A hydrocarbon gas with an empirical formula #CH_2# has a density of 1.88 grams per liter at 0°C and 1.00 atmosphere. What is a possible formula for the hydrocarbon?

Question

Olivia Anton · Accepted Answer

We need to find a molecular mass, and the best way of doing this is the Ideal Gas Equation: #PV=nRT#.

We solve for #n# and #n="Mass"/"Molar mass"# #=# #(PV)/(RT)# And, #"Molar mass"# #=# #(RTxx"mass")/(PV)# #=# #(RT)/Pxx"mass"/V# #=# #(rhoRT)/P# because #"mass"/V=rho="density"# Consequently, #"Molar mass"# #=# #(rhoRT)/P# #(1.88*g*cancel(L^-1)xx0.0821*cancel(L)*cancel(atm)*cancel(K^-1)*mol^-1xx273.15*cancel(K))/(1.00*cancel(atm))# Well, this gives me an answer in #g*mol^-1#, so I might be doing something right. I get (finally!), #"Molar mass"# #=# #42.2*g*mol^-1# Now the molecular formula is always a mulitiple of the empirical formula, of course, the multiple might be #1#. #("Empirical formula")xxn="Molecular formula"# And #nxx(2xx1.00794 +12.01)*g*mol^-1=42.2*g*mol^-1#. Clearly, #n=3#, and molecular formula #=# #C_3H_6#. We have #"propylene"# or #"cyclopropene"#. I ask because it helps me understand how to bowl, and I take it that this is a first-year problem.

Xavier Avery · Answer

undefined The molecular formula of the hydrocarbon gas with an empirical formula CH2 is C2H4.