CHM01: General Chemistry 1 - Study Notes

MAPÚA UNIVERSITY - CHM01: GENERAL CHEMISTRY 1

INSTRUCTOR

  • Ms. Mary Angelique J. Laude, MAPÚA UNIVERSITY

COURSE OUTCOME 5: GAS AND ITS BEHAVIOR

LEARNING OUTCOMES

At the end of this course outcome, learners must be able to:

  • Describe the Kinetic Molecular Theory of Gases: Understand the behavior of gas molecules based on their motion and interactions.

  • Define pressure and provide the common units of pressure.

  • Express the gas laws in equation form.

  • Use the gas laws to determine the pressure, volume, or temperature of a gas under changing conditions.

  • Utilize the ideal gas equation in computations to link pressure, volume, moles, and temperature of an ideal gas.

  • Use Dalton’s Law of Partial Pressures in computations to analyze mixtures of gases.

COURSE ASSIGNMENTS

  • WW/PT %: Details of assignments and their respective weights and deadlines are provided.

    • WW5 (8.33%)

    • WW5.1 (4.165%) Cengage Seatwork - Due: Week 17, Nov 14, 6 PM

    • WW5.2 (4.165%) CO5 Quiz - Due: Week 15

    • PT5 (15.00%)

    • PT5.1 (3.00%) - Labster Simulation (Individual Task) - Due: Week 17, Nov 14, 6 PM

    • PT5.2 (10.00%) - Experiment 5: Gas Laws - Due: Week 14

    • PT5.3 (2.00%) - Self and Peer Evaluation: Week 14-15

    • QA5 (10.00%) - Final Examination: Week 18

LESSON OUTLINE: Gases

  1. Kinetic Molecular Theory of Gases

  2. Units of Pressure

  3. Boyle’s Law

  4. Charles’ Law

  5. Gay-Lussac’s Law

  6. Combined Gas Law

  7. Avogadro’s Law

  8. Ideal Gas Law

  9. Dalton’s Law of Partial Pressures

KINETIC MOLECULAR THEORY OF GASES

The Kinetic Molecular Theory explains the behavior of gases:

  1. Composition: A gas consists of molecules that are separated by distances much larger than their own size. These molecules can be treated as points with mass but negligible volume.

  2. Molecular Motion: Gas molecules are constantly moving in random directions and frequently collide with one another. Collisions are perfectly elastic, meaning total kinetic energy is conserved.

  3. Intermolecular Forces: Gas molecules exert no attractive or repulsive forces on each other.

  4. Kinetic Energy and Temperature: The average kinetic energy of gas molecules is proportional to the temperature of the gas measured in kelvins. Therefore, any two gases at the same temperature possess the same average kinetic energy.

PHYSICAL CHARACTERISTICS OF GASES

  • Volume and Shape: Gases occupy the volume and shape of their containers.

  • Compressibility: Gases are the most compressible state of matter.

  • Mixing: Gases mix evenly and completely when contained within the same volume.

  • Density: Gases have significantly lower densities compared to liquids and solids.

PRESSURE

  • Definition of Pressure: Pressure (
    PP) is defined as all force (
    FF) exerted per unit area (
    AA):
    P=racFAP = rac{F}{A}

  • SI Unit of Pressure: The pascal (Pa) is the SI unit, equivalent to one newton per square meter (N/m² or kg m⁻¹s⁻²).

MEASURING PRESSURE

a. Manometer: A device that measures the pressure of fluids.

  • Barometer: Measures atmospheric pressure.

UNITS OF PRESSURE

  1. 1 atmosphere (atm) = 760 mm of Mercury (mm Hg)

  2. 1 atmosphere (atm) = 760 torr

  3. 1 atmosphere (atm) = 101,325 Pascals (Pa)

  4. 1 atmosphere (atm) = 101.325 kilopascals (kPa)

  5. 1 atmosphere (atm) = 1.01325 Bar

  6. 1 atmosphere (atm) = 14.6959 pound per square inch (psi)

CONVERSION FACTORS

  • Help in converting different pressure units.

