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Math  /  Data & Statistics

Question1. The net ionic equation for the reaction between sodium thiosulphate and hydrochloric acid is given as S2O32−(aq)+2H+(aq)⟶S( s)+SO2( g)+H2O(l)\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{S}(\mathrm{~s})+\mathrm{SO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})
To prove that this reaction follows first order kinetics, a student varied the concentration of S2O32−\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-} while keeping that of H+\mathrm{H}^{+}constant (10 mL(10 \mathrm{~mL} of 2 M HCl)) and observed the rate of appearance of S(s)\mathrm{S}(\mathrm{s}) with time. Starting with 50 mL of 0.15MS2O32−0.15 \mathrm{M} \mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}, he generated the results shown in table 1 .
Table 1: Results for the clock reaction between S2O32−\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-} and H+\mathrm{H}^{+} \begin{tabular}{|l|l|l|l|l|} \hline Beaker & Vol. Na2 S2O3/mL\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} / \mathrm{mL} & Vol. H2O/mL\mathrm{H}_{2} \mathrm{O} / \mathrm{mL} & {[Na2 S2O3]/M\left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] / \mathrm{M}} & Time/s \\ \hline A & 50.0 & 0.0 & 0.15 & 22.5 \\ \hline B & 40.0 & 10.0 & & 27.3 \\ \hline C & 30.0 & 20.0 & & 35.1 \\ \hline D & 40.0 & 30.0 & & 60.0 \\ \hline E & 10.0 & 40.0 & & 159.1 \\ \hline \end{tabular} a) Copy and complete table 1. b) Plot a graph of ln⁡[Na2 S2O3]\ln \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] (M) against time (s).

Studdy Solution

STEP 1

1. The reaction follows first-order kinetics with respect to S2O32−\mathrm{S}_{2} \mathrm{O}_{3}^{2-}.
2. The concentration of H+\mathrm{H}^{+} is constant.
3. The initial concentration of Na2 S2O3\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} is diluted by adding water.

STEP 2

1. Calculate the concentrations of Na2 S2O3\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} for each beaker.
2. Complete Table 1 with the calculated concentrations.
3. Plot ln⁡[Na2 S2O3]\ln \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] against time.

STEP 3

Calculate the concentration of Na2 S2O3\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} for each beaker using the dilution formula:
C1V1=C2V2 C_1V_1 = C_2V_2
For Beaker B:
C2=C1×V1V2=0.15 M×40.0 mL50.0 mL=0.12 M C_2 = \frac{C_1 \times V_1}{V_2} = \frac{0.15 \, \text{M} \times 40.0 \, \text{mL}}{50.0 \, \text{mL}} = 0.12 \, \text{M}

STEP 4

For Beaker C:
C2=0.15 M×30.0 mL50.0 mL=0.09 M C_2 = \frac{0.15 \, \text{M} \times 30.0 \, \text{mL}}{50.0 \, \text{mL}} = 0.09 \, \text{M}

STEP 5

For Beaker D:
C2=0.15 M×20.0 mL50.0 mL=0.06 M C_2 = \frac{0.15 \, \text{M} \times 20.0 \, \text{mL}}{50.0 \, \text{mL}} = 0.06 \, \text{M}

STEP 6

For Beaker E:
C2=0.15 M×10.0 mL50.0 mL=0.03 M C_2 = \frac{0.15 \, \text{M} \times 10.0 \, \text{mL}}{50.0 \, \text{mL}} = 0.03 \, \text{M}

STEP 7

Complete Table 1 with calculated concentrations:
BeakerVol. Na2 S2O3/mLVol. H2O/mL[Na2 S2O3]/MTime/sA50.00.00.1522.5B40.010.00.1227.3C30.020.00.0935.1D20.030.00.0660.0E10.040.00.03159.1\begin{array}{|l|l|l|l|l|} \hline \text{Beaker} & \text{Vol. } \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} / \mathrm{mL} & \text{Vol. } \mathrm{H}_{2} \mathrm{O} / \mathrm{mL} & \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] / \mathrm{M} & \text{Time/s} \\ \hline \text{A} & 50.0 & 0.0 & 0.15 & 22.5 \\ \hline \text{B} & 40.0 & 10.0 & 0.12 & 27.3 \\ \hline \text{C} & 30.0 & 20.0 & 0.09 & 35.1 \\ \hline \text{D} & 20.0 & 30.0 & 0.06 & 60.0 \\ \hline \text{E} & 10.0 & 40.0 & 0.03 & 159.1 \\ \hline \end{array}

STEP 8

Plot ln⁡[Na2 S2O3]\ln \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] against time (s):
Calculate ln⁡[Na2 S2O3]\ln \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] for each concentration:
\begin{align*} \ln(0.15) & \approx -1.897, \\ \ln(0.12) & \approx -2.120, \\ \ln(0.09) & \approx -2.407, \\ \ln(0.06) & \approx -2.813, \\ \ln(0.03) & \approx -3.507. \\ \end{align*}
Plot these values against the corresponding times.
The plot should show a linear relationship, confirming first-order kinetics with respect to S2O32−\mathrm{S}_{2} \mathrm{O}_{3}^{2-}.

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