# What is the ratio predicted from Graham's law for rates of diffusion for #NH_3#/#HCl# ?

##### 1 Answer

**Graham's Law of Diffusion** just bases the ratio of diffusion rates

#z^"*" prop 1/sqrt(M^"*")# .

Or more explicitly, with either gas having

#z_B/z_A = sqrt(M_A/M_B)#

You can see this answer for a more explicit derivation.

(The molar masses here can be used as

#=> color(blue)(z_(NH_3)/(z_(HCl))) = sqrt(M_(HCl)/M_(NH_3))#

#= sqrt("36.4609 g/mol"/"17.0307 g/mol")#

#= color(blue)(1.463)#

So, ammonia gas diffuses a bit less than

Another way to do this is to get the ratio of their molar masses right away:

#"17.0307 g/mol"/"36.4609 g/mol" = 0.467# and as such, we normalize

#M_(NH_3)# to#0.467# and#M_(HCl)# to#1# , as well as#z_(HCl) = 1# .

Ammonia then has a rate of diffusion that is...

#z_(NH_3) prop 1/sqrt(0.467) => 1.463# times as fast.

Whichever way works for you. I would suggest the first way, which is perhaps a bit less confusing.