When 0.451g of biphenyl (C12H10) undergoes combustion in a bomb calorimeter, the temperature rises from 26.7∘C to 29.6∘C.Find ΔErxn for the combustion of biphenyl in kJ/mol biphenyl. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.86 kJ/∘C.

q(v) = Ccal in kJ/C x delta T

That gives you q = dE in kJ for 0.451g
That x molar mass gives dE in kJ/mol.

i understand how to solve this but i do not know the calorimeter constant

nevermind. thank you!

It's in the last sentence.

To find ΔErxn, the change in internal energy for the combustion reaction of biphenyl (C12H10) in kJ/mol biphenyl, we need to use the formula:

ΔErxn = qcalorimeter - qbiphenyl

First, let's find the value of qcalorimeter, the heat absorbed by the bomb calorimeter during the reaction.

qcalorimeter = Ccalorimeter * ΔT

Where:
Ccalorimeter is the heat capacity of the bomb calorimeter (5.86 kJ/∘C)
ΔT is the change in temperature (29.6∘C - 26.7∘C = 2.9∘C)

Now let's calculate qcalorimeter:

qcalorimeter = (5.86 kJ/∘C) * (2.9∘C)
qcalorimeter ≈ 16.994 kJ

Next, let's calculate the value of qbiphenyl, the heat released by the combustion of biphenyl.

qbiphenyl = m * ΔH
Where:
m is the mass of biphenyl (0.451g)
ΔH is the molar enthalpy of combustion of biphenyl (to be determined)

We need to convert the mass of biphenyl to moles:

moles of biphenyl = (mass of biphenyl) / (molar mass of biphenyl)

The molar mass of C12H10 (biphenyl) can be calculated as follows:
(12g/mol * 12) + (1g/mol * 10) = 154 g/mol

moles of biphenyl = (0.451g) / (154 g/mol)
moles of biphenyl ≈ 0.00293 mol

Now, we need to find the enthalpy change for the combustion of biphenyl (ΔH) in kJ/mol. We'll use the equation:

ΔH = q / moles of biphenyl

ΔH = (qcalorimeter) / (moles of biphenyl)
ΔH = 16.994 kJ / 0.00293 mol
ΔH ≈ 5796 kJ/mol

Finally, we can calculate ΔErxn using the formula:

ΔErxn = qcalorimeter - qbiphenyl
ΔErxn = 16.994 kJ - (5796 kJ/mol * 0.00293 mol)
ΔErxn ≈ -0.9782 kJ/mol biphenyl

Therefore, the ΔErxn for the combustion of biphenyl is approximately -0.9782 kJ/mol biphenyl.