Consider the reaction between 56.0 mL of liquid ethanol (C2H5OH; density = 0.789 g/mL) and 26.0 L of O2 at 27.0°C and a pressure of 1.95 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.
To calculate the number of moles of H2O formed, we need to use the balanced equation of the reaction:
C2H5OH + 3O2 -> 2CO2 + 3H2O
First, let's find the number of moles of ethanol in 56.0 mL:
Mass of ethanol = volume x density = 56.0 mL x 0.789 g/mL = 44.184 g
Molar mass of ethanol (C2H5OH) = 2(12.01 g/mol) + 6(1.01 g/mol) + 16.00 g/mol = 46.07 g/mol
Number of moles of ethanol = mass / molar mass = 44.184 g / 46.07 g/mol = 0.9609 mol
Since the reaction is balanced at a 1:3 ratio between ethanol and water, we can see that 3 moles of water are produced for every mole of ethanol.
Number of moles of water = 3 x number of moles of ethanol = 3 x 0.9609 mol = 2.8827 mol
Therefore, if the reaction goes to completion, 2.8827 moles of H2O will be formed.
To calculate the number of moles of H2O formed, we first need to determine the limiting reagent in the reaction. The limiting reagent is the reactant that will be completely consumed, thus determining the maximum amount of product that can be formed.
Step 1: Convert the volume of ethanol to its mass.
Given:
- Volume of ethanol (C2H5OH) = 56.0 mL
- Density of ethanol = 0.789 g/mL
Mass of ethanol = Volume of ethanol x Density of ethanol = 56.0 mL x 0.789 g/mL
Step 2: Convert the mass of ethanol to moles.
To do this, we need to know the molar mass of ethanol (C2H5OH).
Molar mass of C2H5OH = (2 x molar mass of C) + (6 x molar mass of H) + molar mass of O
= (2 x 12.01 g/mol) + (6 x 1.01 g/mol) + 16.00 g/mol
Step 3: Use the given information about the O2 reactant to determine the number of moles available.
Given:
- Volume of O2 = 26.0 L
- Temperature (T) = 27.0°C converted to Kelvin (K) [K = T + 273.15]
- Pressure (P) = 1.95 atm
Using the ideal gas law equation PV = nRT, where P = pressure, V = volume, n = number of moles, R = gas constant, and T = temperature, we can calculate the number of moles of O2.
Step 4: Determine the stoichiometry of the reaction.
The balanced chemical equation for the reaction is:
C2H5OH + 3O2 → 2CO2 + 3H2O
From the balanced equation, we can see that 3 moles of H2O are produced for every 1 mole of ethanol.
Step 5: Determine the limiting reagent.
Compare the moles of ethanol (calculated in Step 2) with the moles of O2 (calculated in Step 3). Whichever is smaller is the limiting reagent.
Step 6: Calculate the number of moles of H2O formed.
Since ethanol is limiting, we can use the stoichiometry of the reaction to calculate the number of moles of H2O produced.
Moles of H2O = Moles of Ethanol x (3 moles of H2O / 1 mole of Ethanol)
By following these steps and inputting the given values, you can calculate the number of moles of H2O formed if the reaction goes to completion.