GAS LAWS

Gas Law

Equation

Key Principle

Boyle's Law

P<em>1V</em>1=P<em>2V</em>2P<em>1V</em>1 = P<em>2V</em>2

Pressure is inversely proportional to volume at constant temperature.

Charles's Law

V<em>1/T</em>1=V<em>2/T</em>2V<em>1/T</em>1 = V<em>2/T</em>2

Volume is directly proportional to temperature at constant pressure.

Gay-Lussac's Law

P<em>1/T</em>1=P<em>2/T</em>2P<em>1/T</em>1 = P<em>2/T</em>2

Pressure is directly proportional to temperature at constant volume.

Avogadro's Law

V<em>1/n</em>1=V<em>2/n</em>2V<em>1/n</em>1 = V<em>2/n</em>2

Volume is directly proportional to the number of moles at constant temperature and pressure.

Combined Gas Law

racP<em>1V</em>1T<em>1=racP</em>2V<em>2T</em>2rac{P<em>1V</em>1}{T<em>1} = rac{P</em>2V<em>2}{T</em>2}

Combines previous laws regarding pressure, volume, and temperature.

BOYLE’S LAW

  1. Concept: Stated by Robert Boyle, it asserts that the volume of a certain mass of gas is inversely proportional to the pressure at constant temperature. Thus, as pressure increases, volume decreases, and vice versa.

  2. Mathematical Representation:
    egin{align*}
    P ext{ is proportional to } & rac{1}{V} \
    ext{or, } & P1V1 = P2V2 \
    ext{where } & n ext{ (amount of gas) and } T ext{ (temperature) are constant.}
    ext{Let } & P1 ext{ be initial pressure and } P2 ext{ the final pressure.}

    ext{Example:} & A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. Find the pressure when the volume is reduced to 154 mL at constant temperature.
    ext{Given:} & P1 = 726 ext{ mmHg}, V1 = 946 ext{ mL}, V2 = 154 ext{ mL} \ ext{Find:} & P2 = ? \
    ext{Solution:} & P2 = rac{P1V1}{V2} = ? \

    ext{Example 2:} & For sulfur dioxide (SO₂) with initial volume (V₁ = 1.53L) at pressure 5.6x10³Pa, find pressure at 1.5x10⁴Pa at constant temperature.

CHARLES’ LAW

  1. Concept: Jacques Charles concluded that with constant pressure, the temperature and volume of a gas are directly proportional.

