| Date | May 2009 | Marks available | 4 | Reference code | 09M.2.hl.TZ2.7 |
| Level | HL | Paper | 2 | Time zone | TZ2 |
| Command term | Draw and Explain | Question number | 7 | Adapted from | N/A |
Question
Nitrogen monoxide reacts at 1280 °C with hydrogen to form nitrogen and water. All reactants and products are in the gaseous phase.
The gas-phase decomposition of dinitrogen monoxide is considered to occur in two steps.
\[\begin{array}{*{20}{l}} {{\text{Step 1:}}}&{{{\text{N}}_2}{\text{O(g)}}\xrightarrow{{{k_1}}}{{\text{N}}_2}({\text{g)}} + {\text{O(g)}}} \\ {{\text{Step 2:}}}&{{{\text{N}}_2}{\text{O(g)}} + {\text{O(g)}}\xrightarrow{{{k_2}}}{{\text{N}}_2}({\text{g)}} + {{\text{O}}_2}{\text{(g)}}} \end{array}\]
The experimental rate expression for this reaction is rate \( = k{\text{[}}{{\text{N}}_2}{\text{O]}}\).
The conversion of \({\text{C}}{{\text{H}}_{\text{3}}}{\text{NC}}\) into \({\text{C}}{{\text{H}}_{\text{3}}}{\text{CN}}\) is an exothermic reaction which can be represented as follows.
\({\text{C}}{{\text{H}}_{\text{3}}}–{\text{N}}\)\( \equiv \)\({\text{C}} \to {\text{transition state}} \to {\text{C}}{{\text{H}}_{\text{3}}}–{\text{C}}\)\( \equiv \)\({\text{N}}\)
This reaction was carried out at different temperatures and a value of the rate constant, \(k\), was obtained for each temperature. A graph of \(\ln k\) against \(1/T\) is shown below.
Define the term rate of reaction.
State an equation for the reaction of magnesium carbonate with dilute hydrochloric acid.
The rate of this reaction in (a) (ii), can be studied by measuring the volume of gas collected over a period of time. Sketch a graph which shows how the volume of gas collected changes with time.
The experiment is repeated using a sample of hydrochloric acid with double the volume, but half the concentration of the original acid. Draw a second line on the graph you sketched in part (a) (iii) to show the results in this experiment. Explain why this line is different from the original line.
The kinetics of the reaction were studied at this temperature. The table shows the initial rate of reaction for different concentrations of each reactant.
Deduce the order of the reaction with respect to NO and \({{\text{H}}_2}\), and explain your reasoning.
Deduce the rate expression for the reaction.
Determine the value of the rate constant for the reaction from Experiment 3 and state its units.
Identify the rate-determining step.
Identify the intermediate involved in the reaction.
Define the term activation energy, \({E_{\text{a}}}\).
Construct the enthalpy level diagram and label the activation energy, \({E_{\text{a}}}\), the enthalpy change, \(\Delta H\), and the position of the transition state.
Describe qualitatively the relationship between the rate constant, \(k\), and the temperature, \(T\).
Calculate the activation energy, \({E_{\text{a}}}\), for the reaction, using Table 1 of the Data Booklet.
Markscheme
decrease in concentration/mass/amount/volume of reactant with time / increase in concentration/mass/amount/volume of product with time / change in concentration/mass/amount/volume of reactant/product with time;
\({\text{MgC}}{{\text{O}}_3}{\text{(s)}} + {\text{2HCl(aq)}} \to {\text{MgC}}{{\text{l}}_2}{\text{(aq)}} + {\text{C}}{{\text{O}}_2}{\text{(g)}} + {{\text{H}}_2}{\text{O(l)}}\);
Ignore state symbols.
;
Plot starts at the origin and levels off.
No mark awarded if axes are not labelled.
new curve reaches same height as original curve;
new curve less steep than original curve;
volume of gas produced is the same because the same amount of acid is used;
reaction is slower because concentration is decreased;
(from experiments 1 and 2 at constant \({\text{[}}{{\text{H}}_2}{\text{]}}\)), [NO] doubles, rate quadruples;
hence, second order with respect to NO;
(from experiments 2 and 3 at constant [NO]), \({\text{[}}{{\text{H}}_{\text{2}}}{\text{]}}\)doubles, rate doubles;
first order with respect to \({{\text{H}}_2}\);
Allow alternative mathematical deductions also.
\({\text{rate}} = k{{\text{[NO]}}^{\text{2}}}{\text{[}}{{\text{H}}_{\text{2}}}{\text{]}}\);
\(k\left( { = (10.00 \times {{10}^{ - 5}})/{{(10.00 \times {{10}^{ - 3}})}^2}(4.00 \times {{10}^{ - 3}})} \right) = 2.50 \times {10^2}\);
Do not penalize if Experiments 1 or 2 are used to determine k.
\({\text{mo}}{{\text{l}}^{ - 2}}{\text{d}}{{\text{m}}^6}{{\text{s}}^{ - 1}}\);
step 1 / equation showing step 1;
O (atom) / oxygen atom;
Do not allow oxygen or O2.
(minimum) energy needed for a reaction to occur / difference in energy between the reactants and transition state;
correct position of activation energy;
correct position of \(\Delta H\) and \(H{\text{(C}}{{\text{H}}_3}{\text{NC)}}\)/reactant line above \(H{\text{(C}}{{\text{H}}_3}{\text{CN)}}\) product line;
Accept \(\Delta E\) instead of \(\Delta H\) on diagram if y-axis is labelled as energy.
Do not penalize if CH3NC and CH3CN are not labelled on diagram.
correct position of transition state;
Allow [2 max] if axes are not labelled on diagram.
as temperature/\(T\) increases rate constant/k increases (exponentially);
from graph gradient \(m = - \frac{{{E_{\text{a}}}}}{R}\);
measurement of gradient from chosen points on graph;
Units of m are K. Do not penalize if not given, but do not award mark for incorrect units.
Value of m is based on any two suitable points well separated on the plot.
correct answer for \({E_{\text{a}}}\);
correct units corresponding to answer;
Note: A typical answer for Ea = 1.6 \( \times \) 102 kJ / kJ\(\,\)mol–1.
Examiners report
Surprisingly, the rate of reaction was only correctly defined by approximately 50% of candidates in (a) (i).
The equation for the reaction of magnesium carbonate with dilute hydrochloric acid was not well answered (part (ii)), and often candidates did not write correct formula or forgot to include water as a product.
Part (iii) was well answered by most candidates.
Part (iv) was well answered by most candidates, although the weaker candidates often only scored two or three marks.
Part (b) (i) was well answered and many candidates scored all four marks. Some candidates used a simple mathematical approach and those that followed this method typically were able to deduce the order correctly.
For (ii) most candidates were able to write the rate expression for the reaction.
In (iii), determining the value of the rate constant and its corresponding units was difficult for many candidates and only the better candidates scored both marks. Many mistakes were seen in the units.
Part (c) (i) was usually well answered.
A common mistake for (ii) involved candidates writing \({{\text{O}}_{\text{2}}}\) instead of O.
The definition of activation energy was well answered.
Part (ii) was a question where most candidates scored at least one/two marks although perfect answers were less common. Reasons leading to the loss of marks included: absence of axes, incomplete libelling of axes and the incorrect identification of the position of the transition state.
Parts (iii) and (iv) were very poorly answered for such a fundamental topic. All sorts of errors were evident, including incorrect gradients, inability to rearrange the Arrhenius Equation etc.
Even the better candidates struggled greatly with this question, even though this comes straight from AS 16.3.2.
