Which of the following statement is false

Options

A. The product of pressure and volume of fixed amount of a gas is independent of temperature
B. Molecules of different gases have the same K.E. at a given temperature
C. The gas equation is not valid at high pressure and low temperature
D. The gas constant per molecule is known as Boltzmann constant

Explanation

To determine which of the following statements is false, we will analyze each statement one by one based on the principles of gas laws and kinetic theory.

1. **Statement 1**: "The product of pressure and volume of a fixed amount of gas is independent of temperature."
- To analyze this, we can refer to the ideal gas law, which is expressed as:
\[ PV = nRT \]
Here, \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin. For a fixed amount of gas (where \(n\) is constant), the equation shows that \(PV\) is directly proportional to \(T\). Therefore, as temperature changes, the product of pressure and volume also changes. This means that the statement is **false**.

2. **Statement 2**: "Molecules of different gases have the same kinetic energy at a given temperature."
- According to the kinetic theory of gases, the average kinetic energy of gas molecules is given by:
\[ KE = \frac{3}{2} kT \]
where \(k\) is the Boltzmann constant and \(T\) is the temperature. This implies that at a given temperature, all gas molecules (regardless of their type) will have the same average kinetic energy. Thus, this statement is **true**.

3. **Statement 3**: "The gas equation is not valid at high pressure and low temperature."
- The ideal gas law is based on the assumption that gas molecules do not interact and occupy no volume. At high pressures, gas molecules are forced closer together, and interactions become significant, leading to deviations from ideal behavior. Similarly, at low temperatures, the kinetic energy of the molecules decreases, and intermolecular forces become more significant. Therefore, this statement is also **true**.

4. **Statement 4**: "The gas constant per molecule is known as the Boltzmann constant."
- The universal gas constant \(R\) is related to the Boltzmann constant \(k\) by the equation:
\[ R = N_A k \]
where \(N_A\) is Avogadro's number. The Boltzmann constant is indeed the gas constant per molecule, making this statement **true**.

**Conclusion**: The false statement among the options is the first one: "The product of pressure and volume of a fixed amount of gas is independent of temperature."