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QUESTION

# A sample of N2O effuses from a container in 43 seconds. How long would it take the same amount of gaseous I2 to effuse from the same container under identical conditions?

It would take 103s.

Graham's Law states that :

"RatepropI/sqrt(M_r)

Where M_r is the relative molecular mass.

For two gases:

R_1prop(1)/(sqrtM_(r(1)) color(red)((1))

and:

R_2prop1/sqrtM_(r(2)) color(red)((2))

Dividing color(red)((1))"by"color(red)((2)) gives:

R_1/R_2=sqrt(M_(r(2))/(M_(r(1)) color(red)((3))

The rate can be written as :

R=V/t

I am assuming here that "same amount" means equal volumes:

Since V is the same for both gases we can write:

R_1=V/t_1

And:

R_2=V/t_2

If we substitute these into color(red)((3)) we get:

t_2/t_1=sqrt(M_(r(2))/(M_(r(1))

So:

t_2=sqrt((M_(r(2)))/(M_(r(1))xxt_1

M_(r(1))=M_r[N_2O]=(2xx14)+16=44

M_(r(2))=M_r[I_2]=(2xx127)=254

So:

t_2=sqrt((254)/(44))xx43=103"s"