calculate the kinetic energy of hydrogen per mole at 0c

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To calculate the kinetic energy of hydrogen gas per mole at 0°C, we can use the formula derived from the kinetic theory of gases. The average kinetic energy of a gas molecule is directly related to its temperature. The formula for the average kinetic energy (KE) of one mole of an ideal gas is given by:

Kinetic Energy Formula

The average kinetic energy per molecule can be expressed as:

KE = (3/2) k T

Where:

• KE = average kinetic energy per molecule
• k = Boltzmann's constant (1.38 x 10^-23 J/K)
• T = absolute temperature in Kelvin

Converting Temperature

First, we need to convert the temperature from Celsius to Kelvin. The conversion is straightforward:

T(K) = T(°C) + 273.15

For 0°C, this gives us:

T = 0 + 273.15 = 273.15 K

Calculating Kinetic Energy for One Mole

Now, to find the kinetic energy for one mole of hydrogen gas, we can use the relationship between the average kinetic energy per molecule and the number of molecules in a mole, which is Avogadro's number (approximately 6.022 x 10²³ molecules/mol).

The total kinetic energy for one mole of gas can be calculated as:

KE(mole) = (3/2) R T

Where:

• R = universal gas constant (8.314 J/(mol·K))

Plugging in the Values

Now we can substitute the values into the equation:

KE(mole) = (3/2) * 8.314 J/(mol·K) * 273.15 K

Calculating this gives:

KE(mole) = (3/2) * 8.314 * 273.15 ≈ 339.5 J/mol

Final Result

Thus, the kinetic energy of hydrogen gas per mole at 0°C is approximately 339.5 Joules per mole. This value reflects the energy associated with the motion of the hydrogen molecules at this specific temperature, illustrating the relationship between temperature and kinetic energy in gases.