Tool 3: Mathematics

Which properties can be monitored to determine the rate of the reaction?

Fe (s) + CuSO₄ (aq) → Cu (s) + FeSO₄ (aq)

    I. change in volume
    II. change in temperature
    III. change in colour

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Which properties can be monitored to determine the rate of the reaction?

Fe (s) + CuSO₄ (aq) → Cu (s) + FeSO₄ (aq)

    I. change in volume
    II. change in temperature
    III. change in colour

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The dotted line represents the formation of oxygen, O₂ (g), from the uncatalysed complete decomposition of hydrogen peroxide, H₂O₂ (aq).

Which curve represents a catalysed reaction under the same conditions?

The dotted line represents the formation of oxygen, O₂ (g), from the uncatalysed complete decomposition of hydrogen peroxide, H₂O₂ (aq).

Which curve represents a catalysed reaction under the same conditions?

Which properties can be monitored to determine the rate of the reaction?

Fe (s) + CuSO₄ (aq) → Cu (s) + FeSO₄ (aq)

    I. change in volume
    II. change in temperature
    III. change in colour

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Which properties can be monitored to determine the rate of the reaction?

Fe (s) + CuSO₄ (aq) → Cu (s) + FeSO₄ (aq)

    I. change in volume
    II. change in temperature
    III. change in colour

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

K_c for 2N₂O (g) $\rightleftharpoons$ 2N₂ (g) + O₂ (g) is 7.3 × 10³⁴.

What is K_c for the following reaction, at the same temperature?

N₂ (g) + $\frac{1}{2}$O₂ (g) $\rightleftharpoons$ N₂O (g)

A. 7.3 × 10³⁴

B. $\frac{1}{\sqrt{7.3\times {10}^{34}}}$

C. $\frac{2}{7.3\times {10}^{34}}$

D. $\frac{1}{2\times 7.3\times {10}^{34}}$

K_c for 2N₂O (g) $\rightleftharpoons$ 2N₂ (g) + O₂ (g) is 7.3 × 10³⁴.

What is K_c for the following reaction, at the same temperature?

N₂ (g) + $\frac{1}{2}$O₂ (g) $\rightleftharpoons$ N₂O (g)

A. 7.3 × 10³⁴

B. $\frac{1}{\sqrt{7.3\times {10}^{34}}}$

C. $\frac{2}{7.3\times {10}^{34}}$

D. $\frac{1}{2\times 7.3\times {10}^{34}}$

The dotted line represents the formation of oxygen, O₂(g), from the uncatalysed complete decomposition of hydrogen peroxide, H₂O₂ (aq).

Which curve represents a catalysed reaction under the same conditions?

The dotted line represents the formation of oxygen, O₂(g), from the uncatalysed complete decomposition of hydrogen peroxide, H₂O₂ (aq).

Which curve represents a catalysed reaction under the same conditions?

Which graph would not show a linear relationship for a fixed mass of an ideal gas with all other variables constant?

A. P against V

B. P against $\frac{1}{\text{V}}$

C. P against T

D. V against T

Which graph would not show a linear relationship for a fixed mass of an ideal gas with all other variables constant?

A. P against V

B. P against $\frac{1}{\text{V}}$

C. P against T

D. V against T

Data collected from a larger number of silicon samples could also be plotted to determine the density using the following axes.

Which statements are correct?

    I. The density is the slope of the graph.
    II. The data will show that mass is proportional to volume.
    III. The best-fit line should pass through the origin.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Data collected from a larger number of silicon samples could also be plotted to determine the density using the following axes.

Which statements are correct?

    I. The density is the slope of the graph.
    II. The data will show that mass is proportional to volume.
    III. The best-fit line should pass through the origin.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of
formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of
formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of
formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

The experiment gave an error in the rate because the pressure gauge was inaccurate.

Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

The experiment gave an error in the rate because the pressure gauge was inaccurate.

Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

The experiment gave an error in the rate because the pressure gauge was inaccurate.

Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

The uncertainty of the 100.0cm³ volumetric flask used to make the solution was ±0.6cm³.

Calculate the maximum percentage uncertainty in the mass of NaHCO₃ so that the concentration of the solution is correct to ±1.0 %.

