Question

Consider the dissolution of 2.50 grams of salt XY in 75.0 mL of water within a calorimeter. The temperature of the water decreased by 0.93 oC. The heat capacity of the calorimeter is 42.2 J/oC. The density of the water (and the solution) is 1.00 g/mL. The specific heat capacity of the solution is 4.184 J/goC. Calculate the enthalpy change for dissolving this salt on a energy per mass basis (units of J/g).

Answer 1

Answer : The enthalpy change for dissolving this salt on a energy per mass basis is 132.4 J/g

Explanation :

Heat released by the reaction = Heat absorbed by the calorimeter + Heat absorbed by the water

$q=[q_1+q_2]$

$q=[c_1\times \Delta T+m_2\times c_2\times \Delta T]$

where,

q = heat released by the reaction

$q_1$ = heat absorbed by the calorimeter

$q_2$ = heat absorbed by the water

$c_1$ = specific heat of calorimeter = $42.2J/^oC$

$c_2$ = specific heat of water = $4.184J/g^oC$

$m_2$ = mass of water = $Density\times Volume=1/mL\times 75.0mL=75.0g$

$\Delta T$ = change in temperature = $0.93^oC$

Now put all the given values in the above formula, we get:

$q=[(42.2J/^oC\times 0.93^oC)+(75.0g\times 4.184J/g^oC\times 0.93^oC)]$

$q=331.08J$

Now we have to calculate the enthalpy change for dissolving this salt on a energy per mass basis.

$\Delta H=\frac{q}{m}$

where,

$\Delta H$ = enthalpy change = ?

q = heat released = 331.08 J

m = mass of salt = 2.50 g

$\Delta H=\frac{331.08J}{2.50g}=132.4J/g$

Therefore, the enthalpy change for dissolving this salt on a energy per mass basis is 132.4 J/g