Total Kinetic energy of 56 g of N2 gas at 27°C is

To find the total kinetic energy of a gas, we can use the formula:

KE = 3/2 * n * k * T

where:

• KE is the kinetic energy
• n is the number of moles
• k is the Boltzmann constant (1.38 * 10^-23 J/K)
• T is the temperature in Kelvin

First, we need to convert the mass of N2 gas to moles. The molar mass of N2 is approximately 28 g/mol. So, 56 g of N2 is 2 moles.

Next, we need to convert the temperature from Celsius to Kelvin. The formula to convert is K = °C + 273.15. So, 27°C is approximately 300.15 K.

Now we can substitute these values into the formula:

KE = 3/2 * 2 moles * 1.38 * 10^-23 J/K * 300.15 K

Solving this gives:

KE = 6.21 * 10^-21 Joules

However, this is the kinetic energy per molecule. To find the total kinetic energy, we need to multiply this by the total number of molecules.

The number of molecules in a mole is Avogadro's number, which is approximately 6.022 * 10^23. So, the total number of molecules is 2 moles * 6.022 * 10^23 = 1.2044 * 10^24 molecules.

Therefore, the total kinetic energy is:

KE = 6.21 * 10^-21 Joules/molecule * 1.2044 * 10^24 molecules = 7476 Joules.