The uncertainty of the 100.0cm³ volumetric flask used to make the solution was ±0.6cm³.

Calculate the maximum percentage uncertainty in the mass of NaHCO₃ so that the concentration of the solution is correct to ±1.0 %.

The uncertainty of the 100.0cm³ volumetric flask used to make the solution was ±0.6cm³.

Calculate the maximum percentage uncertainty in the mass of NaHCO₃ so that the concentration of the solution is correct to ±1.0 %.

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

In a laboratory experiment solutions of potassium iodide and hydrogen peroxide were mixed and the volume of oxygen generated was recorded. The volume was adjusted to 0 at t = 0.

The data for the first trial is given below.

Plot a graph on the axes below and from it determine the average rate of formation of oxygen gas in cm³ O₂ (g) s⁻¹.

Average rate of reaction:

The experiment gave an error in the rate because the pressure gauge was inaccurate. Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

The experiment gave an error in the rate because the pressure gauge was inaccurate. Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

The experiment gave an error in the rate because the pressure gauge was inaccurate. Outline whether repeating the experiment, using the same apparatus, and averaging the results would reduce the error.

Estimate the time at which the powdered zinc was placed in the beaker.

Estimate the time at which the powdered zinc was placed in the beaker.

State what point Y on the graph represents.

State what point Y on the graph represents.

The maximum temperature used to calculate the enthalpy of reaction was chosen at a point on the extrapolated (dotted) line.

State the maximum temperature which should be used and outline one assumption made in choosing this temperature on the extrapolated line.

Maximum temperature:

Assumption:

The maximum temperature used to calculate the enthalpy of reaction was chosen at a point on the extrapolated (dotted) line.

State the maximum temperature which should be used and outline one assumption made in choosing this temperature on the extrapolated line.

Maximum temperature:

Assumption:

To determine the enthalpy of reaction the experiment was carried out five times. The same volume and concentration of copper(II) sulfate was used but the mass of zinc was different each time. Suggest, with a reason, if zinc or copper(II) sulfate should be in excess for each trial.

To determine the enthalpy of reaction the experiment was carried out five times. The same volume and concentration of copper(II) sulfate was used but the mass of zinc was different each time. Suggest, with a reason, if zinc or copper(II) sulfate should be in excess for each trial.

Predict, giving a reason, how the final enthalpy of reaction calculated from this experiment would compare with the theoretical value.

Predict, giving a reason, how the final enthalpy of reaction calculated from this experiment would compare with the theoretical value.

Determine from the graph the rate of reaction at 20 s, in cm³ s⁻¹, showing your working.

Determine from the graph the rate of reaction at 20 s, in cm³ s⁻¹, showing your working.

Describe one systematic error associated with the use of the gas syringe, and how the error affects the calculated rate.

Describe one systematic error associated with the use of the gas syringe, and how the error affects the calculated rate.

Identify one error associated with the use of an accurate stopwatch.

Identify one error associated with the use of an accurate stopwatch.

Determine the density of calcium, in g cm⁻³, using section 2 of the data booklet.

Ar = 40.08; metallic radius (r) = 1.97 × 10⁻¹⁰ m

Determine the density of calcium, in g cm⁻³, using section 2 of the data booklet.

Ar = 40.08; metallic radius (r) = 1.97 × 10⁻¹⁰ m

Estimate the time at which the powdered zinc was placed in the beaker.

Estimate the time at which the powdered zinc was placed in the beaker.

State what point Y on the graph represents.

State what point Y on the graph represents.

The maximum temperature used to calculate the enthalpy of reaction was chosen at a point on the extrapolated (dotted) line.

State the maximum temperature which should be used and outline one assumption made in choosing this temperature on the extrapolated line.

Maximum temperature:

Assumption:

The maximum temperature used to calculate the enthalpy of reaction was chosen at a point on the extrapolated (dotted) line.

State the maximum temperature which should be used and outline one assumption made in choosing this temperature on the extrapolated line.

Maximum temperature:

Assumption:

To determine the enthalpy of reaction the experiment was carried out five times. The same volume and concentration of copper(II) sulfate was used but the mass of zinc was different each time. Suggest, with a reason, if zinc or copper(II) sulfate should be in excess for each trial.

