Respuesta :
The root mean square speed is given by V_rms = âšRT/M where r, t, and m are the rate constant, temperature and molar mass the gas
Average molar kinetic energy of the gas
E = 1/2 M * (V_rms)^2 = 8750 ms/1
So (V_rms)^2 = (2 * 8750) / M
Molar mass of 2 chlorine atoms in kg is 2 * 35 * 10^(-3)
Hence we have (V_rms)^2 = (2 * 8750)/ (2 * 35 * 10^(-3))
(V_rms)^2 = 8750/0.035 = 250000
So V_rms = âš 250000 = 500
Answer:
18.74 m/s is the root mean square speed of chlorine gas molecules under the same conditions.
Explanation:
Average kinetic energy is defined as the average of the kinetic energies of all the particles present in a system. It is determined by the equation:
[tex]K.E=\frac{3RT}{2}[/tex]
where,
K.E = Average kinetic energy
[tex]R[/tex] =Universal gas constant =8.314 J /mol K
T = Temperature of the system
He has an average kinetic energy of 8750 J/mol
[tex]8750 J/mol =\frac{3\times 8.314 J/mol K\times T}{2}[/tex]
T = [tex]\frac{8750 J/mol \times 2}{3\times 8.314 J/mol K}[/tex]
T = 701.63 K
The formula used for root mean square speed is:
[tex]\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
[tex]\nu_{rms}[/tex] = root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature =701.63 K
M = atomic mass = 0.071 kg/mole
[tex]N_A[/tex] = Avogadro’s number = [tex]6.02\times 10^{23}mol^{-1}[/tex]
[tex]\nu_{rms}=\sqrt{\frac{3\times 1.38\times 10^{-23}J/K\times 6.022\times 10^{23} mol^{-1}\times 701.63 K}{0.071 kg/mol}}[/tex]
[tex]\nu_{rms}=18.74 m/s[/tex]
18.74 m/s is the root mean square speed of chlorine gas molecules under the same conditions.
