The activation energy, $$\(E_{A}\)$$, for the reaction between dilute hydrochloric acid, $$\(\mathrm{HCl}(\mathrm{aq})\)$$, and aqueous sodium thiosulfate, $$\(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq})\)$$, can be determined by an initial rates method. $$\[ 2 \mathrm{HCl}(\mathrm{aq})+\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq}) \rightarrow 2 \mathrm{NaCl}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{S}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{~g}) \]$$ The solid sulfur formed is seen as a white suspension in the reaction mixture. The reactants are mixed and the time, $$\(t\)$$, for a fixed quantity of sulfur to be formed is recorded. A measure of the initial rate of the reaction is $$\(\frac{1}{t}\)$$. Standard solutions of $$\(0.100 \mathrm{moldm}^{-3} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq})\)$$ and $$\(0.500 \mathrm{moldm}^{-3} \mathrm{HCl}(\mathrm{aq})\)$$ are supplied. Measurements are taken for a series of temperatures using the following procedure. step 1 A thermostatically controlled water bath is set up. step 2 A $$\(100 \mathrm{~cm}^{3}\)$$ conical flask is labelled $$\(\mathbf{A}\)$$ and a second $$\(100 \mathrm{~cm}^{3}\)$$ conical flask is labelled B. step $$\(310.00 \mathrm{~cm}^{3}\)$$ of $$\(0.100 \mathrm{moldm}^{-3} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq})\)$$ is added to flask $$\(\mathbf{A}\)$$. Flask $$\(\boldsymbol{A}\)$$ is placed in the water bath. step $$\(410 \mathrm{~cm}^{3}\)$$ of $$\(0.500 \mathrm{moldm}^{-3} \mathrm{HCl}(\mathrm{aq})\)$$ is added to flask $$\(\mathbf{B}\)$$. Flask $$\(\mathbf{B}\)$$ is placed in the same water bath. step 5 Wait for 10 minutes. step 6 Flask $$\(\mathbf{A}\)$$ is removed from the water bath and placed on a tile marked with a black cross. step 7 The contents of flask B are added to flask $$\(\mathbf{A}\)$$ and a timer started. step 8 The timer is stopped when the black cross is no longer visible. The time is recorded. A second student carries out the procedure at six different temperatures and analyses their data to give the results in Table 2.2. (i) Use the results from Table 2.2 to plot a graph on the grid in Fig. 2.1 to show the relationship between $$\(\log \left(\frac{1}{t}\right)\)$$ and $$\(\frac{1}{T}\)$$. Use a cross $$\((x)\)$$ to plot each data point. Draw a line of best fit. (ii) Determine the gradient of your line of best fit in Fig. 2.1. State the coordinates of both points you use in your calculation. These must be selected from your line of best fit. Give the gradient to three significant figures. coordinates 1 .......................................... coordinates 2 .......................................... gradient $$\(=\)$$ .......................... K (iii) An equation relating time and temperature variables is shown. $$\[ \log \left(\frac{1}{t}\right)=-\frac{0.434 E_{\mathrm{A}}}{R T}+\text { constant } \]$$ Determine the activation energy, $$\(E_{\mathrm{A}}\)$$, of this reaction using this equation and your answer to (d)(ii). (If you were unable to find the gradient in (d)(ii), then use the value $$\(-3.21 \times 10^{3} \mathrm{~K}\)$$. This is not the correct answer.) Include units in your answer. Show your working. $$\[ \begin{array}{r} E_{\mathrm{A}}= \\ \text { units }= \end{array} \]$$ .......................... .......................... (iv) Use your graph to state whether the results from the experiment are reliable. Justify your answer. ....................................................................................................................................... . .................................................................................................................................

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