Question

NEED ASAP PLEASE

Problem 7. How long will it take for an initially clean surface to become 1% covered if it is bathed by an atmosphere of nitrogen at 77 K and one bar? Assume that every nitrogen molecule that strikes the surface sticks and that a nitrogen molecule covers an area of 1.1x10 pm

Answer 1

Answer given Every information 77k nitrogen. nitrogen molecule that strikes the surface Sticks covers and ind that that a a nitrogen molecule nitrogen an area of 1.18105 pm2. Number of N2- molecules hitting the surface per Cenit area and time : y here N/V Volume, which A=c144). (N/u) ov-au is the number of molecules per unit can be caluculated from ideal gas law. (P. V = Nok.bT] pou Ņ. Kb.T 5) NYU = pl (kb. t) V-av is the Because speed is average speed of the molecules. max well - Bolt 2 mann distributed. Average Speed I var = V(8.16bit lat. m))

Hence :- 4 - (1%). [P/(6.0)]. 169.66.T/Cm)) + (%). p. 162/6. m.kbT]) As per the given conditions. A = (12): 1Esparel(1.28.1.6605E-97kg. 7.8807€ 23J/k: 77k) = 5.67 44 E +27 m2 > Assume that every Can only be covered by portion of a single the surface, nitrogen molecule. let a be the fraction of the surface - not occupied by Na. - The rate which No - molecule hitting "free places" per anit surface is A-x. - - - More over assume that au molecules hitting a "free place at the surface get absorbed. if emultiply the surface specific rate above by you by the area occupied of a single nitrogen. molecule (a) are you get the rate the rate at which fraction of free area " decreases!

-) - dyldt 0-. doldr :-K.X {with KEIE 5 pm. 5.6744 € +27 26-1 5 E - 1972.5.6744€ | 27 m2 s - 61242 € 79501 differential equation by by solving this Seperation of variables. /x dx = - k dt s /x dx = - Skor in (x) = -kit to sinitial condition to find constant c. x6 =o) = 0 Inci) = -kit the time clapsed until 11 of the area, So le X=0.99 1: Incro /k .-In (0.99) 16.242 € 495- = 1.61F - 7257