Problem#8: Metabolism of alcohol (ethanol, C2H5OH) by the body takes place according to the reaction:
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l)
ΔHo = -1367 kJ
Determine the number of “food calories” (Cal) supplied by the alcohol in a 12-oz (355-mL) bottle of “Molson Ice” beer that contains 4.50% alcohol by mass. Assume the density of the beer to be 1.00 g/mL. (1 Cal = 4.18 kJ; MM of C2H5OH = 46.1 g/mol)
4.50% by mass means 4.50 g EtOH/100 g solution. The density is 1.00 g/mL; therefore, that becomes 4.50 g EtOH/100 mL. How much alcohol is contained in 355 mL of the beer?
4.50 g EtOH x 355 mL/100 mL = 15.975 grams EtOH.
You get 1367 kJ for each 46 g EtOH according to the equation; therefore, there are
1367 kJ x 15.975/46 g = 474.73 kJ
Convert 474.73 kJ to kcal and that will be the same as the Cal (food energy).
Check my work. Check my thinking.
To determine the number of food calories supplied by the alcohol in a 12-oz (355-mL) bottle of "Molson Ice" beer, we need to calculate the amount of alcohol (ethanol, C2H5OH) present in the beer, and then convert the energy released during metabolism to food calories.
Step 1: Calculate the mass of alcohol in the beer:
Given that the beer has a density of 1.00 g/mL and contains 4.50% alcohol by mass, we can calculate the mass of alcohol in the beer as follows:
Mass of beer = Volume of beer x Density of beer
= 355 mL x 1.00 g/mL
= 355 g
Mass of alcohol = Mass of beer x % alcohol by mass
= 355 g x (4.50/100)
= 16 g (rounded to 2 decimal places)
Step 2: Calculate the moles of alcohol:
Given the molar mass of C2H5OH is 46.1 g/mol, we can calculate the number of moles of alcohol present in the beer:
Moles of alcohol = Mass of alcohol / Molar mass of C2H5OH
= 16 g / 46.1 g/mol
= 0.347 mol (rounded to 3 decimal places)
Step 3: Calculate the energy released during metabolism:
Given that the enthalpy change (ΔHo) for the reaction is -1367 kJ, we can calculate the energy released in kJ per mole of alcohol:
Energy released per mole of alcohol = ΔHo / Stoichiometric coefficient of alcohol
= -1367 kJ / (1 mol alcohol)
= -1367 kJ/mol
Step 4: Convert kJ to food calories:
Given that 1 Calorie (Cal) is equal to 4.18 kJ, we can convert kJ to food calories:
Energy released per mole of alcohol in food calories = -1367 kJ/mol / (4.18 kJ/Cal)
= -327.75 Cal (rounded to 2 decimal places)
Step 5: Calculate the number of food calories supplied by the alcohol in the beer:
Given that there are 0.347 moles of alcohol in the beer, we can calculate the number of food calories supplied:
Food calories supplied by the alcohol in the beer = Energy released per mole of alcohol in food calories x Moles of alcohol
= -327.75 Cal x 0.347 mol
= -113.61 Cal (rounded to 2 decimal places)
Note: The negative sign in the energy value denotes the release of energy during metabolism.
Therefore, a 12-oz (355-mL) bottle of "Molson Ice" beer that contains 4.50% alcohol by mass supplies approximately 113.61 food calories.
To determine the number of "food calories" supplied by the alcohol in a 12-oz bottle of "Molson Ice" beer, we need to calculate the energy released during the metabolism of alcohol and convert it to calories.
Given:
- Density of the beer = 1.00 g/mL
- Mass of the beer = 355 mL × 1.00 g/mL = 355 g
- Alcohol content by mass = 4.50%
- Molecular mass of C2H5OH (alcohol) = 46.1 g/mol
- ΔHo (enthalpy change) for the reaction = -1367 kJ/mol
First, we need to find the mass of alcohol in the beer.
Mass of alcohol = 4.50% × 355 g = 15.975 g
Next, we need to calculate the number of moles of alcohol.
Number of moles of alcohol = mass of alcohol / molecular mass of alcohol
Number of moles of alcohol = 15.975 g / 46.1 g/mol ≈ 0.3464 mol
Now, we can calculate the energy released during the metabolism of alcohol.
Energy released = ΔHo × number of moles of alcohol
Energy released = -1367 kJ/mol × 0.3464 mol ≈ -473.2528 kJ
Finally, we need to convert the energy from kilojoules (kJ) to "food calories" (Cal).
1 Cal = 4.18 kJ
Number of "food calories" = Energy released / 4.18 kJ/Cal
Number of "food calories" = -473.2528 kJ / 4.18 kJ/Cal ≈ -113.4421 Cal
It is important to note that the negative sign indicates the release of energy during metabolism.
Therefore, the number of "food calories" supplied by the alcohol in a 12-oz bottle of "Molson Ice" beer is approximately 113.4421 Cal.