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Name ______________________________________ Pd ____ Date _____________________ 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, !! = ! ! ! , 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: !! !"#$%&’( ! = 1 2 ! ! ! = 1 2 ! ! ! = !! !"#$%&’( ! Simplifying the above equation gives us Graham’s Law: ! ! = ! ! 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? !!"#$%&’ !"#$%& = !"#$%& !!"#$%&’ = 32.0 2.0 = 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 (NH 3 ) 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? !""#$%! !!"#$%&’ !!!"#$%& = !!"#$%&’ !!!"#$%& !""#$%! = 72.9 17.0 = 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 !"#$%&" ! = !.! ! !" ! = 0.50 ! ! then, !"#$%&" ! = 0.50 ! ! ÷ 1.16 = 0.43 ! ! , you would smell perfume A at = 7.5 ÷ 0.43 ! ! = 17

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Name ______________________________________ Pd ____ Date _____________________

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!

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