  2. Mathematical Representation:
    V = kT ext{ or } V1/T1 = V2/T2wheren(amountofgas)andP(pressure)areconstant.</p></li><li><p><strong>Conversions</strong>:</p><ul><li><p>CelsiustoFahrenheit:where n (amount of gas) and P (pressure) are constant.</p></li><li><p><strong>Conversions</strong>:</p><ul><li><p>Celsius to Fahrenheit:T{F} = 1.8T{C} + 32</p></li><li><p>CelsiustoKelvin:</p></li><li><p>Celsius to Kelvin:T{K} = T{C} + 273.15</p></li></ul></li><li><p><strong>Examples</strong>:</p><ul><li><p>Calculatetemperatureforcarbonmonoxidegasoccupying3.20Lat125°Cwhenbroughtto1.54L.</p></li><li><p>Forasamplecooledfrom34.0°Cto25.0°C,findnewvolumeinL.</p></li></ul></li></ol><h5id="6208f360−15e2−45c8−83f0−7850e13522c6"data−toc−id="6208f360−15e2−45c8−83f0−7850e13522c6"collapsed="false"seolevelmigrated="true">GAY−LUSSAC’SLAW</h5><ol><li><p><strong>Concept</strong>:JosephLouisGay−Lussacstatedthatatconstantvolume,thepressureofagasisdirectlyproportionaltoitsabsolutetemperature.</p></li><li><p><strong>MathematicalRepresentation</strong>:<br></p></li></ul></li><li><p><strong>Examples</strong>:</p><ul><li><p>Calculate temperature for carbon monoxide gas occupying 3.20 L at 125 °C when brought to 1.54 L.</p></li><li><p>For a sample cooled from 34.0°C to 25.0°C, find new volume in L.</p></li></ul></li></ol><h5 id="6208f360-15e2-45c8-83f0-7850e13522c6" data-toc-id="6208f360-15e2-45c8-83f0-7850e13522c6" collapsed="false" seolevelmigrated="true">GAY-LUSSAC’S LAW</h5><ol><li><p><strong>Concept</strong>: Joseph Louis Gay-Lussac stated that at constant volume, the pressure of a gas is directly proportional to its absolute temperature.</p></li><li><p><strong>Mathematical Representation</strong>: <br>P = kT ext{ or } P1/T1 = P2/T2wheren(amountofgas)andV(volume)areconstant.RemembertokeepTemperatureinKelvin.</p></li></ol><h5id="feaf4cde−9e17−4eb6−8c62−8f188cb3382d"data−toc−id="feaf4cde−9e17−4eb6−8c62−8f188cb3382d"collapsed="false"seolevelmigrated="true">COMBINEDGASLAW</h5><ol><li><p><strong>Concept</strong>:TheCombinedGasLawsummarizestherelationshipsestablishedinBoyle’s,Charles’s,andGay−Lussac’slaws,statingthevolumeofagasisinverselyproportionaltoitspressureanddirectlyproportionaltoitsabsolutetemperature.</p></li><li><p><strong>MathematicalRepresentation</strong>:<br>where n (amount of gas) and V (volume) are constant. Remember to keep Temperature in Kelvin.</p></li></ol><h5 id="feaf4cde-9e17-4eb6-8c62-8f188cb3382d" data-toc-id="feaf4cde-9e17-4eb6-8c62-8f188cb3382d" collapsed="false" seolevelmigrated="true">COMBINED GAS LAW</h5><ol><li><p><strong>Concept</strong>: The Combined Gas Law summarizes the relationships established in Boyle’s, Charles’s, and Gay-Lussac’s laws, stating the volume of a gas is inversely proportional to its pressure and directly proportional to its absolute temperature.</p></li><li><p><strong>Mathematical Representation</strong>: <br> rac{P1V1}{T1} = rac{P2V2}{T2}</p></li><li><p><strong>Example</strong>:ForaweatherballoonwithinitialconditionsexpandingtoahigheraltitudewithchangesinTandP,calculatethefinalvolume.</p></li></ol><h5id="d55ea80a−e0cf−497e−b896−0089868075fc"data−toc−id="d55ea80a−e0cf−497e−b896−0089868075fc"collapsed="false"seolevelmigrated="true">AVOGADRO’SLAW</h5><ol><li><p><strong>Concept</strong>:Avogadro’sLawstatesthatthevolumeofgasatconstanttemperatureandpressureisdirectlyproportionaltothenumberofmolespresent.</p></li><li><p><strong>MathematicalRepresentation</strong>:<br></p></li><li><p><strong>Example</strong>: For a weather balloon with initial conditions expanding to a higher altitude with changes in T and P, calculate the final volume.</p></li></ol><h5 id="d55ea80a-e0cf-497e-b896-0089868075fc" data-toc-id="d55ea80a-e0cf-497e-b896-0089868075fc" collapsed="false" seolevelmigrated="true">AVOGADRO’S LAW</h5><ol><li><p><strong>Concept</strong>: Avogadro’s Law states that the volume of gas at constant temperature and pressure is directly proportional to the number of moles present.