[whirlofwings]

A certain compound containing only carbon and hydrogen was found to have a vapor density of 2.550 g/L at 100 degrees C and 760 mm Hg. If the empirical formula of this compound is CH, what is the molecular formula of this compound?

I had some ideas as to how to solve this problem.

First, I thought of using the Specific Heat Formula to find a value, that could resemble a known element.

Q = m CP delta T
1 = m(2.550)(373.15)
1 = m(951.53)
m = 0.00105 g

At this point, I'm really stuck. I know that to find the molecular formula of a compound, I need to divide the empirical mass over the molecular mass. However, I am not sure how to find both masses. I was thinking to find the empirical mass I could calculate CH.

C = 14.011 g
H = 1.007 g

CH = 14.011 + 1.007 = 15.018 g

This appears to be the molecular mass, but I still need the molecular mass.

[Borek]

You know the density of the gas. What is volume of one mole of the gas at given PT?

[whirlofwings]

Thank you for your response. Unfortunately, I do not know how to use the density to find the volume. I am thinking that I would either use d = m/v or the Ideal Gas Law, PV = nRT. I am not sure which one though.

[Arkcon]

OK, you have two formulas.  You have to decide which one to use.  Since d=m/v, can you really use that one?  Don't gasses seem to have any volume, depending on any container.  You'd have an infinite number of answers, that won't work.

[whirlofwings]

I could try the Ideal Gas Law under STP.

That would give me:

PV = nRT

(1)(2.550) = n(0.082058)(273.15)
2.550 = n(22.41)
n = 0.113 mol CH

0.113 mol CH * 13.018 g CH = 1.481 g CH

This gives me the amount of CH under STP, but it does not give me the amount of CH at 100 degrees C and 1 atm. Also, this does not give me the molecular formula.

[AWK]

http://en.wikipedia.org/wiki/Ideal_gas_law

[Borek]

I could try the Ideal Gas Law under STP.

Why under STP? Use ideal gas law to calculate volume under given conditions. That's what the PV=nRT is for - it contains P and T, doesn't it?

[whirlofwings]

Alright, here is the Ideal Gas Law under stated conditions:

760 mmHg = 1 atm

PV = nRT
(1)(2.550) = n(0.082058)(373.15)
2.550 = n(30.619)
n = 0.0832 mol CH

At this point, I could convert moles to grams:

0.0832 mol CH * 13.018 g CH/1 mol CH = 1.084 g CH

I have the empirical mass of CH, but I still don't know the molecular mass of CH.

[Borek]

You are right you need molar mass, somehow you are fixed on CH and you don't see where the molar mass is. For now forget about the CH thing. Assume it doesn't exist. All you need is to calculate molar mass of the gas that has a given density at given P and T.

I have no idea what you calculated:

PV = nRT
(1)(2.550) = n(0.082058)(373.15)

2.550 is not the volume, it is the density, so it doesn't make sense in this context.

Please solve the ideal gas formula for V and calculate volume of the 1 mole of gas at given P and T.

[abhi001234]

molecular mass = 2 x vapour density

[AWK]

molecular mass = 2 x vapour density

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