Chemistry Exam > Chemistry Questions > Select incorrect statement(s):a)The product o...
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Select incorrect statement(s):
- a)The product of pressure and volume of fixed amount of a gas is independent of temperature
- b)The value of universal gas constant depends upon temperature, volume and number of gaseous molecules
- c)The gas constant also know as Boltzmann’s constant
- d)The average energy of molecules depends only on temperature
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Select incorrect statement(s):a)The product of pressure and volume of ...
**Incorrect Statement:**
c) The gas constant also known as Boltzmann's constant
**Explanation:**
The gas constant, denoted by the symbol R, is a physical constant that relates the properties of an ideal gas. It is used in various equations, such as the ideal gas law, to describe the behavior of gases. The gas constant is independent of the type of gas being considered and is the same for all gases.
On the other hand, Boltzmann's constant, denoted by the symbol k, is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is used in statistical mechanics to describe the relationship between temperature and energy.
**Differences between Gas Constant (R) and Boltzmann's Constant (k):**
1. **Definition:**
- The gas constant (R) relates the properties of an ideal gas, such as pressure, volume, and temperature, according to the ideal gas law.
- Boltzmann's constant (k) relates the average kinetic energy of particles in a gas to the temperature of the gas.
2. **Value:**
- The value of the gas constant (R) is approximately 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K), depending on the units used.
- The value of Boltzmann's constant (k) is approximately 1.38 × 10⁻²³ J/K.
3. **Units:**
- The gas constant (R) has units of energy per temperature per mole.
- Boltzmann's constant (k) has units of energy per temperature.
4. **Dependence on Temperature:**
- The gas constant (R) does not depend on temperature, volume, or the number of gaseous molecules. It is a constant value for all gases.
- Boltzmann's constant (k) does depend on temperature. It relates the average kinetic energy of particles to the temperature. As temperature increases, the average kinetic energy of particles also increases.
In summary, the gas constant (R) and Boltzmann's constant (k) are two different physical constants used in different contexts. The gas constant is independent of temperature, while Boltzmann's constant is temperature-dependent. Therefore, statement c) is incorrect.
c) The gas constant also known as Boltzmann's constant
**Explanation:**
The gas constant, denoted by the symbol R, is a physical constant that relates the properties of an ideal gas. It is used in various equations, such as the ideal gas law, to describe the behavior of gases. The gas constant is independent of the type of gas being considered and is the same for all gases.
On the other hand, Boltzmann's constant, denoted by the symbol k, is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is used in statistical mechanics to describe the relationship between temperature and energy.
**Differences between Gas Constant (R) and Boltzmann's Constant (k):**
1. **Definition:**
- The gas constant (R) relates the properties of an ideal gas, such as pressure, volume, and temperature, according to the ideal gas law.
- Boltzmann's constant (k) relates the average kinetic energy of particles in a gas to the temperature of the gas.
2. **Value:**
- The value of the gas constant (R) is approximately 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K), depending on the units used.
- The value of Boltzmann's constant (k) is approximately 1.38 × 10⁻²³ J/K.
3. **Units:**
- The gas constant (R) has units of energy per temperature per mole.
- Boltzmann's constant (k) has units of energy per temperature.
4. **Dependence on Temperature:**
- The gas constant (R) does not depend on temperature, volume, or the number of gaseous molecules. It is a constant value for all gases.
- Boltzmann's constant (k) does depend on temperature. It relates the average kinetic energy of particles to the temperature. As temperature increases, the average kinetic energy of particles also increases.
In summary, the gas constant (R) and Boltzmann's constant (k) are two different physical constants used in different contexts. The gas constant is independent of temperature, while Boltzmann's constant is temperature-dependent. Therefore, statement c) is incorrect.
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Community Answer
Select incorrect statement(s):a)The product of pressure and volume of ...
**Incorrect Statement**
The incorrect statement is:
c) The gas constant also known as Boltzmann's constant
**Explanation**
The gas constant, denoted by the symbol R, is a physical constant that appears in the ideal gas law equation:
PV = nRT
where P represents the pressure, V represents the volume, n represents the number of moles of gas, T represents the temperature, and R is the gas constant.
The gas constant is a proportionality constant that relates the pressure, volume, temperature, and amount of gas in an ideal gas. It is the same for all gases under ideal conditions.
**Boltzmann's Constant**
On the other hand, Boltzmann's constant, denoted by the symbol k, is a physical constant that appears in the context of statistical mechanics and thermodynamics. It relates the average kinetic energy of particles in a gas to the temperature of the gas.
The relationship between the gas constant (R) and Boltzmann's constant (k) is given by:
R = N * k
where N is Avogadro's number, which represents the number of particles (atoms or molecules) in one mole of substance.
In other words, Boltzmann's constant is a fundamental constant that relates the macroscopic properties of gases (such as pressure, volume, and temperature) to the microscopic properties of the individual gas particles (such as their average kinetic energy).
**Conclusion**
Therefore, the incorrect statement is option c) "The gas constant also known as Boltzmann's constant". The gas constant (R) and Boltzmann's constant (k) are related but they are two distinct and separate constants with different physical meanings and applications.
The incorrect statement is:
c) The gas constant also known as Boltzmann's constant
**Explanation**
The gas constant, denoted by the symbol R, is a physical constant that appears in the ideal gas law equation:
PV = nRT
where P represents the pressure, V represents the volume, n represents the number of moles of gas, T represents the temperature, and R is the gas constant.
The gas constant is a proportionality constant that relates the pressure, volume, temperature, and amount of gas in an ideal gas. It is the same for all gases under ideal conditions.
**Boltzmann's Constant**
On the other hand, Boltzmann's constant, denoted by the symbol k, is a physical constant that appears in the context of statistical mechanics and thermodynamics. It relates the average kinetic energy of particles in a gas to the temperature of the gas.
The relationship between the gas constant (R) and Boltzmann's constant (k) is given by:
R = N * k
where N is Avogadro's number, which represents the number of particles (atoms or molecules) in one mole of substance.
In other words, Boltzmann's constant is a fundamental constant that relates the macroscopic properties of gases (such as pressure, volume, and temperature) to the microscopic properties of the individual gas particles (such as their average kinetic energy).
**Conclusion**
Therefore, the incorrect statement is option c) "The gas constant also known as Boltzmann's constant". The gas constant (R) and Boltzmann's constant (k) are related but they are two distinct and separate constants with different physical meanings and applications.
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Select incorrect statement(s):a)The product of pressure and volume of fixed amount of a gas is independent of temperatureb)The value of universal gas constant depends upon temperature, volume and number of gaseous moleculesc)The gas constant also know as Boltzmanns constantd)The average energy of molecules depends only on temperatureCorrect answer is option 'C'. Can you explain this answer?
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