Sagot :
Answer:
The idea here is that you can use the heat absorbed by the solution to find the heat given off by the dissolution of the salt.
More specifically, you can assume that
[tex]ΔHdiss=−qsolution[/tex]
The minus sign is used here because heat lost carries a negative sign.
To find the heat absorbed by the solution, you can use the equation
[tex]q=m⋅c⋅ΔT[/tex]
Here
- q is the heat gained by the water
- m is the mass of the water
- c is the specific heat of water
- ΔT is the change in temperature, defined as the difference between the final temperature and the initial temperature of the sample
As the problem suggests, you can approximate the mass and the specific heat of the solution to be equal to those of the pure water sample.
The temperature increases by 0.121∘C, so you know that
ΔT=0.121∘C→ positive because the final temperature is higher than the initial temperature
Plug in your values to find
[tex]q=125g⋅4.18 Jg−1∘C−1⋅0.121∘C[/tex]
[tex]q=63.22 J[/tex]
So, you know that the solution absorbed 63.22 J, which implies that the dissolution of the salt gave off 63.22 J. In other words, you have
[tex]ΔHdiss=−63.22 J[/tex]
Convert the mass of sodium hydroxide to moles by using the compound's molar mass
[tex]2.4⋅10−4g⋅1 mole NaOH39.997g=6.00⋅10−6 moles NaOH[/tex]
You know that the enthalpy of dissolution when 6.00⋅10−6 moles of sodium hydroxide are dissolved in water, so use this info to find the enthalpy of dissolution when 1 mole of the salt dissolves
[tex]1mole NaOH⋅−63.22 J6.00⋅10−6moles NaOH=−1.054⋅107 J[/tex]
Finally, convert this to kilojoules
[tex]1.054⋅107J⋅1 kJ103J=1.054⋅104 kJ[/tex]
Therefore, you can say that the enthalpy of dissolution, or molar enthalpy of dissolution, for sodium hydroxide is
[tex]ΔHdiss=−1.1⋅104.kJ mol−1[/tex]
The answer is rounded to two sig figs, the number fo sig figs you have for the mass of sodium hydroxide.
SIDE NOTE The accepted value for the enthalpy of dissolution of sodium hydroxide in water at 25∘C is
[tex]ΔHdiss=−44.51 kJ[/tex]
sorry if not very understandable :(