lattice energy and heat hydration

Question

Magnesium chloride (MgCl2) has a lattice energy of −2326 kJ/mol and a heat of hydration of −2486 kJ/mol. What volume of solution could be heated from 25.0 °C to 100.0 °C by the heat evolved from the dissolution of 33.9 g of MgCl2? Assume the solution has a specific heat capacity of 4.00 Jg·°C and a density of 1.05 g/mL.

Answer 1

Molar mass MgCl₂ = 95.2 g / mole

Moles MgCl₂ present = 33.9 g MgCl₂ x 1 mol / 95.2 g = 0.356 moles MgCl₂

The dissolution process involves (i) breaking the lattice apart which requires an input of energy, and (ii) solvating the free ions with water molecules which liberates energy. The heat generated or absorbed (heat of solution) will be the difference between these two values.

2326 kJ/mol put in to breaking bonds

2486 kJ/mol liberated during hydration

Difference = -160 kJ/mol (negative since more heat liberated than added; exothermic)

-160 kJ / mol x 0.356 mols = -56.96 kJ (heat liberated when 33.9 g MgCl₂ is dissolved

heat = q = mC∆T

q = 56.96 kJ = 56960 J (no need for (-) sign since we know it is exothermic as temperature increased)

m = mass = ?

C = specific heat = 4.00 J/gº

∆T = change in temperature = 100º - 25º = 75º

q = mC∆T

56960 J = (m)(4.00 J/gº)(75º)

m = 56960 J / (4.00J/gº)(75º)

m = 190 g

Since the density of solution is 1.05 g / ml, we can find the volume of solution

190 g x 1 ml / 1.05 g = 181 mls

Answer 2

First, we need to convert masses of Hydrogen and Oxygen gases to moles.

Second, using a balanced equation determine how many moles of water we can produced from moles of the gases given.

Lastly, convert mole of water to mass of water using its molar mass.