A 0.513 mol sample of Xe(g) initially at 298 K and 1.00 atm is held at constant

Question

A 0.513 mol sample of Xe(g) initially at 298 K and 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 18.5 K.

Assuming ideal gas behavior, calculate the amount of heat in joules (q) required to affect this temperature change and the total change in internal energy, U. Note that some books use E as the symbol for internal energy instead of U.

Type of gas Molar hear capacity @ canstant volume atoms 3/2R linear molecules 5/2R nonlinear molecules 3R

Explanation / Answer

Mol mass of 1 mole of sample= 131.29u

Mol mass of 0.513 mole of sample= 131.29 x 0.513 = 67.35g

Temperature difference= (18.5-298)= -279.5K

Sp heat capacity= 3/2R (as Xe has atoms)= 0.180 J/K

amount of heat required= m x c x change in temp = 67.35 x 0.180 x -279.5 = 3388.37J

Change in internal energy
U = (3/2)nRT

= 3/2 x 0.513 x 8.314 x 279.5=215.07 J

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