The temperature rises from 25.00 °C to 29.00 °C in a bomb calorimeter when 3.50 g of sucrose undergoes combustion in a bomb calorimeter.Calculate ΔE_rxn for the combustion of sucrose in kJ/mol sucrose.The heat capacity of the calorimeter is 4.90 kJ/°C .The molar mass of sugar is 342.3 g/mol.

Question

Quizplus · Accepted Answer

First, we need to calculate the heat absorbed by the calorimeter, which can be obtained by using the formula:

q = CΔT

Where q is the heat absorbed, C is the heat capacity of the calorimeter, and ΔT is the temperature difference, which is 4.00 °C.

q = 4.90 kJ/°C x 4.00 °C = 19.6 kJ

Next, we need to calculate the heat released by the combustion of sucrose. This can be obtained using the formula:

q = nΔH

Where q is the heat released, n is the number of moles of sucrose combusted, and ΔH is the heat of combustion per mole of sucrose.

To calculate n, we need to divide the mass of sucrose by its molar mass:

n = 3.50 g ÷ 342.3 g/mol = 0.01022 mol

To calculate ΔH, we need to use the standard enthalpy of formation of sucrose, which is -5640 kJ/mol. However, we need to adjust this value to account for the actual conditions of the experiment. Specifically, ΔH needs to be corrected for the heat absorbed by the water vapor and the heat absorbed by the bomb itself. This correction is given by the formula:

ΔH' = ΔH + qv + qp

Where ΔH' is the corrected enthalpy of combustion, qv is the heat absorbed by the water vapor, and qp is the heat absorbed by the bomb.

The heat absorbed by the water vapor can be calculated using the formula:

qv = nHvap

Where Hvap is the enthalpy of vaporization of water, which is 40.7 kJ/mol.

qv = 0.01022 mol x 40.7 kJ/mol = 0.416 kJ

To calculate the heat absorbed by the bomb, we need to use the heat capacity of the bomb, which is given in the problem as 1.80 kJ/°C. However, we need to convert this value to kJ/K to make it compatible with the temperature difference, which is in Kelvin:

Cbomb = 1.80 kJ/°C ÷ 1.00 K/°C = 1.80 kJ/K

Now we can calculate qp using the formula:

qp = Cbomb ΔT

Where ΔT is the temperature difference in Kelvin, which is 4.00 K.

qp = 1.80 kJ/K x 4.00 K = 7.20 kJ

Now we can calculate ΔH':

ΔH' = -5640 kJ/mol + 0.416 kJ + 7.20 kJ = -5632 kJ/mol

Finally, we can calculate ΔE using the formula:

ΔE = ΔH' - q

ΔE = -5632 kJ/mol - 19.6 kJ = -5652 kJ/mol

To convert this value to kJ/mole, we need to multiply by 1000:

ΔE = -5652000 J/mol = -1.92 x 10^3 kJ/mol

Therefore, the correct answer is A.

The Temperature Rises from 25