Answer:
-21.03 kJ/mol
Step-by-step explanation:
∆H is enthalpy. Enthalpy is the total heat content of a system.
So we can establish that ∆H = q (heat)
The formula for heat (q)
q = cm∆T
c = specific heat capacity
m = mass of substance
∆T= change of temperature
Since we are calculating the enthalpy of the SOLUTION. We must account for both the mass of water and the mass of MgSO₄ in our q formula.
All you gotta do is plug and chug at this stage.
∆H = q = cm∆T = (4.184)(19.11+100.0)(6.70) = 3338.986808 Joules
We have now calculated the heat (aka enthalpy) of the solution.
BUT
Remember! The problem asked for enthalpy in kj....
Use this conversion factor.
1000 J = 1 kJ
3338.986808 Joules * 1kJ/1000 J = 3.338986808 kJ
We were asked to find ∆H for the dissolution of MgSO4 in units of kj/mol so we are not finished.
Take the grams of MgSO4 in the problem and convert it into moles using its molar mass.
MgSO4 molar mass = 120.3676 g
1 mol = 120.3676 g MgSO4 <---- Use this as a conversion factor
19.11 g MgSO4 * 1 mol MgSO4/120.3676 g = 0.15876365 mol MgSO4
Now that you've calculated the moles of MgSO4 in this solution. You can divide your heat by it.
q dissolution = 3.338.986808 kJ/ 0.15876365 mol = 21.03 kj/mol
Note that the problem tells us that the temperature of water increases.
This means that the water is experiencing an endothermic process (heat is being absorbed from MgSO4) . Mathematically, this would be indicated by a positive sign. ---> +q
We can assume MgSO4 is losing heat as it is placed into the water. It is experiencing an exothermic process (heat is being lost). Mathematically, this would be indicated by a negative sign. ----> -q
So if we're calculating the enthalpy for the dissolution of MgSO₄ ....the value we've arrived at must be negative.
Answer
∆H = 21.03 kj/mol :)))))
I hope that helped...I feel like my explanation was a bit convoluted.