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

Answer 2

The enthalpy change for dissolving this salt on a energy per mass is 136.32 J/g

How to determine the mass of the water

• Density of water = 1 g/mL
• Volume of water = 75 mL
• Mass of water =?

Mass = Density × Volume

Mass of water = 1 × 75

Mass of water = 75 g

How to determine the heat absorbed by the solution

• Mass of water = 75 g
• Mass of salt =  2.50 g
• Mass of solution (M) = 75 + 2.5 = 77.5 g
• Temperature change (ΔT) = 0.93 °C
• Specific heat capacity of the solution = 4.184 J/gºC
• Heat of solution (Q) =?

Q = MCΔT

Q = 77.5 × 4.184 × 0.93

Q = 301.5618 J

How to determine the heat consumed by the calorimeter

• Heat capacity of the calorimeter (C) = 42.2 J/ºC
• Temperature change (ΔT) = 0.93 °C

• Heat by calorimeter (H) =?

H = CΔT

H = 42.2 × 0.93

H = 39.246 J

How to determine the total heat released

• Heat of solution (Q) = 301.5618 J
• Heat by calorimeter (H) = 39.246 J

• Total heat =?

Total heat = 301.5618 + 39.246

Total heat = 340.8078 J

How to determine the enthalpy change

• Total heat = 340.8078 J
• Mass of salt = 2.5 g

• Enthalpy change (ΔH) =?

ΔH = Total heat / mass

ΔH = 340.8078 / 2.5

ΔH = 136.32 J/g

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