Answer:
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To calculate the approximate thermal energy in kilojoules per mole (kJ/mol) of molecules at a given temperature, you can use the Boltzmann constant (k) and the ideal gas law.
The Boltzmann constant (k) is approximately equal to 8.314 J/(mol·K). To convert this to kilojoules per mole, we divide by 1000:
k = 8.314 J/(mol·K) = 0.008314 kJ/(mol·K)
Now, we need to convert the temperature to Kelvin (K) since the Boltzmann constant is defined in Kelvin. To convert from Celsius to Kelvin, we add 273.15 to the temperature:
T(K) = 75°C + 273.15 = 348.15 K
Finally, we can calculate the thermal energy using the formula:
Thermal energy = k * T
Thermal energy = 0.008314 kJ/(mol·K) * 348.15 K
Thermal energy ≈ 2.894 kJ/mol
Therefore, at 75°C, the approximate thermal energy of molecules is approximately 2.894 kilojoules per mole (kJ/mol).