When 0.3212g of glucose was burned in bomb calorimeter of calorimeter constant 641J/K, the temperature rose by 7.943 K. Calculate a) the standard molar internal energy of combustion b) the standard enthalpy of combustion and c) the standard enthalpy of formation of glucose. (Heat of formation of CO2 and water are -393.5 and -285.8 kJ/mol, respectively.)

To answer these questions, we first need to understand some key concepts: calorimeter constant, enthalpy of combustion, enthalpy of formation, and the relationship between heat and temperature change.

a) The standard molar internal energy of combustion is the energy released per mole of a substance when it undergoes complete combustion. It can be calculated using the following formula:

ΔU°comb = q / n

Where:
ΔU°comb = the standard molar internal energy of combustion
q = heat evolved during combustion (in Joules)
n = number of moles of the substance burned

b) The standard enthalpy of combustion is the enthalpy change associated with the complete combustion of one mole of a substance. It can be calculated using the equation:

ΔH°comb = q / n

Where:
ΔH°comb = the standard enthalpy of combustion
q = heat evolved during combustion (in Joules)
n = number of moles of the substance burned

c) The standard enthalpy of formation is the enthalpy change that occurs when one mole of a compound is formed from its elements in their standard reference forms. It can be calculated using the equation:

ΔH°f = Σ(n × ΔH°f(products)) - Σ(n × ΔH°f(reactants))

Where:
ΔH°f = the standard enthalpy of formation of the compound
n = number of moles of each substance (in this case, glucose, CO2, and H2O)
ΔH°f(products) = standard enthalpy of formation of the products
ΔH°f(reactants) = standard enthalpy of formation of the reactants

Now, let's calculate the values:

Step 1: Calculate the heat evolved during combustion (q)
Given:
Mass of glucose burned = 0.3212 g
Temperature rise = 7.943 K
Calorimeter constant (C) = 641 J/K

q = (m × C × ΔT)

Where:
m = mass of glucose burned (in grams)
C = calorimeter constant (in J/K)
ΔT = temperature rise (in K)

q = (0.3212 g × 641 J/K × 7.943 K)

Step 2: Calculate the number of moles of glucose burned (n)
Using the molar mass of glucose (C6H12O6), we can convert the mass of glucose to moles.

Molar mass of glucose = 6(12.01 g/mol) + 12(1.01 g/mol) + 6(16.00 g/mol) = 180.18 g/mol

n = (m / Molar mass)

n = (0.3212 g / 180.18 g/mol)

Step 3: Calculate the standard molar internal energy of combustion (ΔU°comb)
ΔU°comb = q / n

ΔU°comb = (q / n)

Step 4: Calculate the standard enthalpy of combustion (ΔH°comb)
ΔH°comb = q / n

ΔH°comb = (q / n)

Step 5: Calculate the standard enthalpy of formation of glucose (ΔH°f)
Using the given enthalpies of formation for CO2 (-393.5 kJ/mol) and H2O (-285.8 kJ/mol), we can calculate the enthalpy of formation for glucose.

ΔH°f = Σ(n × ΔH°f(products)) - Σ(n × ΔH°f(reactants))

ΔH°f = ((6 × ΔH°f(CO2)) + (6 × ΔH°f(H2O))) - (1 × ΔH°f(glucose))

Make sure to convert the given enthalpies of formation from kJ/mol to J/mol.

Now, you can perform the calculations and substitute the relevant values into the equations to find the answers.