Chemical Kinetics: Class 12 Chemistry Practice Questions

A pharmaceutical company is studying the degradation of a drug compound X in aqueous solution. The degradation follows the mechanism given below:

Step I : X + H⁺ → Y (slow)
Step II : Y + H₂O → Z + H⁺ (fast)

In a separate kinetics experiment, the rate of decomposition of X was monitored at two temperatures. At 300 K, the rate constant k₁ = 2.0 × 10⁻³ s⁻¹. At 320 K, the rate constant k₂ = 8.0 × 10⁻³ s⁻¹.

A pharmaceutical company is studying the degradation of a drug compound X in aqueous solution. The degradation follows the mechanism given below:

Step I : X + H⁺ → Y (slow)
Step II : Y + H₂O → Z + H⁺ (fast)

In a separate kinetics experiment, the rate of decomposition of X was monitored at two temperatures. At 300 K, the rate constant k₁ = 2.0 × 10⁻³ s⁻¹. At 320 K, the rate constant k₂ = 8.0 × 10⁻³ s⁻¹.

(a) Write the rate law expression for the overall reaction and identify the order with respect to each reactant. Also state the role of H⁺ in this mechanism. [2]
(b) Calculate the energy of activation (Eₐ) for the degradation of drug X.
[Given: 2.303R = 19.15 J K⁻¹ mol⁻¹, log 2 = 0.301] [2]

A pharmaceutical company is studying the thermal decomposition of a drug compound X in solution for shelf-life prediction. The following concentration-time data were recorded at 300 K:

| Time (min) | [X] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 10 | 0.400 |
| 20 | 0.200 |
| 30 | 0.100 |

When the experiment was repeated at 330 K, the half-life of compound X was found to be 2.5 minutes.

(Given: R = 8.314 J K⁻¹ mol⁻¹; log 2 = 0.301)

A pharmaceutical company is studying the thermal decomposition of a drug compound X in solution for shelf-life prediction. The following concentration-time data were recorded at 300 K:

| Time (min) | [X] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 10 | 0.400 |
| 20 | 0.200 |
| 30 | 0.100 |

When the experiment was repeated at 330 K, the half-life of compound X was found to be 2.5 minutes.

(a) Using the concentration-time data, identify the order of the reaction and calculate the rate constant k₁ at 300 K. (2 marks)
(b) Calculate the activation energy (Eₐ) for the decomposition of X. (2 marks)

(Given: R = 8.314 J K⁻¹ mol⁻¹; log 2 = 0.301)

A food technologist is studying the spoilage of packaged fruit juice. She finds that the rate of spoilage follows first-order kinetics with respect to the concentration of a key enzyme responsible for degradation. The enzyme concentration data at 300 K is given in the table above.

A food technologist is studying the spoilage of packaged fruit juice. She finds that the rate of spoilage follows first-order kinetics with respect to the concentration of a key enzyme responsible for degradation. She collects the following data at 300 K:

| Time (minutes) | [Enzyme] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 30 | 0.400 |
| 60 | 0.200 |

She also knows that the activation energy for this enzymatic spoilage reaction is 55,000 J mol⁻¹.

(a) Using the data, verify that the spoilage reaction is first order and calculate the rate constant k at 300 K. (2 marks)
(b) Calculate the temperature at which the rate constant becomes double its value at 300 K. (Given: R = 8.314 J K⁻¹ mol⁻¹, log 2 = 0.301) (2 marks)

A food scientist is studying the spoilage of a packaged fruit juice. She models the degradation of vitamin C (ascorbic acid) in the juice as a first-order reaction. She measures the concentration of vitamin C at different time intervals and records the following data:

Time (min): 0, 20, 40
[Vitamin C] (mol L⁻¹): 0.800, 0.400, 0.200

She also notices that when the storage temperature is raised from 300 K to 320 K, the rate constant doubles.

A food scientist is studying the spoilage of a packaged fruit juice. She models the degradation of vitamin C (ascorbic acid) in the juice as a first-order reaction. She measures the concentration of vitamin C at different time intervals and records the following data:

| Time (min) | [Vitamin C] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 20 | 0.400 |
| 40 | 0.200 |

She also notices that when the storage temperature is raised from 300 K to 320 K, the rate constant doubles.

(a) Using the data, verify that the degradation of vitamin C follows first-order kinetics. Also calculate the rate constant k at 300 K. [2 marks]

(b) The scientist claims: "Storing the juice at a lower temperature will double the shelf life of the product." Using the Arrhenius equation, calculate the activation energy (Ea) for this reaction and comment on whether a further 20 K drop (from 300 K to 280 K) would again double the shelf life. [2 marks]

A food technologist is studying the spoilage of a fruit juice stored at different temperatures. She finds that the rate constant for the spoilage reaction (first order) is 2.0 × 10⁻³ min⁻¹ at 27°C and 8.0 × 10⁻³ min⁻¹ at 47°C.

A food technologist is studying the spoilage of a fruit juice stored at different temperatures. She finds that the rate constant for the spoilage reaction (first order) is 2.0 × 10⁻³ min⁻¹ at 27°C and 8.0 × 10⁻³ min⁻¹ at 47°C.

