Determining Molecular Formula of Hydrocarbon from Reactions

[cobaltcalcium]

This problem was proposed to us by our Chemistry professor. Consider a sample of a hydrocarbon at 0.959atm and 298K. Upon combusting the entire sample in oxygen, you collect a mixture of gaseous carbon dioxide and water vapor at 1.51atm and 375K. This mixture has a density of 1.391 g/L and occupies a volume four times as large as that of the pure hydrocarbon. Determine the molecular formula of the hydrocarbon.


I really do not know how to go about the problem. I think there's a relationship between the information that I am not seeing properly.

 

[ace123]

Well here's a hint. In the formula for pressure. PV=nRT. n is the number of moles. Does that help you?

 

[rocomath]

how can you re-write PV=nRT so that you can find molecular mass?

density equals what? how do you find moles?

 

[cobaltcalcium]

I know the ideal gas law, how to find moles etc. Density = mass/volume. But I'm still getting confused with what to do with all the data.

 

[ace123]

Well the moles of the 2 are going to be the same. Think you can do it now?

 

[cobaltcalcium]

This is what's on my scratch paper so far:

054 moles at 1.51atm/375k yields 1 liter
now molar wt for water is 18 g/m and CO2 is 44 g/m

say x is number of moles hydrogen needed
and y is number of moles carbon needed
from above we build a formula total moles equal to .054
so
x + y= .054
x=.054 -y
and we know that number moles times molar wt gives the weight and from above we know total weight is 1.391 g
so x *18g + y* 44g = 1.391g
or
18x + 44y = 1.39
x= (1.39 - 44y)/18
x= .077 - 2.44y
so combine
.077-2.44y = .054 - y
.077 - .054 = 2.44 y - y
.023 = 1.44 y
y = .016 mole
and
x=.054-.016
x= .038 mole
water to CO2 molar ratio is .038 /.016
or about 2 to 1
because water has 2 hydrogens and CO2 has only 1 carbon
the hydrogen to carbon ratio is 4 to 1
now find the size of the hydrocarbon buy finding the ratio of moles hydrocarbon to moles of CO2 /water mixture
ideal gas law ... pv=nrt or n=pv/rt
if the 1 subset is for before reaction
and the 2 subset is for after
r=(p1 v1)/(n1 t1) before
and
r= (p2 v2)/(n2 t2)
so
(p1 v1)/(n1 t1) = (p2 v2)/(n2 t2)
also some equalities
p2=(1.51/.959) p1= 1.57 p1
t2= 1.25 t1
v2 = 4 v1
so
( p1 v1 t2 )/(p2 v2 t1) = n1/n2
(p1 v1 1.25 t1)/(1.57 p1 4 v1 t1) =n1/n2
(1.25/ 4 * 1.57) =
n1/n2 = .2
5 n1 = n2
so you need 5 times more moles in the product then in the reactant.

Am I doing this right?