The amount of energy required by the reaction is \(\boxed{418\,{\text{J}}}\) .
Further Explanation:
Given:
The volume of \(HCl\) mixed in the calorimeter is \(10.0\,{\text{ml}}\) .
The volume of \(NaOH\) mixed in the calorimeter is \(115\,{\text{ml}}\) .
The initial temperature of the solution is \({22.45\:^{\circ}\text{C}}\) or \(295.6\,{\text{K}}\) .
The final temperature of the solution is \({23.25\:^{\circ}\text{C}}\) or \(296.4\,{\text{K}}\) .
The specific heat capacity of water is \(4.18\,{{\text{J}}\mathord{\left/{\vphantom{{\text{J}}{{\text{g}}\cdot{\text{K}}}}}\right.\kern-
ulldelimiterspace}{{\text{g}}\cdot{\text{K}}}}\) .
Concept:
The total volume of the calorimeter after the addition of \(HCl\) and \(NaOH\) is:
\(\begin{aligned}V&=115+10\\&=125\,{\text{ml}}\\\end{aligned}\)
The density of the given solution is \(1\,{{\text{g}}\mathord{\left/{\vphantom{{\text{g}}{{\text{ml}}}}}\right.\kern-
ulldelimiterspace}{{\text{ml}}}}\) . Therefore, the mass of the solution is:
\(\begin{aligned}m&={\text{density}}\times{\text{volume}}\\&=1\,{{\text{g}}\mathord{\left/{\vphantom{{\text{g}}{{\text{ml}}}}}\right.\kern-
ulldelimiterspace}{{\text{ml}}}}\times125\,{\text{ml}}\\&=125\,{\text{g}}\\\end{aligned}\)
The change in temperature of the calorimeter is.
\(\begin{aligned}\Delta T&={T_f}-{T_i}\\&=296.4-295.6\\&=0.8\\\end{aligned}\)
Now, the amount of heat absorbed by the calorimeter to complete the reaction is given as:
\(q=m\times C\times\Delta T\)
Here, \(q\) is the amount of heat required for the reaction and \(C\) is the heat capacity of the calorimeter.
Substitute the values in the above expression.
\(\begin{aligned}q&=125\times4.18\times0.8\\&=125\times3.344\\&=418\,{\text{J}}\\\end{aligned}\)
Thus, the amount of energy required by the reaction is \(\boxed{418\,{\text{J}}}\) .
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Heat and Thermodynamics
Keywords:
10 ml of 1.00 m HCl, 115 ml of 0.100 m NaOH, constant pressure, calorimeter, heat capacity, same as 125g of water, temperature rises, energy required.
