Question:
Find the false statement for ideal gases.
Find the false statement for ideal gases.
Show Hint
For an ideal gas, average kinetic energy depends only on absolute temperature:
\[
KE=\frac{3}{2}RT
\]
It does not depend on pressure, volume, or molecular mass.
Updated On: Jun 24, 2026
- Kinetic energy of \(1\) mol of gas depends on mass of the gas molecule.
- Kinetic energy increases with increase in temperature.
- Kinetic energy of \(1\,g\) of \(H_2\) is higher than that \(8\,g\) of \(O_2\) at the same temperature.
- At a given temperature, kinetic energy does not depend on the pressure of the gas.
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The Correct Option is A
Solution and Explanation
Step 1: Recall the expression for kinetic energy of an ideal gas.
For an ideal gas, the average kinetic energy of one mole is \[ KE=\frac{3}{2}RT \] where \[ R \] is the gas constant and \[ T \] is the absolute temperature.
Thus, kinetic energy depends only on temperature and not on the nature or mass of the gas molecules.
Step 2: Analyze each statement.
Statement (1):
It says that kinetic energy depends on the mass of gas molecules.
This is incorrect because \[ KE=\frac{3}{2}RT \] contains only temperature.
Hence, statement (1) is false.
Statement (2):
Since kinetic energy is directly proportional to temperature, \[ KE\propto T \] Therefore, kinetic energy increases with increase in temperature. This statement is true.
Statement (3):
\[ 1\,g \] of \[ H_2 \] corresponds to \[ \frac{1}{2}\text{ mole} \] and \[ 8\,g \] of \[ O_2 \] also corresponds to \[ \frac{8}{32}=\frac{1}{4}\text{ mole} \] Since total kinetic energy depends on number of moles, \[ \frac{1}{2}\text{ mole of }H_2 \] has greater kinetic energy than \[ \frac{1}{4}\text{ mole of }O_2 \] Thus, statement (3) is true.
Statement (4):
At a fixed temperature, kinetic energy depends only on temperature and not on pressure. Hence, this statement is also true.
Step 3: Final conclusion.
Therefore, the false statement is \[ \boxed{\text{Kinetic energy of }1\text{ mol of gas depends on mass of the gas molecule}} \]
For an ideal gas, the average kinetic energy of one mole is \[ KE=\frac{3}{2}RT \] where \[ R \] is the gas constant and \[ T \] is the absolute temperature.
Thus, kinetic energy depends only on temperature and not on the nature or mass of the gas molecules.
Step 2: Analyze each statement.
Statement (1):
It says that kinetic energy depends on the mass of gas molecules.
This is incorrect because \[ KE=\frac{3}{2}RT \] contains only temperature.
Hence, statement (1) is false.
Statement (2):
Since kinetic energy is directly proportional to temperature, \[ KE\propto T \] Therefore, kinetic energy increases with increase in temperature. This statement is true.
Statement (3):
\[ 1\,g \] of \[ H_2 \] corresponds to \[ \frac{1}{2}\text{ mole} \] and \[ 8\,g \] of \[ O_2 \] also corresponds to \[ \frac{8}{32}=\frac{1}{4}\text{ mole} \] Since total kinetic energy depends on number of moles, \[ \frac{1}{2}\text{ mole of }H_2 \] has greater kinetic energy than \[ \frac{1}{4}\text{ mole of }O_2 \] Thus, statement (3) is true.
Statement (4):
At a fixed temperature, kinetic energy depends only on temperature and not on pressure. Hence, this statement is also true.
Step 3: Final conclusion.
Therefore, the false statement is \[ \boxed{\text{Kinetic energy of }1\text{ mol of gas depends on mass of the gas molecule}} \]
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