To determine the enthalpy of reaction the experiment was carried out five times. The same volume and concentration of copper(II) sulfate was used but the mass of zinc was different each time. Suggest, with a reason, if zinc or copper(II) sulfate should be in excess for each trial.

Predict, giving a reason, how the final enthalpy of reaction calculated from this experiment would compare with the theoretical value.

Predict, giving a reason, how the final enthalpy of reaction calculated from this experiment would compare with the theoretical value.

Determine from the graph the rate of reaction at 20 s, in cm³ s⁻¹, showing your working.

Determine from the graph the rate of reaction at 20 s, in cm³ s⁻¹, showing your working.

Describe one systematic error associated with the use of the gas syringe, and how the error affects the calculated rate.

Describe one systematic error associated with the use of the gas syringe, and how the error affects the calculated rate.

Identify one error associated with the use of an accurate stopwatch.

Identify one error associated with the use of an accurate stopwatch.

Calculate the percentage uncertainty of the day 5 titre.

Calculate the percentage uncertainty of the day 5 titre.

Calculate the percentage uncertainty of the day 5 titre.

Calculate the percentage uncertainty of the day 5 titre.

Calculate the percentage uncertainty of the day 5 titre.

Calculate the percentage uncertainty of the day 5 titre.

Determine the initial rate of reaction of limestone with nitric acid from the graph.

Show your working on the graph and include the units of the initial rate.

Determine the initial rate of reaction of limestone with nitric acid from the graph.

Show your working on the graph and include the units of the initial rate.

Explain why the rate of reaction of limestone with nitric acid decreases and reaches zero over the period of five days.

Explain why the rate of reaction of limestone with nitric acid decreases and reaches zero over the period of five days.

Which graph represents the relationship between the rate constant, $k$, and temperature, $T$, in kelvin?

Which graph represents the relationship between the rate constant, $k$, and temperature, $T$, in kelvin?

Proteins are polymers of amino acids.

A paper chromatogram of two amino acids, A1 and A2, is obtained using a non-polar solvent.

© International Baccalaureate Organization 2020.

Determine the ${\mathrm{R}}_{\mathrm{f}}$ value of A1.

Proteins are polymers of amino acids.

A paper chromatogram of two amino acids, A1 and A2, is obtained using a non-polar solvent.

© International Baccalaureate Organization 2020.

Determine the ${\mathrm{R}}_{\mathrm{f}}$ value of A1.

Calculate the percentage uncertainty and percentage error in the experimentally determined value of $K_{\mathrm{c}}$ for methanol.

Calculate the percentage uncertainty and percentage error in the experimentally determined value of $K_{\mathrm{c}}$ for methanol.

Calculate the percentage uncertainty and percentage error in the experimentally determined value of $K_{\mathrm{c}}$ for methanol.

Calculate the percentage uncertainty and percentage error in the experimentally determined value of $K_{\mathrm{c}}$ for methanol.

Comment on the magnitudes of random and systematic errors in this experiment using the answers in (e).

Comment on the magnitudes of random and systematic errors in this experiment using the answers in (e).

Proteins are polymers of amino acids. A paper chromatogram of two amino acids, A1 and A2, is obtained using a non-polar solvent.

© International Baccalaureate Organization 2020.

Determine the ${\mathrm{R}}_{\mathrm{f}}$ value of A1.

Proteins are polymers of amino acids. A paper chromatogram of two amino acids, A1 and A2, is obtained using a non-polar solvent.

© International Baccalaureate Organization 2020.

Determine the ${\mathrm{R}}_{\mathrm{f}}$ value of A1.

The rate equation for a reaction is:

rate = k[A][B]

Which mechanism is consistent with this rate equation?

A.  2A $\rightleftharpoons$ I       Fast
     I + B → P    Slow

B.  A + B $\rightleftharpoons$ I   Fast
     I + A → P    Slow

C.  A → I          Slow
     I + B → P    Fast

D.  B $\rightleftharpoons$ I         Fast
     I + A → P    Slow

The rate equation for a reaction is:

rate = k[A][B]

Which mechanism is consistent with this rate equation?

