Question

2.60 moles of chlorine gas are at a temperature of 291 K. Take the molar mass of chlorine to be 70.9 g/mol. Evaluate the number of molecules of chlorine that have speeds between 3.00 ✕ 102 m/s and 3.02 ✕ 102 m/s.

________ molecules ?

Answer 1

chlorine gas with n = 2.6 moles

temperature is T1 = 291 k

molar mass is MW = 70.9 g/mol

so the mass of chlorine gas is n = m/MW ==> m = n*MW = 2.6*70.9 g = 184.34 g = 0.18434 kg

we know that from Boltz man distribution

dN /N = (m/(2pi*k*T))^1/2 (-mv^2/e^(2kT)dv)

dN = N(m/(2pi*k*T))^1/2 (-mv^2/e^(2kT)dv)

dN = 2.6*(0.18434/(2pi*1.38*10^-23*291))^(1/2) ((-0.18434*300^2)/e^(2*1.38*10^-23*291*2)

dN = (1.1659214)*10^14

the number of chlorine gas molecules that have speeds between 3.00 ✕ 102 m/s and 3.02 ✕ 102 m/s is (1.1659214)*10^14