Question

Calculate the average translational kinetic energy, Ex, for one mole of gas at 537 K. Translational kinetic energy is sometimes called average kinetic energy Ex = J/mol Calculate the average translational kinetic energy for a single gas molecule at 537 K. J/molecule

Answer 1

To solve this question, we firest need to know what is the average translational Kinetic energy. Here, it is given that translational Kinesi'c energy is sometimes called average Kinolic energy. We Know that Kinetic energy is the energy possessed by a body when it is in motion. The average kinetic energy is the average of au the particles in motion. it is given by io kinetic Energy CKIE) K.E. = 3 nRT I equation ④ where n = no. of moles of the species Ci at present R = Gas constant T = Temperature in Kelvin. In case 1: No. of molee given = 1 m in) Temperature given = 587K. (T). Gras constant (R)= 8.314 ] K-1 moi!

K.E. = 3 x 1x 8.314 I x 5 344) xx mol) Thom ear IK.E. = 6696.93 ] mol-1 for the second case, from ean Og KIE. = 3 nRT N Now n - no. of moles - 7 No. of molecules Avogadros no. 'ik.E. N x RXT. NA - 3 xNx ( 2 ) XT XNXK XT - Bolzmann constant where K-R NA inkiE. = 3 XNXKXT. given N= 1 T = 537K. and k = R = 8.3145 I lollk 6.022X1023 molecules mol NA =1.38 x10-237/K/molecule KE - 3 x 1 x 5375) x 1.38 x 102 J K x molewe) k.£. = 1.1116 x 10-20 1 / molecule