Gases

This document provides a deep dive into the behavior, properties, and mathematical laws governing gases, emphasizing ideal gas behavior and its applications.

1. Molecular Weight and Moles (Review)

  • Molecular Weight (Formula Mass):

    • The sum of atomic masses in a compound.

    • Example: Water (H₂O): 2(1.008)+15.999=18.015 g/mol2(1.008) + 15.999 = 18.015 \text{ g/mol}2(1.008)+15.999=18.015 g/mol

  • Avogadro’s Number:

    • 1 mole=6.022×10231 \text{ mole} = 6.022 \times 10^{23}1 mole=6.022×1023 molecules, atoms, or ions.

  • Conversions:

    • Moles → Grams: Grams=Moles×Molar Mass\text{Grams} = \text{Moles} \times \text{Molar Mass}Grams=Moles×Molar Mass

    • Grams → Moles: Moles=GramsMolar Mass\text{Moles} = \frac{\text{Grams}}{\text{Molar Mass}}Moles=Molar MassGrams​

  • Example Problems:

    1. Find the molecular weight of penicillin G (C₁₆H₁₈N₂O₄S).

    2. Calculate the mass of 0.0626 moles of NaHCO₃.

    3. Convert 5.27 g of citric acid (C₆H₈O₇) to moles.

2. Features of Gases

  • Gas Laws Developed By:

    • Robert Boyle → Pressure-Volume Relationship.

    • Jacques Charles → Temperature-Volume Relationship.

    • Amedeo Avogadro → Moles-Volume Relationship.

Key Properties of Gases

  1. Compressibility:

    • Gases can be compressed due to large intermolecular spaces.

  2. Mix Homogeneously:

    • Gases mix evenly, forming homogeneous mixtures (e.g., air).

  3. Expand to Fill Containers:

    • Gases assume the shape and volume of their containers.

  4. Exert Pressure on Surfaces:

    • Gas particles collide with container walls, creating pressure.

3. Atmospheric Pressure & Units

  • Definition:

    • The force per unit area exerted by gas molecules.

    • Measured using a mercury barometer.

  • Pressure Units & Conversions:

    1 atm=760 mmHg=101.3 kPa=14.7 psi1 \text{ atm} = 760 \text{ mmHg} = 101.3 \text{ kPa} = 14.7 \text{ psi}1 atm=760 mmHg=101.3 kPa=14.7 psi

Temperature Conversions

K=°C+273.15K = °C + 273.15K=°C+273.15 °F=(°C×95)+32°F = (°C \times \frac{9}{5}) + 32°F=(°C×59​)+32

Example Problem

  • Given:

    • A 0.500-gallon milk carton at 25.2°C and 1 atm.

  • Find:

    1. Temperature in Kelvin.

    2. Pressure in mmHg.

    3. Volume in Liters.

4. Kinetic Molecular Theory (KMT) of Gases

Postulates:

  1. Gas molecules move randomly.

  2. Gas molecules occupy negligible volume compared to the container.

  3. No intermolecular forces (no attraction or repulsion).

  4. Collisions are elastic (no loss of kinetic energy).

  5. Average kinetic energy (KE) is proportional to temperature (Kelvin).

    • Formula: KEavg=32kBTKE_{\text{avg}} = \frac{3}{2} k_B TKEavg​=23​kB​T Where kBk_BkB​ = Boltzmann’s constant.

  • Ideal vs. Real Gases:

    • Real gases deviate from KMT at low temperatures and high pressures due to intermolecular attractions.

5. Gas Laws

Boyle’s Law (Pressure-Volume Relationship)

P1V1=P2V2P_1 V_1 = P_2 V_2P1​V1​=P2​V2​

  • At constant temperature, volume and pressure are inversely proportional.

  • Example:

    • If volume doubles, pressure is halved.

Charles’s Law (Temperature-Volume Relationship)

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}T1​V1​​=T2​V2​​

  • At constant pressure, volume and temperature are directly proportional.

  • Example:

    • If temperature doubles, volume doubles.

Avogadro’s Law (Moles-Volume Relationship)

V1n1=V2n2\frac{V_1}{n_1} = \frac{V_2}{n_2}n1​V1​​=n2​V2​​

  • Volume is proportional to the number of gas molecules.

  • Example:

    • If moles double, volume doubles.

Ideal Gas Law

PV=nRTPV = nRTPV=nRT

Where:

  • PPP = Pressure (atm)

  • VVV = Volume (L)

  • nnn = Moles

  • RRR = 0.0821 L·atm/(mol·K)

  • TTT = Temperature (K)

  • Limitations:

    • Deviates for high pressures or low temperatures.

Applications

  1. Determine Molecular Mass: M=mRTPVM = \frac{mRT}{PV}M=PVmRT​

  2. Find Gas Density: D=MPRTD = \frac{MP}{RT}D=RTMP​

6. Dalton’s Law of Partial Pressures

Ptotal=P1+P2+P3+…P_{\text{total}} = P_1 + P_2 + P_3 + \dotsPtotal​=P1​+P2​+P3​+…

  • Each gas in a mixture behaves independently.

  • Example:

    • Find the partial pressures of O₂ and CH₄ in a 15.0 L vessel.

7. Standard Temperature and Pressure (STP)

  • Standard Conditions:

    • T=273.15KT = 273.15 KT=273.15K (0°C).

    • P=1P = 1P=1 atm.

    • 111 mole of gas occupies 22.4 L at STP.

8. Example Problems

  1. Find gas temperature when given P, V, and n.

  2. Calculate volume of Argon when conditions change from 0°C, 700 mmHg, and 15 mL to STP.

  3. Determine the density of He gas at 15.2 atm and 22°C.

  4. Find the molar mass of an unknown gas given mass, volume, T, and P.

  5. Calculate partial pressures of gases in a mixture.

Key Takeaways

  • Boyle’s Law: Pressure inversely proportional to Volume.

  • Charles’s Law: Volume directly proportional to Temperature.

  • Avogadro’s Law: Volume directly proportional to Moles.

  • Ideal Gas Law: Relates pressure, volume, moles, and temperature.

  • Dalton’s Law: Total gas pressure is the sum of partial pressures.

  • STP: Standard conditions make gas volume calculations simpler.

This summary fully details all sections of the PDF, including equations, concepts, and example problems. Let me know if you need further clarifications! 🚀

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