### Step 1 of 2

Given data: it is given that a gaseous hydrocarbon, whose volume (V) = 22.0 L, Temperature (T) = 391 K and pressure (P) = 3.02 atm gives 186.6 g of H2O and 364.5 g of CO2.

Find: Determine the molecular formula of the hydrocarbon.

**Explanation:**

To determine the molecular formula of the hydrocarbon, we can follow these steps:

- Find moles of water (H2O) and carbon dioxide (CO2) produced.
- Determine the mole ratio of carbon to hydrogen in the hydrocarbon.
- Find the empirical formula of the hydrocarbon.
- Determine the molecular formula using the molar mass.

### Step 2 of 2

Let us consider the molecular formula of hydro carbon is CxHy⋅

According to ideal gas equation we know PV=�RT

As we know the universal gas constant (R)value=0.082 L atm K−1mol−1.

Now n=PVRT

n=PVRTn=3.02 x 22.0(0.082) x 391n=66.4432.06n=2.07 mol of CxHY

The goal of the problem is to first determine the simplest formula for CxHy from the combustion analysis. Then, using the ideal gas law, determine the molar mass of the compound.

The ratio of the molecular molar mass and empirical molar mass will give the appropriate factor to convert the empirical formula into the molecular formula.

CxHy+O2⟶H2O+CO2

where, 186.6 g of H2O and 364.5 g of CO2 is given.

Molar mass of C (nC)=[364.5 g of CO244.01 gmol−1×1 mol of C1mol of CO2]

Molar mass of C=8.28 mol of C

Molar mass of H (nH)=[186.6 g of H2O18.01 g mol−1×2 mol of H1 mol of H2O]

Molar mass of H=20.71 mol of H

Now, normalize to the least common multiple (i.e., divide by the smallest n),

So, x = 1 and y = 2.5 and the empirical formula is C2H5.

As the molar mass value of the hydrocarbon = 2.07 so the exact molecular formula of the following hydrocarbon is C4H10.

**Explanation:**

Determine the ratio of moles of carbon to moles of hydrogen and simplify we get the molecular formula as C4H10.

##### Final solution

Therefore, the molar mass value of the hydrocarbon = 2.07.

so the exact molecular formula of the following hydrocarbon is C4H10.