Collecting and processing data: notes and practice questions

Two students independently investigated the effect of hydrochloric acid concentration on the rate of reaction with excess calcium carbonate:

$\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}$

Student A measured the time taken to produce $40.0\text{ cm}^3$ of carbon dioxide gas at four different acid concentrations. Student A performed a single trial at each concentration.

(a) Comment on the reliability of Student A's data.

(b) Student B performed three trials at each acid concentration, obtaining closely agreeing times for each. However, the temperature of the acid was not kept constant, rising from $20.0\text{ }^\circ\text{C}$ for the lowest concentration to $29.0\text{ }^\circ\text{C}$ for the highest concentration.

Comment on the validity of Student B's conclusion that the observed increase in rate was due solely to the increase in acid concentration.

Two students independently investigate the effect of temperature on the rate of reaction between zinc and excess dilute hydrochloric acid:

$\text{Zn(s)} + 2\text{HCl(aq)} \rightarrow \text{ZnCl}_2\text{(aq)} + \text{H}_2\text{(g)}$

Each student measures the volume of hydrogen gas collected in a gas syringe over the first $60\text{ s}$ of the reaction at four temperatures: $20\text{ }^\circ\text{C}$, $30\text{ }^\circ\text{C}$, $40\text{ }^\circ\text{C}$, and $50\text{ }^\circ\text{C}$.

• Student A uses zinc granules and performs a single trial at each temperature.

• Student B performs three trials at each temperature. However, after completing the trials at $20\text{ }^\circ\text{C}$ and $30\text{ }^\circ\text{C}$, Student B runs out of zinc granules and uses the same mass of powdered zinc for the trials at $40\text{ }^\circ\text{C}$ and $50\text{ }^\circ\text{C}$.

(a) Comment on the reliability of the data obtained by Student A compared to Student B.

(b) Comment on the validity of Student B's conclusion regarding the effect of temperature on the reaction rate.

A student investigates the absorbance of aqueous copper(II) sulfate solutions of different concentrations using a colorimeter at a wavelength of 635 nm. The quantitative measurements and qualitative observations are recorded in the table below.

(a) Describe the relationship between the concentration of $\text{CuSO}_4\text{(aq)}$ and absorbance shown by the data.

(b) Describe the qualitative trend in the appearance of the solution as the concentration increases.

A student carried out an experiment to determine the enthalpy change of combustion of ethanol, $\text{C}_2\text{H}_5\text{OH}(l)$, using a spirit burner to heat a beaker containing water. The temperature of the water was measured using a thermometer with an uncertainty of $\pm 0.2\ ^\circ\text{C}$ for each reading.

The recorded temperature data are shown below:

(a) Calculate the percentage uncertainty in the temperature increase, $\Delta T$.

(b) The student calculated their experimental enthalpy change of combustion of ethanol to be $-1140\text{ kJ mol}^{-1}$. The literature value for the standard enthalpy change of combustion of ethanol is $-1367\text{ kJ mol}^{-1}$.

Calculate the percentage error in the student's experimental result.

Nitrogen dioxide, a pollutant from car exhausts, reacts with water in the atmosphere to form nitric acid and nitrous acid. This is a disproportionation reaction.

$2NO_{2}(g) + H_{2}O(l) \rightleftharpoons HNO_{3}(aq) + HNO_{2}(aq)$

(a) Deduce the oxidation states of nitrogen in the reactant and products.

Reactant: $NO_{2}$

Products: $HNO_{3}$, $HNO_{2}$

(b) Explain, with reference to the equilibrium, why more nitrogen dioxide gas dissolves when the reaction occurs in alkaline rainwater.

(c) The solubility of nitrogen dioxide gas in water was measured by different scientific groups. A summary of their results is shown.

(i) Identify a problem in comparing the data from the different sources as presented in the table.

(ii) The units of solubility are converted to mol dm⁻³. Complete the table by calculating the value for source A. Assume the atmospheric pressure is 100 kPa and the density of the resulting solution is 1.00 g cm⁻³.

(iii) Suggest an explanation for the effect of temperature on the solubility of nitrogen dioxide gas.

(d) Suggest one reason why nitrogen dioxide is considered a major air pollutant.

(e) Nitrous acid, $HNO_2$, is a weak acid. The graph shows the percentage of nitrous acid and its conjugate base, the nitrite ion ($NO_2^-$), present at different pH values.

(GRAPH IS A STANDARD SPECIATION PLOT FOR A WEAK ACID. X-AXIS: pH from 0 to 8. Y-AXIS: Percentage from 0 to 100. A curve for HA starts at 100% and goes down, a curve for A- starts at 0% and goes up. The two curves cross at pH = 3.3, where each is at 50%.)

(i) Deduce the pH range where nitrous acid, $HNO_{2}$, is the dominant nitrogen-containing species in the solution.

(ii) Determine, with reference to the graph, the $pK_a$ of nitrous acid.

(f) Nitrous acid can react with secondary amines to form N-nitrosamines, which are potent carcinogens. An example is the reaction with dimethylamine, $(CH_3)_2NH$.

