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Graham’s  Law  Worksheet     Answer Key

Graham’s  Law  predicts  the  rate  at  which  two  gases  will  diffuse  based  on  their  particle  masses.    It  is  derived  from  

the  equation  for  thermal  energy,  𝐸!! =!!𝑚𝑣!,  where  m  =  the  particle’s  mass  and  v  =  the  particle’s  velocity;  and  

the  assumption  that  two  gas  particles  at  the  same  temperature  have  the  same  thermal  energy:  

𝐸!!  !"#$%&'(  ! =12𝑚!𝑣!! =

12𝑚!𝑣!! = 𝐸!!  !"#$%&'(  !  

Simplifying  the  above  equation  gives  us  Graham’s  Law:  

𝑣!𝑣!=

𝑚!

𝑚!  

Graham’s  Law  is  used  to  calculate  the  relative  rate  of  diffusion  and  effusion  of  two  particles  of  different  mass.    Qualitatively,  it  tells  us  that  the  lighter  particle  moves  faster  than  the  heavier  particle.  

Example:    A  hydrogen  particle  has  a  mass  of  2.0  amu  (atomic  mass  unit)  and  an  oxygen  particle  has  a  mass  of  32.0  amu.    If  the  two  particles  are  released  at  opposite  ends  of  a  100.0  cm  tube  where  will  they  meet  in  the  tube?  

𝑣!!"#$%&'𝑣!"#$%&

=𝑚!"#$%&

𝑚!!"#$%&'=

32.0  𝑎𝑚𝑢2.0  𝑎𝑚𝑢

= 4          

In  the  same  amount  of  time,  the  hydrogen  particle  will  travel  4  times  as  far  as  the  oxygen  particle.    Therefore,  the  two  particles  will  meet  at  20.0  cm  from  the  oxygen  end  of  the  tube.    

1. Hydrogen  chloride  particles  (HCl)  have  a  mass  of  72.9  amu  and  ammonia  particles  (NH3)  have  a  mass  of    17.0  amu.    If  hydrogen  chloride  and  ammonia  particles  are  released  at  opposite  ends  of  a  100.0  cm  tube  where  will  they  meet  in  the  tube?  

𝑣!""#$%!𝑣!!"#$%&'  !!!"#$%&

=𝑚!!"#$%&'  !!!"#$%&

𝑚!""#$%!=

72.9  𝑎𝑚𝑢17.0  𝑎𝑚𝑢

= 2.07          

In the same amount of time, the ammonia particles will travel 2.07 times as

far as the hydrogen chloride particles. Therefore, the two particles will meet at

32.6 cm from the hydrogen chloride end of the tube.

2. Two  perfumes  are  released  at  the  same  time.    You  are  standing  7.5  meters  from  both  of  them.    Perfume  A  has  a  particle  mass  of  275  amu  and  Perfume  B  has  a  particle  mass  of  205  amu.      a. Which  perfume  will  you  smell  first?     You would smell perfume B first, because the smaller particles move faster than the heavier particles.

b. If  you  smell  the  first  perfume  in  15  seconds,  how  long  from  the  time  they  were  released  will  it  take  you  to  smell  the  second  perfume?  

 !!"#$%&"  !

!!"#$%&"  != !!"#$%&"  !

!!"#$%&"  != !"#  !"#

!"#  !"#= 1.16  ,  also    𝑣!"#$%&"  ! =

!.!  !!"  !

= 0.50  !!  

  then,  𝑣!"#$%&"  ! = 0.50!!÷ 1.16 = 0.43!

!  ,  you  would  smell  perfume  A  at  𝑡 = 7.5  𝑚 ÷ 0.43!

!= 17  𝑠  

3. Create  your  own  Graham’s  Law  question  and  answer  it  in  the  space  below.  

  Several possible questions and answers.