Kinetic Energy of a Monoatomic Gas

To calculate the kinetic energy of a monoatomic gas, we need to use the formula:

Kinetic Energy = 1/2 * m * v^2

Where:
- Kinetic Energy is the energy possessed by an object due to its motion,
- m is the molar mass of the gas,
- v is the velocity of the gas particles.

Given:
- Molar mass (m) = 20.2 g/mol
- Velocity (v) = 5×10^4 m/s

Conversion of Molar Mass:
The given molar mass is in grams per mole, but we need to convert it to kilograms per mole to ensure consistent units throughout the calculation.

- Molar mass (m) = 20.2 g/mol = 0.0202 kg/mol

Conversion of Velocity:
The given velocity is in meters per second (m/s), which is already in the required unit.

Calculating Kinetic Energy:
Now, we can substitute the given values into the kinetic energy formula and solve for the kinetic energy.

- Kinetic Energy = 1/2 * m * v^2
= 1/2 * 0.0202 kg/mol * (5×10^4 m/s)^2
= 1/2 * 0.0202 kg/mol * (5×10^4)^2 m^2/s^2
= 1/2 * 0.0202 kg/mol * 25×10^8 m^2/s^2
= 0.0101 kg/mol * 25×10^8 m^2/s^2
= 2.525×10^6 kg·m^2/mol·s^2

Final Answer:
The kinetic energy of the monoatomic gas is 2.525×10^6 kg·m^2/mol·s^2.

Explanation:
The kinetic energy of a gas is determined by both the mass of the gas particles and their velocity. In this case, the molar mass of the gas is given as 20.2 g/mol, which is converted to kilograms per mole by dividing by 1000. The velocity of the gas particles is given as 5×10^4 m/s.

By substituting these values into the kinetic energy formula and performing the necessary calculations, we find that the kinetic energy of the monoatomic gas is 2.525×10^6 kg·m^2/mol·s^2.