Question

A 0.158 g sample of magnesium metal reacts completely with 100.0 mL of 1.0 M hydrochloric acid in a coffee cup calorimeter. The temperature of the solution rose from 25.6°C to 32.8°C. What is ∆Hrxn? Assume the specific heat of the solution is 4.184 J/mol-K and the density is 1.0 g/mL.

Answer 1

Explanation:

The given data is as follows.

     mass = 0.158 g,      volume = 100 ml

     Molarity = 1.0 M,      $\Delta T$ = $(32.8 - 25.6)^{o}C = 7.2^{o}C$  

The given reaction is as follows.

         $Mg(s) + 2HCl(aq) \rightarrow MgCl_{2}(aq) + H_{2}(g)$  

So, moles of magnesium will be calculated as follows.

         No. of moles = $\frac{mass}{\text{molar mass}}$                            

                               = $\frac{0.158 g}{24.305 g/mol}$

                               = $6.5 \times 10^{-3}$

                               = 0.0065 mol

Now, formula for heat released is as follows.

              Q = $m \times C \times \Delta T$

                  = $\text{volume} \times \text{density} \times C \times \Delta T$

                  = $100 ml \times 1.0 g/ml \times 4.184 \times 7.2^{o}C$

                  = 3010.32 J

Hence, heat of reaction will be calculated as follows.

            $\Delta H_{rxn} = \frac{\text{-heat released}}{\text{moles of Mg}}$

                      = $\frac{3010.32 J}{0.0065 mol}$

                      = -4.63 J/mol

or,                  = $-463 \times 10^{-5} kJ/mol$                (as 1 kJ = 1000 J)

Thus, we can conclude that heat of given reaction is $-463 \times 10^{-5}$ kJ/mol.