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At what temperature C would one mole of diatomic oxygen have 5.0 x 10^3 J of kinetic energy

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Final answer:

The temperature at which one mole of diatomic oxygen has 5.0 x 10^3 J of kinetic energy is approximately -32.15 °C, calculated using the relationship between kinetic energy and temperature for gases.

Step-by-step explanation:

In physics, especially thermodynamics, the kinetic energy of gas molecules is related to temperature through the equipartition theorem.

According to this theorem, for a diatomic gas such as oxygen (O2), each molecule has 5 degrees of freedom: 3 translational and 2 rotational, because the vibrational modes only come into play at much higher temperatures.

The total kinetic energy (KE) of one mole of a diatomic gas is given by KE = (5/2)nRT, where n is the number of moles, R is the universal gas constant (8.314 J/mol·K), and T is the temperature in kelvins (K).

Given that one mole of diatomic oxygen has 5.0 x 103 J of kinetic energy, we can calculate the temperature.

Setting up the equation 5.0 x 103 J = (5/2)(1 mol)(8.314 J/mol·K)T,

we solve for T.

Dividing both sides of the equation by (5/2)(8.314) gives us T ≈ 241 K.

To convert this to Celsius (°C), we use the conversion formula C = K - 273.15, which results in a temperature of approximately -32.15 °C.

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