Question #6cee9

The ratio of rates #Cl_2:N_2=0.63#

Graham's Law states that:

Rate of effusion #prop1/sqrt(M_r)#

Where #M_r# is the relative molecular mass.

For two gases:

#R_1/R_2=sqrt(M_(r(2))/(M_(r(1)))#

#M_r[Cl_2]=(35.5xx2)=71#

#M_r[N_2]=(14xx2)=28#

So #R_(Cl_2)/(R_(N_2)##=sqrt((28)/(71))=0.63#

Use Grahams's law, which states that the rate of effusion of a gas is inversely proportional to the square root of molar mass.

#r_"eff" prop 1/sqrt(M_M)#

This means that the rate of effusion of chlorine gas will be

#r_"chlorine" prop 1/sqrt(M_("M chlorine"))#

Likewise, the rate of effusion of nitrogen gas will be

#r_"nitrogen" prop 1/sqrt(M_("M nitrogen"))#

If you divide these two expressions, you'll get the ratio of effusion rates of chlorine and nitrogen

#r_"chlorine"/r_"nitrogen" = (1/sqrt(M_("M chlorine")))/(1/sqrt(M_("M nitrogen"))) = sqrt(M_("M nitrogen"))/sqrt(M_("M chlorine"))#

The numerical value of this ratio will be

#r_"chlorine"/r_"nitrogen" = (sqrt(28.014cancel("g/mol")))/(sqrt(70.906cancel("g/mol"))) = color(green)(0.629)#

Here is a video which shows how to solve a different problem using Graham's law.

Video from: Noel Pauller

Hope this helps!