If equal masses of O2 and N2 are placed in identical containers at the same temperature, which of the following statements is (are) true?

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If equal masses of O2 and N2 are placed in identical containers at the same temperature, the following statements are true:

1. The number of molecules of O2 is greater than the number of molecules of N2. This is because O2 has a molecular weight of 32 g/mol, while N2 has a molecular weight of 28 g/mol. Since the masses are equal, the number of molecules of O2 will be greater.

2. The pressure exerted by the O2 is greater than the pressure exerted by the N2. This is because pressure is directly proportional to the number of molecules and the temperature. Since the number of molecules of O2 is greater, it will exert a greater pressure.

3. The volume occupied by the O2 is greater than the volume occupied by the N2. This is because the volume occupied by a gas is directly proportional to the number of molecules and inversely proportional to the pressure. Since the number of molecules of O2 is greater, and its pressure is also greater, it will occupy a larger volume.

To determine which statement(s) are true, let's consider some key properties of oxygen (O2) and nitrogen (N2) gases.

1. Both oxygen (O2) and nitrogen (N2) are diatomic gases composed of two atoms each.
2. The masses of one oxygen (O2) molecule and one nitrogen (N2) molecule are different due to the different atomic masses for oxygen and nitrogen.
3. The molar mass of oxygen (O2) is approximately 32 g/mol, while the molar mass of nitrogen (N2) is approximately 28 g/mol.

Now, let's analyze each statement:

Statement 1: The oxygen gas will exert a higher pressure than the nitrogen gas.

To determine the pressure of a given amount of gas, we can use the ideal gas law, which states that pressure (P) is directly proportional to the number of moles (n) and the temperature (T), and inversely proportional to the container volume (V). Mathematically, this can be expressed as: P ∝ n/V.

Since the masses of oxygen (O2) and nitrogen (N2) are equal, the number of moles of both gases will also be equal (as they have the same molar mass). Additionally, if the gases are placed in identical containers at the same temperature, the volume will also be the same. Therefore, according to the ideal gas law, both gases will exert the same pressure. Hence, Statement 1 is false.

Statement 2: The oxygen gas will have a higher density than the nitrogen gas.

Density is defined as mass (m) divided by volume (V). Mathematically, this can be expressed as: Density (ρ) = m/V.

As the masses of oxygen (O2) and nitrogen (N2) are equal in this scenario, and both gases are placed in identical containers, the volume will also be the same. Therefore, the density of both gases will be equal. Thus, Statement 2 is false.

Statement 3: The nitrogen gas will have a higher average kinetic energy than the oxygen gas.

The average kinetic energy of a gas is directly proportional to its temperature. Since the temperature in both containers is the same, the average kinetic energy of both the oxygen gas and the nitrogen gas will be the same. Hence, Statement 3 is true.

In summary:
- Statement 1 is false.
- Statement 2 is false.
- Statement 3 is true.