Question

The salt cesium sulfate (Cs₂SO₄) is soluble in water. When 15.7 g of Cs₂SO₄ is dissolved in 113.00 g of water, the temperature of the solution decreases from 25.00 °C to 23.38 °C. Based on this observation, calculate the dissolution enthalpy, δdissh, of Cs₂SO₄. Assume that the specific heat capacity of the solution is 4.184 J g⁻¹ °C⁻¹, and that the energy transfer to the calorimeter is negligible.

δdissh=Fill in the blank ___________kJ/mol

A) 5.23
B) 8.46
C) 12.87
D) 15.74

Answer 1

The dissolution enthalpy of Cs₂SO₄ is calculated using the heat energy change from temperature drop and mass of Cs₂SO₄, resulting in 17.82 kJ/mol. This result, however, does not match the answer choices provided, suggesting a potential error in the calculation or the given choices.

Step-by-step explanation:

To calculate the dissolution enthalpy of cesium sulfate (Cs₂SO₄), we need to use the information provided about the temperature change and mass of the substances involved. Using the formula δdissh = -q/n, with q being the heat absorbed or released and n being the number of moles, we can find the answer.

To determine q, we use the formula q = mcΔT, where m is the mass of the water, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
So, q = (m)(c)(ΔT) = (113.00 g)(4.184 J g⁻¹ °C⁻¹)(23.38 °C - 25.00 °C) = (113.00 g)(4.184 J g⁻¹ °C⁻¹)(-1.62 °C).
Calculating this gives us q = -772.82976 J. To convert joules to kilojoules, we divide by 1000, giving us -0.77283 kJ.

Now, to find the number of moles (n) of Cs₂SO₄, we apply the molar mass of Cs₂SO₄ (361.87 g/mol):
n = mass / molar mass = 15.7 g / 361.87 g/mol = 0.043392 mol.

Finally, we calculate δdissh = -q/n = -(-0.77283 kJ)/0.043392 mol = 17.82 kJ/mol, which is not one of the answers provided. Thus, we need to verify all calculations and ensure there are no mistakes or typos in the question or the answer choices. If all calculations are correct, we might conclude that there's a discrepancy in the question or the choices given.