I've been trying to do this problem but I would get confused and stuck..
Consider a sample of a hydrocarbon at 0.959 atm and 298 K. Upon combustion the entire sample in oxygen, you collect a mixture of gaseous carbon dioxide and water vapor at 1.51 atm and 375 K. This mixture has a density of 1.391 g/L and occupies a volume four times as large as that of the pure hydrocarbone. Determine the molecular formula of the hydrocarbon.
To determine the molecular formula of the hydrocarbon, we need to analyze the given information and use the ideal gas law, stoichiometry, and the concept of density to solve the problem. Here is a step-by-step explanation of how to approach this problem:
Step 1: Convert the given pressure and temperature values to appropriate units.
- Convert 0.959 atm and 1.51 atm to their equivalent in Pascal (Pa). (1 atm = 101325 Pa)
- Convert 298 K and 375 K to their equivalent in Kelvin (K).
Step 2: Determine the number of moles of each gas.
- Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.
- Rearrange the equation to solve for n: n = PV / (RT).
- Calculate the number of moles of carbon dioxide and water vapor generated upon combustion.
Step 3: Determine the volume of the pure hydrocarbon and the number of moles.
- Since the volume of the mixture is four times larger than that of the hydrocarbon, you can divide the given volume by four to find the volume of the hydrocarbon.
- Use the ideal gas law equation to calculate the number of moles of the hydrocarbon.
Step 4: Determine the empirical formula of the hydrocarbon.
- Determine the ratio of moles of carbon dioxide and water vapor produced in the combustion reaction.
- Find the smallest whole-number ratio of carbon and hydrogen atoms.
Step 5: Determine the molecular formula of the hydrocarbon.
- Use the empirical formula and the molar mass of the hydrocarbon to determine the molecular formula.
- Calculate the molar mass by adding the atomic masses of each element in the empirical formula.
By following these steps, you should be able to determine the molecular formula of the hydrocarbon.