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ICSE Class 9 Chemistry Question 21 of 29

Study of Gas Laws — Question 2

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Question 2

(a) State the law which the following graph verifies.

State the law which the graph verifies. Study of Gas Laws, Concise Chemistry Solutions ICSE Class 9.

(b) Derive the mathematical expression for it.

(c) Give one application/use where the above law is employed.

Answer

(a) Charles' law — It states that pressure remaining constant, the volume of a given mass of dry gas increases or decreases by 1273\dfrac{1}{273} of its volume at 0°C for each 1°C increase or decrease in temperature, respectively.

(b) Let V0 be the volume of a fixed mass of a gas at 0°C and let V be its volume at temperature t°C at constant pressure. Then according to Charles' law,

V = Vo + V0273\dfrac{\text{V}_0}{273}t (when P is constant)

V = Vo (1 + t273\dfrac{\text{t}}{273})

= Vo (273 + t273\dfrac{\text{273 + t}}{273})

V = V0273\dfrac{\text{V}_0}{273}T where T = 273 + t

For a given mass of a gas,

V0273\dfrac{\text{V}_0}{273} = constant

∴ V = k x T (where k is constant)

or V α T and VT\dfrac{\text{V}}{\text{T}} = K

Suppose a gas occupies V1 cm3 at T1 temperature and V2 cm3 at T2 temperature, then by Charles law,

    V1 α T1

or V1 = kT1 (k is constant)

or V1T1\dfrac{\text{V}_1}{\text{T}_1} = k and

    V2 α T2

or V2T2\dfrac{\text{V}_2}{\text{T}_2} = k

∴ V1T1\dfrac{\text{V}_1}{\text{T}_1} = V2T2\dfrac{\text{V}_2}{\text{T}_2} = k (at constant pressure)

(c) Volume of a given mass of a gas is directly proportional to its temperature, hence, density decreases with an increase in temperature. This is the reason that hot air is filled into balloons used for meteorological purposes.

Chapter Overview: Study of Gas Laws

Gas laws describe the behaviour of gases in terms of pressure (P), volume (V), and temperature (T). Boyle's Law states that at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure (PV = constant). Charles' Law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature (V/T = constant). These laws combine to give the Combined Gas Law: P1V1/T1 = P2V2/T2. Temperature must always be in Kelvin (K = °C + 273). Standard Temperature and Pressure (STP) is defined as 0°C (273 K) and 760 mm Hg (1 atm). The chapter also introduces the concept of absolute zero (−273°C or 0 K), where theoretically a gas would have zero volume. Students must solve numerical problems using these laws, convert between temperature scales, and understand the graphical representations of these relationships.

Key Formulas

Law / Formula Expression & Conditions
Boyle's LawP1V1 = P2V2 (at constant T and mass)
Charles' LawV1/T1 = V2/T2 (at constant P and mass); T in Kelvin
Combined Gas LawP1V1/T1 = P2V2/T2
Kelvin ConversionT(K) = T(°C) + 273
STP0°C (273 K) and 760 mm Hg (1 atm or 101.3 kPa)
Absolute Zero−273°C (0 K); theoretically the lowest possible temperature
Pressure Units1 atm = 760 mm Hg = 76 cm Hg = 101325 Pa

Must-Know Concepts

  • Boyle's Law graph: P vs V is a hyperbola; PV vs P is a straight horizontal line
  • Charles' Law graph: V vs T(K) is a straight line through the origin; V vs T(°C) intercepts at −273°C
  • Always convert temperature to Kelvin before using Charles' Law or Combined Gas Law
  • Gas laws apply to ideal gases; real gases deviate at high pressure and low temperature
  • When solving problems, identify which variable is constant to choose the correct law
  • At STP, 1 mole of any gas = 22.4 L (this connects to the mole concept in Class X)

Important Diagrams to Practice

  • P vs V graph (hyperbola) and PV vs P graph (horizontal line) for Boyle's Law
  • V vs T(K) graph (straight line through origin) for Charles' Law
  • V vs T(°C) graph showing extrapolation to absolute zero (−273°C)

Common Mistakes

  • Using temperature in °C instead of Kelvin in Charles' Law calculations
  • Confusing inversely proportional (Boyle's) with directly proportional (Charles')
  • Not converting pressure units consistently (mixing mm Hg with atm)
  • Applying gas laws to liquids or solids (they apply only to gases)
  • Forgetting to check that mass is constant when applying gas laws

Scoring Tips

  • Step 1 in every problem: convert temperature to Kelvin
  • Write down given values clearly with proper units before applying the formula
  • State which law you are using and the condition that makes it applicable
  • For graph questions, label axes correctly and mention the nature of the curve
  • Practice combined gas law problems - these are the most frequently asked

Frequently Asked Questions

Why must temperature be in Kelvin for gas law calculations?

The Celsius scale has an arbitrary zero point (freezing point of water). Charles' Law requires an absolute scale where 0 represents zero molecular motion (and theoretically zero volume). The Kelvin scale starts at absolute zero (−273°C), making it a true proportional scale for gas behaviour.

Can a gas actually reach absolute zero?

No. According to the Third Law of Thermodynamics, absolute zero can never be reached, only approached. At temperatures near absolute zero, gases liquefy and then solidify. Gas laws do not apply to liquids or solids.

What is the difference between an ideal gas and a real gas?

An ideal gas perfectly obeys all gas laws - its molecules have zero volume and no intermolecular forces. Real gases deviate from ideal behaviour at high pressures (molecules are close together) and low temperatures (intermolecular forces become significant). At normal conditions, most gases behave approximately ideally.