(i) Deduce a balanced chemical equation for the formation of N-nitrosodimethylamine, $(CH_3)_2NNO$, from dimethylamine and nitrous acid.

(ii) The rate of N-nitrosamine formation is highly dependent on pH. The reaction rate is highest under mildly acidic conditions where there is a sufficient concentration of both the unprotonated amine and nitrous acid. State two conditions that could be maintained in an industrial process to minimize the formation of N-nitrosamines.

(g) To combat the effects of acid rain, powdered limestone ($CaCO_3$) is sometimes added to lakes. Suggest two distinct reasons why this 'liming' process is effective at restoring the aquatic ecosystem.

(a) A student investigated the catalytic decomposition of aqueous hydrogen peroxide:

$2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)}$

The concentration of $\text{H}_2\text{O}_2\text{(aq)}$ remaining in the reaction mixture was determined at $60\text{ s}$ intervals. The data obtained are shown in the table.

Calculate the average rate of consumption of $\text{H}_2\text{O}_2\text{(aq)}$ between $t = 0\text{ s}$ and $t = 60\text{ s}$, stating its unit.

(b) The initial concentration of $\text{H}_2\text{O}_2\text{(aq)}$ was recorded as $1.000\text{ mol dm}^{-3}$ with an absolute uncertainty of $\pm 0.025\text{ mol dm}^{-3}$.

Calculate the percentage uncertainty in this initial concentration.

(c) The accepted literature value for this average rate of consumption under identical conditions is $4.25 \times 10^{-3}\text{ mol dm}^{-3}\text{ s}^{-1}$.

Calculate the percentage error of the experimental rate determined in part (a).

(a) A student carried out an experiment to determine the enthalpy change of neutralization between $50.0\text{ cm}^3$ of $1.00\text{ mol dm}^{-3}\text{ HCl}(aq)$ and $50.0\text{ cm}^3$ of $1.00\text{ mol dm}^{-3}\text{ NaOH}(aq)$. The solutions were mixed in an open glass beaker. The initial temperature of each solution was $20.5\text{ }^\circ\text{C}$ and the maximum temperature reached was $25.9\text{ }^\circ\text{C}$. The calculated enthalpy change was $-45.1\text{ kJ mol}^{-1}$, which is significantly less exothermic than the literature value of $-57.2\text{ kJ mol}^{-1}$.

Suggest one reason why the maximum temperature recorded during data collection was lower than the expected theoretical value.

(b) Suggest two modifications to the experimental apparatus or procedure that would address the issue identified in part (a) and improve the accuracy of the determined enthalpy change.

An experiment was conducted to investigate the effect of temperature on the rate of reaction between excess calcium carbonate chips and 100 cm³ of 0.5 mol dm⁻³ hydrochloric acid. The volume of carbon dioxide gas produced was collected in a gas syringe. The results for the reaction at 25 °C (Experiment 1), 35 °C (Experiment 2), and 45 °C (Experiment 3) are plotted on the graph below.

(a) By annotating the graph, determine the initial rate of reaction for Experiment 2, in cm³ s⁻¹.

(b) Estimate the time required for Experiment 1 to produce half of the total volume of CO₂.

(c) Suggest two reasons, in terms of collision theory, why the rate of reaction in Experiment 3 (45 °C) is greater than in Experiment 1 (25 °C).

(d) Calculate the percentage increase in the volume of CO₂ produced after 20 seconds when the temperature is increased from 25 °C (Experiment 1) to 45 °C (Experiment 3).

(e) The experiment was performed in a sealed flask connected to the gas syringe. Sketch a graph of the total mass of the apparatus against time for Experiment 1 and provide a reason for its shape.

A food chemist is analyzing the components of a new artificial sweetener mixture using paper chromatography. A small spot of the mixture is applied to a chromatography paper, and the paper is placed in a sealed chamber with a solvent system consisting of $70\%$ ethanol and $30\%$ water. After some time, the solvent front moves up the paper, separating the components.

(a) Define the stationary phase and the mobile phase in this paper chromatography experiment.

(b) Explain why it is important that the initial spot of the sweetener mixture is applied above the solvent level in the chamber, and why the solvent front should not be allowed to reach the very top of the chromatography paper.

(c) After the chromatography run, the solvent front travelled $9.0\text{ cm}$ from the start line. Two distinct components, Sweetener A (yellow) and Sweetener B (blue), were observed to have travelled $7.2\text{ cm}$ and $4.5\text{ cm}$ respectively from the start line.

Calculate the retardation factor, $R_F$, for Sweetener A and Sweetener B. Show your working.

(d) The stationary phase (paper) is polar due to cellulose, and the mobile phase is a moderately polar mixture of $70\%$ ethanol and $30\%$ water.

Deduce, with a reason, which sweetener (A or B) is more polar.

(e) If Sweetener A and another component had very similar $R_F$ values and were not well separated, suggest one modification to the experiment that could improve their separation.