A container holds 0.019 moles of monatomic Argon (atomic mass 39.9) at a tempera

Question

A container holds 0.019 moles of monatomic Argon (atomic mass 39.9) at a temperature of 63 °C and a volume of 365 cm Constants: k 1.38x102 J/K; R-8.31 J/mol-K; 1 u 1.66x10 kg; 1 atm 1.01x10 Pa Draw a diagram of this (a box with a random bunch of particles zooming around, labeled appropriately; remember that every variable you use in an equation needs to be defined on you diagram). a) Find the pressure of the gas. i) Convert the volume to m3. ii) Convert the temperature to Kelvins. ii) Find the pressure. (Remember: 3 sig figs, SI units, and a box.) b) Find the rms velocity of the gas in two ways. Each method requires a units conversion. i) Use molar mass and R. ii) Use particle mass and k.

Explanation / Answer

a)

i) V = 365 cm^3

= 365*10^-6 m^3

ii) T = 63 C

= 63 + 273

= 336 K

iii) use P*V = n*R*T

P = n*R*T/V

= 0.019*8.314*336/(365*10^-6)

= 1.45*10^5 Pa

b)

i) Vrms = sqrt(3*R*T/M)

= sqrt(3*8.314*336/(39.9*10^-3))

= 458 m/s

ii) Vrms = sqrt(3*k*T/m)

= sqrt(3*1.38*10^-23*336/(39.9*1.67*10^-27))

= 457 m/s

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