Question

25.0 mL of 1.0 M HCl is combined with 35.0 mL of 0.5 M NaOH. The initial temperature of the solutions is ${25}^{o}C$, the density of the solution is 1.0 g/mL, the specific heat capacity of the solution is 4.184 J/$g^{o}C$, the reaction is completed in an insulated coffee cup, and the standard enthalpy of reaction for $H_{\left(aq\right)}^{+}+O{H}_{\left(aq\right)}^{-}\to H_2{O}_{\left(1\right)}$ is - 56 kJ/mol. What is the final temperature of the solution?

• A. ${28.9}^{o}C$
• B. ${30.1}^{o}C$
• C. ${32.8}^{o}C$
• D. none of the above.

Answer 1

The correct option is A ${28.9}^{o}C$

$HCl+NaOH\to NaCl+H_{2}O$

milliMol of $HCl=25ml\times 1M=25$ millimol

millimol of $NaOH=35ml\times 0.5M=17.5$ millimol

$1mol$ of water formation release energy = $56kJ$

$17.5m$ mol of water formation release energy = $56\times 17.5\times {10}^{-3}$

$=980$ joule

mass of solution = volume $\times$ density

$=(25+35)\times 1g/ml$

$=60g$

$mC\Delta T=980$ joule

$60\times 4.184\times \Delta T=980$

$\Delta T=\frac{980}{60\times 4.184}=3.90$

$T_2-{25}^{o}C=3.90$

$T_2=25+3.9$

$={28.9}^{o}C$

option A