# 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

#### Answer:

The molar mass of diacetyl,

#### Explanation:

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

where

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**

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

**Unknown**

Solve for

Rearrange the equation to isolate

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

The molecular formula for diacetyl is

#### Answer:

#### 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

where

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

The temperature, in Kelvin, is

and the pressure, in atmospheres, is

Finally, plugging in all our known variables, we have

To check this, the molecular formula of diacetyl is