Final answer:
To find the solution for substance Z, we calculate the heat absorbed by the water when Z dissolves, convert it to joules per mole using the molar mass of Z, and then to kilojoules. The ΔHsolution for Z is -34.052 kJ/mol.
Step-by-step explanation:
The question asks to calculate the ΔHsolution for substance Z when a sample of 2.21 grams of Z is dissolved in 500 grams of water, resulting in a temperature change from 23.512°C to 23.269°C. Assuming no heat is lost or gained by the cup itself and using the specific heat of water (4.184 J/g°C), first, we find the amount of heat (q) absorbed or released by the solution using the formula:
q = mass of water × specific heat of water × ΔT
where ΔT is the change in temperature. We then calculate ΔHsolution per mole of Z by using the molar mass of Z (148 g/mol).
The heat q absorbed by the water is:
q = 500 g × 4.184 J/g°C × (23.269°C - 23.512°C)
q = 500 g × 4.184 J/g°C × (-0.243°C)
q = -508.268 J
This value is negative because the temperature decreased, indicating that the solution absorbed heat. To find the heat per mole of Z, we convert the mass of Z (2.21 g) to moles:
moles of Z = 2.21 g ÷ 148 g/mol = 0.0149324 mol
Next, we calculate ΔHsolution:
ΔHsolution = q / moles of Z = -508.268 J / 0.0149324 mol
ΔHsolution = -34052.269 J/mol
The answer needs to be in kilojoules per mole:
ΔHsolution = -34.052 kJ/mol
The ΔHsolution for substance Z is -34.052 kJ/mol, indicating an exothermic dissolution process.