Consider the reaction between 52.0 mL of liquid ethanol (C2H5OH; density = 0.789 g/mL) and 25.4 L of O2 at 27.0°C and a pressure of 1.65 atm. The products of the reaction are CO2(g) and H2O(g). Calculate the number of moles of H2O formed if the reaction goes to completion.
This is a limiting reagent (LR) problem; you know that because amounts are given for BOTH reactants.
C2H5OH + 3O2 ==> 2CO2 + 3H2O
grams ethanol = volume x density = approx 40 but that's an estimate as are all of the other calculations here.
mols ethanol = grams/molar mass = approx 0.9.
Use PV = nRT and solve for n for O2 at the conditions listed. My estimate is approx 1.7 mols.
Using the coefficients in the balanced equation, convert mols ethanol to mols H2O. Do the same for mols O2 to mols H2O. It is likely you will obtain two values which means one of them is wrong; the correct value in LR problems is ALWAYS the smaller one and the reagent producing that number is the LR.
To calculate the number of moles of H2O formed, we can use the given information about the reaction and the stoichiometry of the balanced equation.
Step 1: Calculate the number of moles of ethanol
Given:
Volume of ethanol = 52.0 mL
Density of ethanol = 0.789 g/mL
First, we need to find the mass of ethanol:
Mass of ethanol = Volume of ethanol × Density of ethanol
= 52.0 mL × 0.789 g/mL
= 40.908 g
Next, we need to convert the mass of ethanol to moles using the molar mass of ethanol. The molar mass of ethanol (C2H5OH) is the sum of the atomic masses of carbon (C), hydrogen (H), and oxygen (O).
Molar mass of ethanol = (2 × atomic mass of C) + (6 × atomic mass of H) + (1 × atomic mass of O)
= (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + (1 × 16.00 g/mol)
= 46.07 g/mol
Number of moles of ethanol = Mass of ethanol / Molar mass of ethanol
= 40.908 g / 46.07 g/mol
= 0.888 mol (rounded to three decimal places)
Step 2: Calculate the number of moles of water formed
The balanced chemical equation for the reaction between ethanol and oxygen is:
C2H5OH + 3O2 → 2CO2 + 3H2O
From the balanced equation, we can see that three moles of water are produced for every mole of ethanol consumed.
Number of moles of H2O = Number of moles of ethanol × (3 moles of H2O / 1 mole of C2H5OH)
= 0.888 mol × 3
= 2.664 mol (rounded to three decimal places)
Therefore, if the reaction goes to completion, 2.664 moles of H2O will be formed.