Separate samples of $$\(\mathrm{Na}_{2} \mathrm{CO}_{3}\)$$ and $$\(\mathrm{NaHCO}_{3}\)$$ react with $$\(\mathrm{HCl}(\mathrm{aq})\)$$ to produce the same products, as shown in Table 2.1. The value for $$\(\Delta H_{1}\)$$ is determined by experiment using the following method. - $$\(\quad 50.0 \mathrm{~cm}^{3}\)$$ of $$\(2.00 \mathrm{moldm}^{-3} \mathrm{HCl}(\mathrm{aq})\)$$ is added to a polystyrene cup. - The initial temperature of the acid is recorded as $$\(19.6^{\circ} \mathrm{C}\)$$. - $$\(\quad 0.0400 \mathrm{~mol}\)$$ of $$\(\mathrm{Na}_{2} \mathrm{CO}_{3}\)$$ is added and the mixture is stirred. - All the solid $$\(\mathrm{Na}_{2} \mathrm{CO}_{3}\)$$ disappears and a colourless solution is produced. The maximum temperature recorded during the reaction is $$\(26.2^{\circ} \mathrm{C}\)$$. (i) Describe one other observation that shows the reaction is complete. ................................................................................................................................. (ii) Calculate the value of $$\(\Delta H_{1}\)$$ in $$\(\mathrm{kJ} \mathrm{mol}^{-1}\)$$. Assume the specific heat capacity of the reaction mixture is the same as for water and no heat is lost to the surroundings. Show your working. $$\[ \Delta H_{1}= \]$$ .......................... $$\(\mathrm{kJmol}^{-1}\)$$ (iii) Thermal decomposition occurs when $$\(\mathrm{NaHCO}_{3}\)$$ is heated. $$\[ \text { reaction } 3 \quad 2 \mathrm{NaHCO}_{3} \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \]$$ Calculate the enthalpy change for reaction $$\(3, \Delta H_{r}\)$$, using the data in Table 2.1 and the value of $$\(\Delta H_{1}\)$$ calculated in (b)(ii). (If you were unable to calculate a value for $$\(\Delta H_{1}\)$$ in (b)(ii), assume the enthalpy change is $$\(-38.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\)$$. This is not the correct value.) $$\(\Delta H_{\mathrm{r}}=\)$$ .......................... $$\(\mathrm{kJ} \mathrm{mol}^{-1}\)$$

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