If 50.00mL of 1.10M NaOH is added to 25.00mL of 1.86M HCl, with both solutions originally at 24.70 degrees Celsius, what will be the final solution temperature? (Assume that no heat is lost to the surrounding air and that the solution produced in the neutralization reaction has a density of 1.02g/mL and a specific heat of 3.98J/g*degrees Celcius.)
Express answer in four significant figures.
The heat of neutralization is -55.84 kJ/mol H20 produced.
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To find the final solution temperature, we can use the concept of heat transfer in a neutralization reaction. The heat released during the reaction is equal to the heat gained by the final solution.
To calculate the heat released, we need to determine the number of moles of water produced. Since NaOH and HCl react in a 1:1 ratio to produce water, the number of moles of NaOH is equal to the number of moles of HCl used.
First, we need to calculate the moles of NaOH and HCl used:
Moles of NaOH = Volume of NaOH (in L) * Molarity of NaOH
= 0.050 L * 1.10 mol/L
= 0.055 mol NaOH
Moles of HCl = Volume of HCl (in L) * Molarity of HCl
= 0.025 L * 1.86 mol/L
= 0.0465 mol HCl
Since the reaction is 1:1, the moles of water produced will be equal to the moles of HCl used.
Now, let's calculate the heat released during the neutralization reaction:
Heat released = Moles of water * Heat of neutralization
= 0.0465 mol * -55.84 kJ/mol
= -2.59 kJ (note: the negative sign indicates heat released)
Next, we need to calculate the total mass of the final solution:
Mass of final solution = Volume of final solution * Density of final solution
= (50.00 mL + 25.00 mL) * 1.02 g/mL
= 76.5 g
Now, we can calculate the heat gained by the final solution using the specific heat capacity formula:
Heat gained = Mass of final solution * Specific heat capacity * Change in temperature
Rearranging the equation, we can solve for the change in temperature:
Change in temperature = Heat gained / (Mass of final solution * Specific heat capacity)
= (-2.59 kJ) / (76.5 g * 3.98 J/g * °C)
≈ -0.008 °C
Finally, we can find the final solution temperature by adding the change in temperature to the initial temperature:
Final solution temperature = Initial solution temperature + Change in temperature
= 24.70 °C + (-0.008 °C)
≈ 24.69 °C
Therefore, the final solution temperature, rounded to four significant figures, is 24.69 °C.