB In situations that are at atmospheric pressure and near the melting point of ice (STP), we can use a simple conversion that 1 mol of gas = 22.4 L Example: Sodium metal (0.350 g) is dropped into water and reacts completely. How much hydrogen gas in liters is produced if the reaction occurs at STP? 2 Na(s) + 2 H₂O(l) → H₂(g) + 2 NaOH(aq) Stoichiometry Problems that are not at STP use the Ideal Gas Law Untitled picture.png Machine generated alternative text: P (atm), V (L), and T (K) of gas A use PV=nRT P (atm), V (L), or T (K) of gas B use PV=nRT grams of A + by molar mass of A Coefficient B moles of A Coefficent A moles of B x by molar mass of B grams ofB Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png Machine generated alternative text: P (atm), V (L), and T (K) of gas A use PV=nRT P (atm), V (L), or T (K) of gas B use PV=nRT grams of A + by molar mass of A Coefficient B moles of A Coefficent A moles of B x by molar mass of B grams ofB In most situations gases are not at STP and its necessary to use PV=nRT Example: What volume, in liters, of sulfur dioxide gas at 455 K and 2.03 atm is needed to produce 100 g of sulfur trioxide 2 SO₂(g) + O₂(g) →2 SO₃(g) Trimix is a general name for a type of gas blend used by technical divers and contains nitrogen, oxygen and helium. In one Trimix blend, the partial pressures of each gas are 55.0 atm oxygen, 90.0 atm nitrogen, and 50.0 atm helium. What is the percent oxygen (by volume) in this Trimix blend? (Helium is added to reduce nitrogen narcosis at depth) A gas mixture was prepared to contain 50% by mass of O₂ and Ne. When the total pressure of the mixture is 1.50 atm, what is the partial pressure of O₂? 1) Remember to convert to mols of gas Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
A weather balloon calibrated at 0.00 °C to have a volume of 22.0 L has what volume at -32.0 °C assuming pressure is held constant? 1) Remember to convert temperature to K 25.0 L of an ideal gas at 278 K and 4.11 atm are heated to 393 K with a new pressure of 7.00 atm. What is the new volume (in L)? What volume, in liters, of carbon monoxide gas at 78.5 °C and 848 torr is needed to produce 3.21 g of methanol, CH₃OH? CO(g) + 2 H₂(g) → CH₃OH(g) 1) remember to convert temp to K and pressure to atm Finding Molar Masses and Densities of Gases Density of a Gas 𝜌=﷐ℳn﷮𝑉﷯=﷐ℳP﷮𝑅𝑇﷯ Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink 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Example: Consider a 0.500 L sample of carbon dioxide gas (CO2) at 600 torr and 50°C. What is the density of this sample of gas? 1) Find moles of CO2 Then find the density. Speeds of Gases Untitled picture.png 00 一 e > sulS 一 一 一 0 1 902E 旵 Particles of different speeds can be selected using a series of rotating disks (velocity selectors) to determine the velocity distribution of a gas at a given temperature. These distribution follows a Maxwell-Boltzmann distribution where curves start at zero, reach a maximum then tail off to zero as the speed increases. Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png 300 K 1000 K 1000 2000 Molecular speed/m•s-l Distribution of Nitrogen gas speed at different temperatures Untitled picture.png 500 1 ooo 2000 Molecular speed (m/s) 3000 Distribution of different gases speeds at the same temperature How can we predict the average speed of a molecule at a given temperature? According to the last postulate of the Kinetic Molecular Theory, the average (mean) kinetic energy per mole of a gas is proportional to the Kelvin temperature: Untitled picture.png When we solve for the proportionality constant, c, we find that it equals 3R/2 Untitled picture.png Because R is equal to J∙mol-1∙K-1 we need to use the value R = 8.314 J∙mol-1∙K-1 Rearranging and solving for the velocity gives the root-mean-square (rms) equation: Untitled picture.png Vrms BRT Mkg
Untitled picture.png Vrms BRT Mkg Examples of the rms speed of four common gases Untitled picture.png Gas 02 C02 -1 Molar mass/kg•mol 0.0020 0.0280 0.0320 vrms/m•s 1 t = 200C łooooc 1900 4000 510 1060 480 1000 410 850 Example: Calculate the rms speed of a nitrogen molecule at 20 °C Effusion of Gases Diffusion: The mixing of samples of gases Effusion: The leaking of a gas through a small opening. Graham's law compares the rate of effusion of gases that have the same average kinetic energy Graham’s Law of Effusion (ℳ = 𝑀𝑜𝑙𝑎𝑟 𝑀𝑎𝑠𝑠) ﷐𝑟𝑎𝑡﷐𝑒﷮𝐴﷯﷮𝑟𝑎𝑡﷐𝑒﷮𝐵﷯﷯=﷐﷮﷐﷐ℳ﷮𝐵﷯﷮﷐ℳ﷮𝐴﷯﷯﷯ A gas sample at 30°C contains hydrogen gas (particle mass = 2.02 g per mole) and oxygen (particle mass = 32 g per mole). Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Example: If the average speed of the oxygen gas is 480 m/s Which gas has a greater average kinetic energy? At the same temperature the gases will have the same kinetic energy Which gas is traveling faster? Hydrogen is going to be travelling faster because it is the lightest What is the average speed of the hydrogen gas? Non-Ideal (Real) Gases Real gases have attractions and repulsions between particles and the particles take up space meaning they have a volume (they are not point particles) Real Gases behave close to ideal gases when they are: At high temperatures, so they are moving too fast to interact with the other particles 2. At Low pressures, so they are far apart and don't interact much (and don't have a large volume) 3. When they are small non-polar gas particles (they have less interactions with each other) Untitled picture.png Compressibility factor z Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png Compressibility factor z Untitled picture.png The van der Waals Equation for real gases is: P is the observed pressure of the gas sample V is the volume of the container a is a parameter related to the attraction between particles b is a parameter related to the volume per particle. The van der Waals equation can be viewed as a “correction” to the ideal gas law to account for the finite size of the molecules and attractive forces between them. • At high pressures the volume of gas is no longer negligible. Thus the volume of the container should be smaller and we correct this with the b factor • Gas molecules near a wall of a container experiences a net inward drag due to its attraction to other molecules. Thus, it strikes the walls with smaller force. This is corrected with the a factor. Often times we want to find the pressure so we'll rewrite the equation as: Untitled picture.png nRT Untitled picture.png Ο 00 ο οοο Οοο c Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink 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Untitled picture.png nRT Untitled picture.png Ο 00 ο οοο Οοο c van der Waals constants of several gases: Untitled picture.emf Name Ammonia Argon Carbon dioxide Hydrogen Methane Nitrogen Oxygen Water Formula NH3 C02 CH4 02 H 20 a (atm L2 mol-2) 4.170 1.345 3.592 0.2444 2.253 1.390 1.360 5.464 b (L mol-I) 0.03707 0.03219 0.04267 0.02661 0.04278 0.03913 0.03183 0.03049 Example: Oxygen is supplied to hospitals and chemical laboratories under pressure in large steel cylinders. Typically, such cylinders have an internal volume of 28.0 L and contain 6.80 kg oxygen. Use the van der Waals equation to estimate the pressure inside such cylinders at 20°C in atmospheres and in pounds per square inch. Additionally, is the attractive force or repulsive force more important at these conditions? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
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