I'm inclined to think that E = qv.
E = q+w and w = p*delta v. In a closed system, however, the p*delta v must be zero since delta v is zero and E = q.
I've calculated the standard enthalpy but am unsure of how to go about finding the standard internal energy. Any suggestions?
E = q+w and w = p*delta v. In a closed system, however, the p*delta v must be zero since delta v is zero and E = q.
ΔH = q/n
where ΔH is the change in enthalpy (in J/g), q is the heat absorbed (in J), and n is the amount of substance (in mol).
Given that the heat capacity of the bomb calorimeter is 641 J/K and the temperature rose by 7.739 K, you can calculate the heat absorbed by the bomb calorimeter using the formula:
q = C * ΔT
where C is the heat capacity (in J/K) and ΔT is the change in temperature (in K).
Plugging in the values, you get:
q = 641 J/K * 7.739 K = 4962.599 J
The amount of substance, n, can be calculated using the molar mass of glucose (C6H12O6).
molecular weight of glucose = 6 * atomic weight of Carbon + 12 * atomic weight of Hydrogen + 6 * atomic weight of Oxygen
= 6 * 12.01 g/mol + 12 * 1.01 g/mol + 6 * 16.00 g/mol
= 180.18 g/mol
Given that 0.312 g of glucose was burned, the number of moles of glucose is:
n = mass / molecular weight = 0.312 g / 180.18 g/mol = 0.001731 mol
Now, substituting the values back into the formula for ΔH:
ΔH = q/n = 4962.599 J / 0.001731 mol = 2864208.29 J/mol
Therefore, the standard enthalpy of combustion is 2,864,208.29 J/mol.
To find the standard internal energy of combustion, you can use the relation:
ΔE = ΔH - PΔV
where ΔE is the change in internal energy (in J), ΔH is the change in enthalpy (in J), P is the pressure (in atm), and ΔV is the change in volume (in L).
In the case of a bomb calorimeter, the volume change is assumed to be negligible since it is a closed system. Therefore, ΔV is considered to be zero.
Since the bomb calorimeter is at constant volume, the equation simplifies to:
ΔE = ΔH
So in this case, the standard internal energy of combustion is the same as the standard enthalpy of combustion.
Therefore, the standard internal energy of combustion is 2,864,208.29 J/mol.