A generic solid, X, has a molar mass of 78.2 g/mol. In a constant-pressure calorimeter, 12.6 g of X is dissolved in 337 g of water at 23.00 °C. X (s) yeilds X (aq) The temperature of the resulting solution rises to 24.40 °C. Assume the solution has the same specific heat as water, 4.184 J / (g·°C), and that there/'s negligible heat loss to the surroundings. How much heat was absorbed by the solution? What is the enthalpy of the reaction?

a) Q = 2047.8 J (ΔH is negative because it's an exothermic reaction)

b) ΔH = - 12.7 kJ / mol

Explanation:

Step 1: Data given

Molar mass of X = 78.2 g/mol

In a constant-pressure calorimeter, 12.6 g of X is dissolved in 337 g of water at 23.00 °C.

The temperature rise to 24.40 °C

The specific heat of the solution = 4.184 J/g°C

Step 2: Calculate the total mass

Total mass of the solution is given by

Total mass = 12.6 grams + 337 grams = 349.6 grams

Step 3: Calculate heat

Q = m*c*ΔT

⇒ m = the total mass = 349.6 grams

⇒ c = the specific heat of solution = 4.184 J/g°C

⇒ ΔT = The change of temperature = T2 - T1 = 24.40 - 23.00 = 1.40 °C

Q = 2047.8 J (ΔH is negative because it's an exothermic reaction)

What is the enthalpy of the reaction?

Calculate number of moles = mass / molar mass

Moles X = 12.6 grams / 78.2 g/mol

Moles X = 0.161 moles

ΔH = - 2047.8 J / 0.161 moles

ΔH = - 12719.3 J/mol = - 12.7 kJ / mol