States of Matter

A. Solid State

\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]

Properties & Key Points:

  • In solids, particles are closely packed and only vibrate about fixed positions. Solids have a definite shape and volume.
  • Density: Mass per unit volume of a solid.
  • Mass: The amount of matter in the solid.
  • Volume: The space occupied by the solid.
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B. Liquid State

\[\text{Pressure} = \frac{F}{A}\]

Properties & Key Points:

  • In liquids, particles are close but can move past each other, allowing liquids to flow. Liquids have a definite volume but take the shape of the container.
  • Pressure: Force per unit area exerted by the liquid.
  • F: Force exerted by the liquid.
  • A: Area over which the force is applied.
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C. Gaseous State

\[PV = nRT\]

Properties & Key Points:

  • Gases have widely spaced particles that move freely, allowing gases to expand and fill any container.
  • P: Pressure of the gas.
  • V: Volume of the gas.
  • n: Number of moles of the gas.
  • R: Ideal gas constant.
  • T: Temperature of the gas.
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A. Boyle's Law

\[P V = \text{constant} \quad \text{(at constant T and n)}\]

Properties & Key Points:

  • Boyle's law states that the pressure of a gas is inversely proportional to its volume at constant temperature.
  • P: Pressure of the gas.
  • V: Volume of the gas.
  • T: Temperature (constant).
  • n: Number of moles of gas (constant).
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B. Charles's Law

\[\frac{V_1}{T_1} = \frac{V_2}{T_2} \quad \text{(at constant P and n)}\]

Properties & Key Points:

  • Charles's law states that the volume of a gas is directly proportional to its temperature at constant pressure.
  • V: Volume of the gas.
  • T: Temperature of the gas.
  • P: Pressure (constant).
  • n: Number of moles of gas (constant).
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C. Avogadro's Law

\[\frac{V_1}{n_1} = \frac{V_2}{n_2} \quad \text{(at constant T and P)}\]

Properties & Key Points:

  • Avogadro's law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.
  • V: Volume of the gas.
  • n: Number of moles of gas.
  • P: Pressure (constant).
  • T: Temperature (constant).
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D. Ideal Gas Law

\[PV = nRT\]
\[P = \frac{nRT}{V}\]
\[V = \frac{nRT}{P}\]

Variables:

**Values of \( R \)**

Properties & Key Points:

  • The ideal gas law combines Boyle's, Charles's, and Avogadro's laws to describe the behavior of gases.
  • P: Pressure of the gas.
  • V: Volume of the gas.
  • n: Number of moles of gas.
  • R: Ideal gas constant.
  • T: Temperature of the gas.
  • \( R = 8.314 \, \text{J/mol} \times \text{K} \) (SI unit).
  • \( R = 0.0821 \, L \times atm/mol \times K \) (for pressure in atm, volume in liters).
  • \( R = 1.987 \, cal/mol \times \text{K} \) (calories).
  • \( R = 0.0831 \,L \times bar/mol \times \text{K} \) (for pressure in bar, volume in liters).
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E. Combined Gas Law

\[\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \quad \text{(at constant n)}\]

Properties & Key Points:

  • The combined gas law is a combination of Boyle’s, Charles’s, and Avogadro’s laws that relates pressure, volume, and temperature for a fixed amount of gas.
  • P: Pressure of the gas.
  • V: Volume of the gas.
  • T: Temperature of the gas.
  • n: Number of moles of gas (constant).
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F. Dalton's Law of Partial Pressures

\[P_{\text{total}} = P_1 + P_2 + P_3 + \dots\]

Properties & Key Points:

  • Dalton’s law states that the total pressure exerted by a gas mixture is the sum of the partial pressures exerted by individual gases.
  • \(P_{\text{total}}\): Total pressure exerted by the gas mixture.
  • \(P_1, P_2, P_3, \dots\): Partial pressures exerted by individual gases.
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G. Graham's Law of Diffusion

\[\frac{\text{Rate of Diffusion of Gas 1}}{\text{Rate of Diffusion of Gas 2}} = \sqrt{\frac{M_2}{M_1}}\]

Properties & Key Points:

  • Graham’s law relates the rate of diffusion of a gas to its molar mass. The rate of diffusion is inversely proportional to the square root of the molar mass of the gas.
  • Rate of Diffusion: The speed at which gas molecules spread.
  • \(M_1, M_2\): Molar masses of gas 1 and gas 2.
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H. Gay-Lussac’s Law

\[\frac{P_1}{T_1} = \frac{P_2}{T_2} \quad \text{(at constant V and n)}\]

Properties & Key Points:

  • Gay-Lussac’s law states that the pressure of a gas is directly proportional to its temperature at constant volume.
  • P: Pressure of the gas.
  • T: Temperature of the gas.
  • V: Volume (constant).
  • n: Number of moles of gas (constant).
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I. Boyle's Law (Revised for Isothermal Process)

\[P V = \text{constant}\]

Properties & Key Points:

  • Boyle's law for an isothermal process (constant temperature) states that pressure and volume of an ideal gas are inversely related.
  • P: Pressure of the gas.
  • V: Volume of the gas.
  • T: Temperature (constant).
  • n: Number of moles of gas (constant).
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J. Charle's Law (Revised for Isobaric Process)

\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]

Properties & Key Points:

  • Charles's law for an isobaric process (constant pressure) states that the volume of a gas is directly proportional to its temperature.
  • V: Volume of the gas.
  • T: Temperature of the gas.
  • P: Pressure (constant).
  • n: Number of moles of gas (constant).
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K. Ideal Gas Constant (R)

\[R = 8.314 \, \text{J/mol·K}\]

Properties & Key Points:

  • The ideal gas constant relates pressure, volume, temperature, and number of moles for any ideal gas.
  • R: Ideal gas constant.
  • J: Joules (unit of energy).
  • mol: Moles of gas.
  • K: Kelvin (unit of temperature).
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