Question

Determine the root-mean-square speed of CO2 molecules that have an average kinetic energy of 4.2 *10^-21 J per molecule

Answer 1

Kinetic energy KE of a gas is given as

KE = (3/2)*R/Na * T

where R is the gas constant R = 8.314 J/K

Na is Avogadros constant Na = 6.022*10²³

T is the temperature

Given that KE = 4.2 *10^-21 J per molecule

So,

4.2 *10^-21 J = 1.5*(8.314J/K/6.022*10²³ )*T

T = 4.2 *10^-21 J*6.022*10²³/(1.5*8.314)

T = 202.81 K

Root mean square velocity vrms is given as

vrms = sqrt(3RT/M)

where M is the molar mass of the gas

molar mass of CO2 = molar mass of C + molar mass of O*2

= 12g/mole + 16g/mole*2

= 44 g/mole

Putting values in the formula for vrms we get

vrms = sqrt(3*8.314 J/K-mole *202.81 K/ 44g/mole)

= sqrt(114.965) m/s

= 10.722 m/s