The problem statement, all variables and given/known data
When 5.00 g of NaOH(s) are added to 100 g of water using a calorimeter (with Cp = 493.24 J/K), the temperature rises from 25.0 to 37.5 °C. Calculate the molar heat of solution.
NaOH(s)--->Na(aq)+OH(aq)
Assume that the specific heat capacity of water is 4.18 J/gK and that of the NaOH(aq) solution is the same.
q = [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccal x (Tfinal-Tinitial)]
Substitute and solve for q = delta H solution.
q/5.00 = delta H/gram.
delta H/g x (molar mass NaOH) = delta H in J/mol. Convert to kJ/mol.
To calculate the molar heat of solution, we need to determine the amount of heat absorbed or released during the process. We can do this using the equation:
q = m * Cp * ΔT
where:
q is the heat absorbed or released
m is the mass of the substance (in this case, the water)
Cp is the specific heat capacity of the substance (in this case, water)
ΔT is the change in temperature
Let's calculate the heat absorbed by the water:
m_water = 100 g
Cp_water = 4.18 J/gK
ΔT_water = 37.5 °C - 25.0 °C = 12.5 °C
q_water = m_water * Cp_water * ΔT_water
= 100 g * 4.18 J/gK * 12.5 °C
= 5235 J
Now, we need to calculate the heat of solution. Since the reaction is exothermic, the heat absorbed by the water is equal to the heat released by the NaOH.
q_NaOH = - q_water
= - 5235 J
To find the molar heat of solution, we need to divide the heat released by the moles of NaOH used. We can calculate the moles of NaOH using its molar mass.
m_NaOH = 5.00 g/mol
Molar mass of NaOH = 23.0 g/mol + 16.0 g/mol + 1.0 g/mol = 40.0 g/mol
moles_NaOH = m_NaOH / Molar mass of NaOH
= 5.00 g / 40.0 g/mol
= 0.125 mol
molar_heat_of_solution = q_NaOH / moles_NaOH
= - 5235 J / 0.125 mol
= - 41880 J/mol
The molar heat of solution of NaOH is therefore -41880 J/mol, where the negative sign indicates that the reaction is exothermic.