Calculate the molar mass in "g"/"mol"of diacetyl (butanedione) given that in the gas phase 100 degrees Celsius and 747 torr, a 0.3060 g sample of diacetyl occupies a volume of 0.111L?

2 Answers
May 26, 2017

The molar mass of diacetyl, "C"_4"H"_6"O"_2", as calculated based on the question parameters is "85.83 g/mol". Its actual molar mass is "86.09 g/mol".

Explanation:

You can use the ideal gas law to answer this question. The equation is:

PV=nRT,

where P is pressure, V is volume, n is moles, R is the gas constant, and T is the temperature in Kelvins. Add 273.15 to the Celsius temperature to get the temperature in Kelvins: 100^@"C" + 273.15="373 K".

We will use the ideal gas law to determine moles of diacetyl gas, then divide the given mass by the moles of diacetyl gas to determine its molar mass.

Known

m="0.3060 g"

P="747 torr"

V="0.111 L"

R=62.364color(white)(.)"L torr K"^(-1) "mol"^(-1)
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Physical_Properties_of_Matter/States_of_Matter/Properties_of_Gases/Gas_Laws/The_Ideal_Gas_Law

T="373 K"

Unknown

n=?

"molar mass = ? g/mol"

Solve for n.
Rearrange the equation to isolate n. Insert the known data and solve.

n=(PV)/(RT)

n=(747color(red)cancel(color(black)("torr"))xx0.111color(red)cancel(color(black)("L")))/((62.364color(white)(.)color(red)cancel(color(black)("L"))color(red)cancel(color(black)("torr")) color(red)cancel(color(black)("K")))^(-1) "mol"^(-1)xx373color(red)cancel(color(black)("K")))="0.003565 mol"

Now that you have moles, divide the mass of diacetyl given in the question by the moles.

"Molar mass diacetyl" = (0.3060"g diacetyl")/(0.003565"mol diacetyl")="85.83 g/mol diacetyl" rounded to four significant figures

The molecular formula for diacetyl is ("CH"_3"CO)"_2 or "C"_4"H"_6"O"_2" and its known molar mass to three sig figs is "86.09 g/mol". https://www.ncbi.nlm.nih.gov/pccompound?term=%22diacetyl%22

"Percent error" = abs(("known value"-"experimental value")/("accepted value"))xx100

"Percent error"=abs((86.09-85.83)/(86.09))xx100="0.3020%"

May 26, 2017

85.9 "g"/"mol"

Explanation:

What we can do here is calculate the density of the diacetyl, and use that to directly calculate the molar mass. We will use the equation

M = (dRT)/P

where M is the molar mass of the substance,
d is its density, in "g"/"L",
R is the universal gas constant, equal to 0.08206 ("L"-"atm")/("mol"-"K"),
T is the absolute temperature (in "K"), and
P is the pressure of the gas (in "atm")

Where is this equation derived from? Read the steps below if you would like to know, otherwise, skip to the next step.

Well, let's recall our ideal-gas equation, and rearrange it to solve for units similar to that of density, "mol"/"L", which is n/V:

PV = nRT

P = (nRT)/V

P/(RT) = n/V

Now, let's multiply both sides of the equation by M, the molar mass with units "g"/"mol":

(PM)/(RT) = (nM)/V

If we list the right side of the equation in terms of units, we have

cancel("mol")/"L" xx "g"/cancel("mol") = "g"/"L"

Which is the units for density. Thus, the value (nM)/V is the density of the gas, and if we plug this back into our equation:

(PM)/(RT) = (nM)/V = d

Thus, d = (MP)/(RT), and rearranging to solve for the molar mass yields our original equation, M = (dRT)/P.

The density of the diacetyl is

d = (0.3060"g")/(0.111 "L") = 2.76 "g"/"L"

The temperature, in Kelvin, is

100^oC + 273 = 373 "K"

and the pressure, in atmospheres, is

747 cancel("torr")((1 "atm")/(760 cancel("torr"))) = 0.983 "atm"

Finally, plugging in all our known variables, we have

M = ((2.76 "g"/cancel("L"))(0.08206 (cancel("L")-cancel("atm"))/("mol"-cancel("K")))(373 cancel("K")))/(0.983 cancel("atm")) = color(red)(85.9 "g"/"mol"

To check this, the molecular formula of diacetyl is ("CH"_3"CO")_2, and from this the molar mass is found to be 86.1 "g"/"mol", which measures up well with our result.