What are the steps to solve this problem? "The enthalpies of combustion of glucose and ethanol are -2813kj/mol and -1369kj/mol, use Hess's law to calculate the enthalpy change when 0.500 kg of glucose is allowed to ferment." Please help.
To solve this problem using Hess's Law, follow these steps:
Step 1: Write out the chemical equation for the fermentation of glucose.
C6H12O6(aq) → 2 C2H5OH(aq) + 2 CO2(g)
Step 2: Calculate the molar mass of glucose.
The molar mass of glucose (C6H12O6) is:
C = 12.01 g/mol x 6 = 72.06 g/mol
H = 1.008 g/mol x 12 = 12.096 g/mol
O = 16.00 g/mol x 6 = 96.00 g/mol
Total molar mass = 72.06 g/mol + 12.096 g/mol + 96.00 g/mol = 180.156 g/mol
Step 3: Convert the given mass of glucose to moles.
Given mass = 0.500 kg = 500 g
Moles of glucose = given mass / molar mass
Moles of glucose = 500 g / 180.156 g/mol = 2.773 mol
Step 4: Calculate the enthalpy change for the fermentation reaction.
Using Hess's Law, we need to consider the enthalpies of combustion of glucose and ethanol.
The enthalpy change for the combustion of glucose is -2813 kJ/mol.
The enthalpy change for the combustion of ethanol is -1369 kJ/mol.
But we need to remember that 2 moles of ethanol are produced per mole of glucose.
Step 5: Apply Hess's Law to calculate the enthalpy change for fermentation.
Enthalpy change = (2 moles of ethanol x enthalpy change of ethanol) - (enthalpy change of glucose)
Enthalpy change = (2 mol x -1369 kJ/mol) - (-2813 kJ/mol)
Enthalpy change = -2738 kJ - (-2813 kJ)
Enthalpy change = -2738 kJ + 2813 kJ
Enthalpy change = 75 kJ
Step 6: Interpret the result.
The enthalpy change for the fermentation of 0.500 kg of glucose is 75 kJ.
Therefore, the enthalpy change when 0.500 kg of glucose is allowed to ferment is 75 kJ.
To solve this problem using Hess's law and calculate the enthalpy change when 0.500 kg of glucose is allowed to ferment, follow these steps:
Step 1: Write the balanced chemical equation for the fermentation of glucose.
C6H12O6 (s) → 2 C2H5OH (l) + 2 CO2 (g)
Step 2: Calculate the molar mass of glucose:
Molar mass of glucose (C6H12O6) = (6 * atomic mass of carbon) + (12 * atomic mass of hydrogen) + (6 * atomic mass of oxygen)
You can find the atomic masses of carbon, hydrogen, and oxygen from the periodic table. Summing up these values will give you the molar mass.
Step 3: Calculate the number of moles of glucose:
Number of moles = mass / molar mass
First, convert the given mass from grams to kilograms since the molar mass was calculated based on kg.
Number of moles of glucose = 0.500 kg / molar mass of glucose
Step 4: Determine the enthalpy change for the combustion of glucose:
Enthalpy change for the combustion of glucose = -2813 kJ/mol (given)
Step 5: Calculate the enthalpy change for the fermentation of glucose:
According to Hess's law, the enthalpy change for the fermentation of glucose is equal to the difference between the enthalpies of combustion of ethanol and glucose.
Enthalpy change for fermentation of glucose = [2 * Enthalpy change for combustion of ethanol] - [2 * Enthalpy change for combustion of glucose]
(Since 2 moles of ethanol are produced per 1 mole of glucose in the fermentation reaction.)
Step 6: Substitute the known values into the equation and solve:
Enthalpy change for fermentation of glucose = [2 * -1369 kJ/mol] - [2 * -2813 kJ/mol]
Step 7: Perform the calculations to find the final answer.
Note that the enthalpy change for fermentation of glucose needs to be multiplied by the number of moles calculated in Step 3 to get the enthalpy change for the given mass of glucose.
Write and balance the combustion equation for ethanol + O2 ==> CO2 + H2O as eqn 1. Then reverse that equation multiply it by an integer to make mols CO2 cancel with mols CO2 in the next equation you write (also, change the sign for delta H and multiply by the same factor you use above).
The second equation is the combustion equation for glucose +O2 ==> CO2 + H2O. Balance that.
Then add the reverse and multiplied equation 1 to equation 2. Add the delta H values to find the overall dH for the new reaction.