</p></li><li><p><strong>Mathematical Representation</strong>: <br>V = kn ext{ or } V1/n1 = V2/n2whereP(pressure)andT(temperature)areconstant.</p></li><li><p><strong>Example</strong>:Determinefinalvolumebyincreasing0.965molofgasto1.80molunderconstantconditions.</p></li></ol><h5id="da0a05fd−a484−4dcc−8033−adf310eea784"data−toc−id="da0a05fd−a484−4dcc−8033−adf310eea784"collapsed="false"seolevelmigrated="true">IDEALGASLAW</h5><ol><li><p><strong>Definition</strong>:TheIdealGasLawcombinesvariousgaslawstoexpresstherelationshipbetweenpressure,volume,temperature,andthenumberofmolesofgasinadefinedequation:<br>where P (pressure) and T (temperature) are constant.</p></li><li><p><strong>Example</strong>: Determine final volume by increasing 0.965 mol of gas to 1.80 mol under constant conditions.</p></li></ol><h5 id="da0a05fd-a484-4dcc-8033-adf310eea784" data-toc-id="da0a05fd-a484-4dcc-8033-adf310eea784" collapsed="false" seolevelmigrated="true">IDEAL GAS LAW</h5><ol><li><p><strong>Definition</strong>: The Ideal Gas Law combines various gas laws to express the relationship between pressure, volume, temperature, and the number of moles of gas in a defined equation: <br>PV = nRT<br>where:</p></li></ol><ul><li><p><br>where:</p></li></ol><ul><li><p>R = 0.0820574 ext{ atm} imes ext{L} imes ext{mol}^{-1} imes ext{K}^{-1}</p></li></ul><h5id="181e1e86−7c30−4d42−b08f−2fd5a4fbbebe"data−toc−id="181e1e86−7c30−4d42−b08f−2fd5a4fbbebe"collapsed="false"seolevelmigrated="true">DALTON’SLAWOFPARTIALPRESSURES</h5><ol><li><p><strong>Concept</strong>:EstablishedbyJohnDaltonin1801,thislawstatesthatthetotalpressureofagasmixtureisthesumofthepartialpressuresofitscomponentgases.</p></li><li><p><strong>MathematicalRepresentation</strong>:<br></p></li></ul><h5 id="181e1e86-7c30-4d42-b08f-2fd5a4fbbebe" data-toc-id="181e1e86-7c30-4d42-b08f-2fd5a4fbbebe" collapsed="false" seolevelmigrated="true">DALTON’S LAW OF PARTIAL PRESSURES</h5><ol><li><p><strong>Concept</strong>: Established by John Dalton in 1801, this law states that the total pressure of a gas mixture is the sum of the partial pressures of its component gases.</p></li><li><p><strong>Mathematical Representation</strong>: <br>PT = PA + PB + PC + …</p></li><li><p><strong>MoleFraction</strong>:</p></li></ol><ul><li><p>Molefraction(</p></li><li><p><strong>Mole Fraction</strong>:</p></li></ol><ul><li><p>Mole fraction (XA)isdefinedas:) is defined as:XA = rac{nA}{nA+nB+nC+…}</p></li></ul><ol><li><p><strong>PartialPressureCalculation</strong>:Agas′spressureinamixisdeterminedusingtheformula:<br></p></li></ul><ol><li><p><strong>Partial Pressure Calculation</strong>: A gas's pressure in a mix is determined using the formula:<br>PAB = XA P_{Total}$$

  3. Practical Example: Solve for partial pressures given a total pressure; partial pressures of component gases like N₂, CO₂, H₂, and SO₂ can be calculated based on moles present.

FINAL REMARKS

  • Ensure familiarity with all gas laws and their applications for practical problems in chemistry. Regularly review units and conversions to maintain accuracy in calculations.

REFERENCES

  • IUPAC. Compendium of Chemical Terminology, 2nd ed. (Gold Book).

  • Kotz, J.C., Treichel, P.M., Townsend, J., & Treichel, D.A. (2015). Chemistry and Chemical Reactivity, 9th Edition.

  • Silberberg, M.S., & Amateis, P.G. (2021). Chemistry: The Molecular Nature of Matter and Change (9th ed.).

  • Rodil, M.S.P. (2017). Conceptual Science and Beyond General Chemistry 1.

CLOSING

  • Thank you for participating in Mapúa University's General Chemistry course. Stay engaged with ongoing assessments and practical exercises!