When 50 grams of hydrocarbon X are burned with oxygen the products are carbon dioxide and water. If 65 grams of water and 100 grams of carbon dioxide are produced, how many grams of oxygen were needed for the reaction?

This was a question on my chemistry homework but I'm unsure of how to figure it out. I tried to find an equations for the reaction but failed.

To solve this question, we need to use the concept of stoichiometry, which relates the number of moles of reactants and products in a chemical reaction.

First, let's determine the moles of water and carbon dioxide produced in the reaction:

Moles of water = mass of water / molar mass of water
Molar mass of water (H2O) = 2 * molar mass of hydrogen + molar mass of oxygen = 2 * 1 + 16 = 18 g/mol
Moles of water = 65 g / 18 g/mol

Moles of carbon dioxide = mass of carbon dioxide / molar mass of carbon dioxide
Molar mass of carbon dioxide (CO2) = molar mass of carbon + 2 * molar mass of oxygen = 12 + 2 * 16 = 44 g/mol
Moles of carbon dioxide = 100 g / 44 g/mol

Now, let's determine the moles of hydrocarbon X burned:

Molar mass of hydrocarbon X is not given, so we cannot directly calculate the moles based on its mass.

However, since hydrocarbon X completely reacts to produce carbon dioxide and water, we can use the law of conservation of mass to find the mass of carbon and hydrogen in hydrocarbon X. This will help us find the empirical formula for X and its molar mass.

First, let's find the mass of carbon in the products (carbon dioxide):

Moles of carbon in carbon dioxide = moles of carbon dioxide * (1 mole carbon / 1 mole carbon dioxide)
Moles of carbon in carbon dioxide = (100 g / 44 g/mol) * (1 mol C / 1 mol CO2)
Moles of carbon in carbon dioxide = 100 / 44 mol

Now, let's find the mass of hydrogen in the products (water):

Moles of hydrogen in water = moles of water * (2 moles hydrogen / 1 mole water)
Moles of hydrogen in water = (65 g / 18 g/mol) * (2 mol H / 1 mol H2O)
Moles of hydrogen in water = 130 / 18 mol

Since hydrocarbon X only contains carbon and hydrogen, we can use the mass of carbon and hydrogen in the products to find the empirical formula and molar mass of hydrocarbon X.

Mass of carbon in hydrocarbon X = mass of carbon in products = (mass of carbon in carbon dioxide) / (moles of carbon in carbon dioxide)
Mass of carbon in hydrocarbon X = 100 / 44 g / (100 / 44 mol) = 100 g / mol

Mass of hydrogen in hydrocarbon X = mass of hydrogen in products = (mass of hydrogen in water) / (moles of hydrogen in water)
Mass of hydrogen in hydrocarbon X = 130 / 18 g / (130 / 18 mol) = 130 g / mol

Now, let's determine the empirical formula and molar mass of hydrocarbon X:

The empirical formula shows the relative ratio of atoms in a compound. To find it, we need to divide the molar masses by the molar mass of the smallest atom.

Empirical formula:

Empirical formula of hydrocarbon X = C: (100 g / mol) / (12 g / mol) = 8.33 ā‰ˆ 8
Empirical formula of hydrocarbon X = H: (130 g / mol) / (1 g / mol) = 130

The empirical formula of hydrocarbon X is C8H130.

Now that we know the empirical formula, we can calculate the molar mass of hydrocarbon X:

Molar mass of hydrocarbon X = 12 (C) + 130 (H) = 190 g/mol

Finally, let's determine the moles of hydrocarbon X:

Moles of hydrocarbon X = mass of hydrocarbon X / molar mass of hydrocarbon X
Moles of hydrocarbon X = 50 g / 190 g/mol

Now, using the balanced equation (which we do not have), we can determine the moles of oxygen required for the reaction. The balanced equation will show the stoichiometric coefficients of each reactant and product.

Without the balanced equation, it is not possible to determine the exact amount of oxygen needed for the reaction. You may need to check your textbook or notes to see if the balanced equation for the given reaction is provided. If not, you may need to ask your teacher for further guidance or clarification.