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What volume of CO₂ is absorbed when 100 ml of a gas mixture containing O₂, CO₂, and Ne is treated with NaOH, reducing the volume to 70 ml?
What volume of CO₂ is absorbed when 100 ml of a gas mixture containing O₂, CO₂, and Ne is treated with NaOH, reducing the volume to 70 ml?
In the reaction of a hydrocarbon with oxygen, if 16 ml of hydrocarbon results in the production of 48 ml of CO₂, what is the value of 'x' in the molecular formula CxHy?
In the reaction of a hydrocarbon with oxygen, if 16 ml of hydrocarbon results in the production of 48 ml of CO₂, what is the value of 'x' in the molecular formula CxHy?
After a hydrocarbon explosion, a contraction of 48 ml is observed with KOH. What does this indicate about the amount of CO₂ produced?
After a hydrocarbon explosion, a contraction of 48 ml is observed with KOH. What does this indicate about the amount of CO₂ produced?
When a mixture of CH₄ and C₂H₂ is exploded and treated with KOH, a reduction of 165 ml is observed. What information does this provide about the original volumes of CH₄ and C₂H₂?
When a mixture of CH₄ and C₂H₂ is exploded and treated with KOH, a reduction of 165 ml is observed. What information does this provide about the original volumes of CH₄ and C₂H₂?
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If 16 ml of hydrocarbon is reacted with excess oxygen, and produces an equivalent volume of water, what is the total volume of gases that must be accounted for after the reaction?
If 16 ml of hydrocarbon is reacted with excess oxygen, and produces an equivalent volume of water, what is the total volume of gases that must be accounted for after the reaction?
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What will happen to the volume of the gas mixture consisting of CH₄ and C₂H₂ after complete combustion?
What will happen to the volume of the gas mixture consisting of CH₄ and C₂H₂ after complete combustion?
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Which reagent is typically used to absorb CO₂ during eudiometry?
Which reagent is typically used to absorb CO₂ during eudiometry?
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In the reaction 1 C₂H₂ + $\frac{5}{2}$ O₂ → 2 CO₂ + H₂O, how many moles of O₂ are consumed per mole of C₂H₂?
In the reaction 1 C₂H₂ + $\frac{5}{2}$ O₂ → 2 CO₂ + H₂O, how many moles of O₂ are consumed per mole of C₂H₂?
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What is the correct expression for the second virial coefficient B under normal conditions?
What is the correct expression for the second virial coefficient B under normal conditions?
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At which temperature does the equation TB = a / Rb hold true?
At which temperature does the equation TB = a / Rb hold true?
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Which of the following statements about the law of corresponding states is incorrect?
Which of the following statements about the law of corresponding states is incorrect?
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What is the equation for the inversion temperature Ti in terms of the constants a and b?
What is the equation for the inversion temperature Ti in terms of the constants a and b?
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In the collision theory, the collision number Z₁ is defined as which of the following?
In the collision theory, the collision number Z₁ is defined as which of the following?
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What do the variables Tc, Pc, and Vc represent in the law of corresponding states?
What do the variables Tc, Pc, and Vc represent in the law of corresponding states?
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How is the average velocity Vav of gas particles determined?
How is the average velocity Vav of gas particles determined?
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Under what condition does a real gas behave ideally, according to the compressibility factor Z?
Under what condition does a real gas behave ideally, according to the compressibility factor Z?
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What does the mean free path (λ) represent in gas molecules?
What does the mean free path (λ) represent in gas molecules?
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Which factor affects the collision frequency (Z₂) the least?
Which factor affects the collision frequency (Z₂) the least?
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When the temperature of an ideal gas is increased while keeping pressure constant, which of the following changes is true for collision frequency (Z₂)?
When the temperature of an ideal gas is increased while keeping pressure constant, which of the following changes is true for collision frequency (Z₂)?
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If the number of molecules per unit volume (N*) increases, what happens to the mean free path (λ)?
If the number of molecules per unit volume (N*) increases, what happens to the mean free path (λ)?
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How is the diffusion coefficient (D.C.) of an ideal gas related to mean speed and mean free path?
How is the diffusion coefficient (D.C.) of an ideal gas related to mean speed and mean free path?
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What happens to the diffusion coefficient (D.C.) of an ideal gas when its absolute temperature is increased four times and pressure is doubled?
What happens to the diffusion coefficient (D.C.) of an ideal gas when its absolute temperature is increased four times and pressure is doubled?
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What is the relationship between pressure (P), temperature (T), and the number of molecules per unit volume (N*)?
