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Which gas molecules have the highest average kinetic energy at a given temperature?
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7. Gases
Kinetic Energy of Gases
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What is the kinetic energy of CO2 at 288 K in joules per mole?
A
3.58 kJ/mol
B
3.58 J/mol
C
3.58 x 10^-3 J/mol
D
3.58 x 10^3 J/mol
Verified step by step guidance1
Identify the formula for the average kinetic energy of a gas molecule, which is given by \( KE = \frac{3}{2} k_B T \), where \( k_B \) is the Boltzmann constant \( 1.38 \times 10^{-23} \text{ J/K} \) and \( T \) is the temperature in Kelvin.
Convert the kinetic energy from per molecule to per mole by using Avogadro's number \( N_A = 6.022 \times 10^{23} \text{ mol}^{-1} \). The formula becomes \( KE_{\text{mole}} = \frac{3}{2} k_B T N_A \).
Substitute the given temperature \( T = 288 \text{ K} \) into the formula: \( KE_{\text{mole}} = \frac{3}{2} \times 1.38 \times 10^{-23} \times 288 \times 6.022 \times 10^{23} \).
Calculate the expression to find the kinetic energy in joules per mole. This involves multiplying the constants and the temperature.
Convert the result from joules to kilojoules if necessary by dividing by 1000, and compare with the given options to identify the correct answer.
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