Another chemist texts you to come pick up another unknown gas for your professor

Question

Another chemist texts you to come pick up another unknown gas for your professor. They caution that the gas is unstable and explosive at temperatures above 100 degree C. You know the canister will contain 1.1 *10^20 particles, has a heat capacity of 20.8 J/mol middot K, and based on your knowledge of calorimetry will have 1 J of thermal energy by the time you can pick it up. Calculate the temperature of the gas to determine if you will need to cool it down before transporting it to your professor.

Explanation / Answer

n = 1.1*1020 particles, CH = 20.8 J/mol K, Thermal Energy = 1J

E = nC(Tf - Ti) = 1.1*1020*20.8*(Tf - 373) = 1

22.88*(Tf - 373) = 1

Tf - 373 = 1/22.88 = 0.0437

Tf = 373+0.0437 = 373.0437 K

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