A.  2A $\rightleftharpoons$ I       Fast
     I + B → P    Slow

B.  A + B $\rightleftharpoons$ I   Fast
     I + A → P    Slow

C.  A → I          Slow
     I + B → P    Fast

D.  B $\rightleftharpoons$ I         Fast
     I + A → P    Slow

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

Formulate an equation for the reaction of one mole of phosphoric acid with one mole of sodium hydroxide.

A student performed an experiment to find the melting point of sulfur, obtaining 118.0 °C. The literature value is 115.2 °C. What was the percentage error?

A.  $\frac{118.0-115.2}{115.2}\times 100\%$

B.  $\frac{115.2}{118.0}\times 100\%$

C.  $\frac{118.0-115.2}{118.0}\times 100\%$

D.  $\frac{118.0}{115.2}\times 100\%$

A student performed an experiment to find the melting point of sulfur, obtaining 118.0 °C. The literature value is 115.2 °C. What was the percentage error?

A.  $\frac{118.0-115.2}{115.2}\times 100\%$

B.  $\frac{115.2}{118.0}\times 100\%$

C.  $\frac{118.0-115.2}{118.0}\times 100\%$

D.  $\frac{118.0}{115.2}\times 100\%$

A student performed an experiment to find the melting point of sulfur, obtaining 118.0 °C. The literature value is 115.2 °C. What was the percentage error?

A.  $\frac{118.0-115.2}{115.2}\times 100\%$

B.  $\frac{115.2}{118.0}\times 100\%$

C.  $\frac{118.0-115.2}{118.0}\times 100\%$

D.  $\frac{118.0}{115.2}\times 100\%$

A student performed an experiment to find the melting point of sulfur, obtaining 118.0 °C. The literature value is 115.2 °C. What was the percentage error?

A.  $\frac{118.0-115.2}{115.2}\times 100\%$

B.  $\frac{115.2}{118.0}\times 100\%$

C.  $\frac{118.0-115.2}{118.0}\times 100\%$

D.  $\frac{118.0}{115.2}\times 100\%$

20 cm³ of 1 mol dm⁻³ sulfuric acid was added dropwise to 20 cm³ of 1 mol dm⁻³ barium hydroxide producing a precipitate of barium sulfate.

H₂SO₄(aq) + Ba(OH)₂(aq) → 2H₂O (l) + BaSO₄(s)

Which graph represents a plot of conductivity against volume of acid added?

20 cm³ of 1 mol dm⁻³ sulfuric acid was added dropwise to 20 cm³ of 1 mol dm⁻³ barium hydroxide producing a precipitate of barium sulfate.

H₂SO₄(aq) + Ba(OH)₂(aq) → 2H₂O (l) + BaSO₄(s)

Which graph represents a plot of conductivity against volume of acid added?

20 cm³ of 1 mol dm⁻³ sulfuric acid was added dropwise to 20 cm³ of 1 mol dm⁻³ barium hydroxide producing a precipitate of barium sulfate.

H₂SO₄(aq) + Ba(OH)₂(aq) → 2H₂O (l) + BaSO₄(s)

Which graph represents a plot of conductivity against volume of acid added?

20 cm³ of 1 mol dm⁻³ sulfuric acid was added dropwise to 20 cm³ of 1 mol dm⁻³ barium hydroxide producing a precipitate of barium sulfate.

H₂SO₄(aq) + Ba(OH)₂(aq) → 2H₂O (l) + BaSO₄(s)

Which graph represents a plot of conductivity against volume of acid added?

Determine the percentage uncertainty of the mass of product after heating.

Determine the percentage uncertainty of the mass of product after heating.

Determine the percentage uncertainty of the mass of product after heating.

Determine the percentage uncertainty of the mass of product after heating.

Determine the percentage uncertainty of the mass of product after heating.

Determine the percentage uncertainty of the mass of product after heating.

Suggest an explanation, other than product being lost from the crucible or reacting with nitrogen, that could explain the yield found in (b)(iii).

Suggest an explanation, other than product being lost from the crucible or reacting with nitrogen, that could explain the yield found in (b)(iii).

Suggest an explanation, other than product being lost from the crucible or reacting with nitrogen, that could explain the yield found in (b)(iii).