Question

Given,25.0 mL of 1.0 M HCl is combined with 35.0mL of 0.5 M NaOH. The initial temperature of the solutions is ${{25}^{\circ }}C$, the density of the solution is 1.0 g/mL, the specific heat capacity of the solution is 4.184$J/{{g}^{\circ }}C$, the reaction is completed in an insulated coffee cup, and the standard enthalpy of reaction for ${{H}^{+}}_{(aq)}+O{{H}^{-}}_{(aq)}\to {{H}_{2}}{{O}_{(l)}}$ is - 56 kJ/mol. What is the final temperature of the solution?
(A) 28.9 $^{\circ }C$
(B) 30.1$^{\circ }C$
(C) 32.8$^{\circ }C$
(D) none of the above

Answer 1

Hint: Calculate the no. of moles of water formed and the energy released in that water formation. Then by using the formula $q=mC\Delta T$ we can find the final temperature.

Complete answer:
The reaction can be represented chemically as-
     \[HCl+NaOH\to NaCl+{{H}_{2}}O\]
Millimoles of HCl$=25ml\times 1M=25\text{millimoles}$
Millimoles of NaOH$=35ml\times 0.5M=17.5\text{millimoles}$
the standard enthalpy of reaction of water formation, that is, 1 mole of water formation releases 56 kJ/mol of energy as given in the question.
Energy released by 17.5millimoles of water formation $=56\times 17.5\times {{10}^{-3}}=980J=q$
As we know that,$mass=volume\times density$
Let the density of water be 1g/ml.
And total volume of solution$=25+35=60ml$
Therefore, mass of solution $=60ml\times 1g/ml=60g=m$
Now, considering the following relationship-
     \[q=mC\Delta T\]
Where,
     \[\begin{align}
  & q=heat \\
 & m=mass \\
 & C=\text{Specific heat capacity} \\
 & \Delta T=\text{change in temperature = }{{\text{T}}_{Final}}-{{T}_{Initial}} \\
\end{align}\]
Rearranging the equation, we get-
     \[\Delta T=\dfrac{q}{mC}\]
Putting values of q,m and C in the above equation, we get
     \[\Delta T=\dfrac{980}{60\times 4.184}={{3.9}^{\circ }}C\]
     \[\begin{align}
  & \Delta T=\text{change in temperature = }{{\text{T}}_{Final}}-{{T}_{Initial}} \\
 & 3.9={{T}_{Final}}-25 \\
 & {{T}_{Final}}={{28.9}^{\circ }}C \\
\end{align}\]

Therefore, the final temperature of the solution is 28.9 $^{\circ }C$. So the correct option is (A) 28.9 $^{\circ }C$.

Note:
Be careful with the terms heat capacity and specific heat capacity. Heat capacity is given by the ratio of the amount of heat energy transferred to an object to the resulting increase in its temperature. Specific heat capacity is a measure of the amount of heat required to raise the temperature of one gram of a pure substance by one Kelvin.