What is the relationship between pressure (P), temperature (T), and the number of molecules per unit volume (N*)?
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In the equation λ = Vav/Z₁, what does Z₁ represent?
In the equation λ = Vav/Z₁, what does Z₁ represent?
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Study Notes
Eudiometry
- Eudiometry is a technique for determining the composition of a gas mixture by measuring the volume changes that occur when the mixture is reacted with specific reagents.
- For example, passing a gas mixture through a solution of NaOH will absorb acidic gases like CO₂ and SO₂.
- Passing the mixture through alkaline pyrogallol will absorb O₂.
- This allows for the determination of the volume of each gas present in the mixture.
- Eudiometry - Mole Concept*
- CxHy + (x + 1/4y) O₂ → x CO₂ + 1/2y H₂O
- The equation above helps us calculate the volumes of reactants and products in a chemical reaction involving a hydrocarbon (CxHy) and oxygen.
Virial Equation of State
- The Virial Equation of State describes the behavior of real gases, taking into account the intermolecular interactions between gas molecules.
- The equation is expressed as Z = 1 + B/V + C/V² + D/V³ + ... where Z is the compressibility factor, V is the molar volume, and B, C, D, ... are the virial coefficients which account for attractive and repulsive forces.
- The second virial coefficient (B) is related to the Van der Waals constants a and b by B = b - a/RT, where T is the temperature and R is the ideal gas constant.
- The Boyle's Temperature (TB) is the temperature at which the second virial coefficient is zero, meaning the real gas behaves ideally: TB = a/Rb.
Inversion Temperature
- The inversion temperature (Ti) of a gas is the temperature at which a real gas, upon expansion, neither cools nor heats.
- This temperature is related to the Boyle's Temperature by Ti = 2a/Rb = 2TB.
Equation of Law of Corresponding State
- This law states that the behavior of real gases is similar when they are at comparable reduced conditions, which are relative to their critical properties (critical temperature (Tc), critical pressure (Pc), and critical volume (Vc)).
- The reduced temperature, pressure, and volume are defined as T/Tc, P/Pc, and V/Vc, respectively.
- The law of corresponding states states that the reduced pressure and volume of two different gases at their respective Tc are the same.
Law of Corresponding State
- Two gases having the same reduced pressure and reduced volume would also possess the same reduced temperature.
Collision Theory
- Collision theory explains the rate of chemical reactions at a molecular level.
- It assumes that gas molecules are considered as hard spheres.
- The number of collisions a gas particle suffers in one second is known as the collision number (Z₁). It depends on the radius of the gas molecule, average velocity, and the number density of gas particles.
- Z₁ = √2(πσ²) (Vav) (N*)
- Collision frequency (Z₂) is the total number of collisions per second per unit volume and is calculated as: Z₂ = √2 (πσ²) (Vav) N*²/2.
Factors Affecting Collision Frequency
- Collision Frequency (Z₂) is directly proportional to the square of the pressure (P²) and inversely proportional to the 3/2 power of the absolute temperature (T): Z₂ ∝ P²/T3/2.
- It's also inversely proportional to the square of the volume (V): Z₂ ∝ 1/V².
- At constant pressure, the collision frequency decreases with increasing temperature.
- At constant volume, the collision frequency increases with increasing temperature.
Mean Free Path (λ)
- The mean free path is the average distance a gas molecule travels between two successive collisions.
- It is calculated as: λ = Vav/Z₁, where Vav is the average velocity and Z₁ is the collision number.
- This equation can be simplified as: λ = 1/√2πσ²N*.
Factors Affecting Mean Free Path
- The Mean Free Path (λ) is inversely proportional to the pressure (P) and directly proportional to the absolute temperature (T): λ ∝ T/P.
- It's also directly proportional to the volume (V): λ ∝ V.
Summary of Key Equations and Factors:
- Collision number (Z₁) = √2(πσ²) Vav x N*
- Collision frequency (Z₂) = √2(πσ²) (Vav) x N*²/ 2
- Z₂ ∝ P²/T3/2
- Z₂ ∝ 1/V²
- Mean free path (λ) = 1/√2πσ²N*
- λ ∝ T/P
- λ ∝ V
- σ = radius of the gas molecule
- Vav = average velocity of the gas molecules
- N* = number of gas molecules per unit volume
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Explore the principles of eudiometry and the Virial Equation of State in this quiz. Understand how gas compositions are determined and how real gases behave based on intermolecular interactions. Test your knowledge of these significant concepts in physical chemistry!