(a) Calculate the activation energy (Eₐ) for the spoilage reaction. (Given: R = 8.314 J K⁻¹ mol⁻¹; log 4 = 0.602) [2 marks]
(b) The technologist observes that the juice kept at 27°C has an initial spoilage-indicator concentration of 0.04 mol L⁻¹. How long (in minutes) will it take for this concentration to reduce to 0.01 mol L⁻¹? [1 mark]
(c) If the spoilage reaction were zero order instead of first order (with the same rate constant at 27°C), how would the half-life of the reaction change with a decrease in the initial concentration of the spoilage indicator? Give reason. [1 mark]

A food chemist is studying the decomposition of vitamin C (ascorbic acid) in a juice bottle at room temperature. The concentration drops from 0.080 mol L⁻¹ to 0.020 mol L⁻¹ in 60 minutes under first-order kinetics. Experimental rate data at different initial concentrations are provided.

A food chemist is studying the decomposition of a vitamin C (ascorbic acid) solution in a juice bottle kept at room temperature. She finds that the concentration of vitamin C drops from 0.080 mol L⁻¹ to 0.020 mol L⁻¹ in 60 minutes, and the reaction follows first-order kinetics.

The following data were collected at different initial concentrations of vitamin C to confirm the rate law:

| Experiment | [Vitamin C] / mol L⁻¹ | Initial Rate / mol L⁻¹ min⁻¹ |
|---|---|---|
| 1 | 0.040 | 2.4 × 10⁻³ |
| 2 | 0.080 | 4.8 × 10⁻³ |
| 3 | 0.020 | 1.2 × 10⁻³ |

(a) Using the data in the table, confirm the order of the reaction with respect to vitamin C. Write the rate law expression.
(b) Calculate the rate constant k for the decomposition reaction using the integrated rate law. State its unit.
(c) The chemist claims that doubling the initial concentration of vitamin C will double the initial rate but will NOT change the half-life of the reaction. Justify this claim.

A food preservation company stores fruit juices at 5°C instead of 25°C to prevent microbial spoilage. The spoilage reaction follows the Arrhenius equation with an activation energy (Eₐ) of 75 kJ mol⁻¹. The company's food technologist claims that refrigeration slows the spoilage rate by more than 10 times compared to room temperature storage.

[Given: R = 8.314 J K⁻¹ mol⁻¹; log 2.303 = 0.3623; use log e = 0.4343]

A food preservation company stores fruit juices at 5°C (refrigerator temperature) instead of 25°C (room temperature). The activation energy for the spoilage reaction is 75 kJ mol⁻¹. A food technologist claims that refrigeration slows the spoilage rate by a factor of more than 10.

(a) Using the Arrhenius equation, calculate the ratio k₂₅/k₅ (rate constant at 25°C to rate constant at 5°C). [2]
(b) Is the technologist's claim correct? Justify your answer. [1]
(c) Which among the following graphs correctly represents the fraction of molecules (f) having kinetic energy equal to or greater than activation energy (Eₐ) as temperature increases from T₁ to T₂ (T₂ > T₁)?
(i) The area under the curve beyond Eₐ decreases as temperature increases.
(ii) The area under the curve beyond Eₐ increases as temperature increases.
(iii) The area under the curve beyond Eₐ remains the same at both temperatures.
(iv) The curve shifts to lower energy values as temperature increases. [1]

A pharmaceutical company is testing a new drug that decomposes in the bloodstream according to first-order kinetics. A pharmacologist monitors the drug concentration and records the following data:

Time (min): 0, 30, 60
Concentration (mol L⁻¹): 0.800, 0.400, 0.200

A pharmaceutical company is testing a new drug that decomposes in the bloodstream according to first-order kinetics. A pharmacologist monitors the drug concentration and records the following data:

Time (min): 0, 30, 60
Concentration (mol L⁻¹): 0.800, 0.400, 0.200

(a) Using the data, calculate the rate constant k for the decomposition. (2 marks)
(b) The drug is considered therapeutically ineffective once its concentration falls to 6.25% of the initial dose. Calculate the time required for this to occur. (1 mark)
(c) A second drug, under identical conditions, has a half-life that doubles when the initial concentration is doubled. Identify the order of this second reaction and give one reason for your answer. (1 mark)

The half-life of a first-order reaction is 30 minutes. What is the rate constant (k) for this reaction?

The half-life of a first-order reaction is 693 s. What is the rate constant of the reaction?

The rate constant of a first-order reaction is 2.31 × 10⁻² min⁻¹. What are the units of the rate constant for a zero-order reaction?

For a first order reaction, the half-life is independent of the initial concentration of the reactant. Give reason.

The rate constant of a first-order reaction is 0.693 min⁻¹. Calculate the half-life of the reaction.

The concentration of a reactant decreases from 0.8 mol L⁻¹ to 0.1 mol L⁻¹ in 21 minutes in a first order reaction. Calculate the rate constant of the reaction. (Given: log 2 = 0.301)

For a first-order reaction, the half-life is independent of the initial concentration of the reactant. Give reason.

A food scientist is studying the spoilage of a packaged juice. She models the decomposition of ascorbic acid (Vitamin C) in the juice as a first-order reaction. She observes that at 27°C, the concentration of ascorbic acid drops from 0.080 mol L⁻¹ to 0.020 mol L⁻¹ in 80 minutes. When the storage temperature is raised to 47°C, the rate constant increases to 5.42 × 10⁻² min⁻¹.

(a) Calculate the rate constant k at 27°C. [2 marks]
(b) Calculate the activation energy Eₐ for this decomposition.
[Given: 2.303 R = 19.15 J K⁻¹ mol⁻¹, log 2 = 0.301] [2 marks]

For the decomposition of azomethane, CH₃N₂CH₃(g) → CH₃CH₃(g) + N₂(g), the following data were obtained at 600 K:

Time (s) [CH₃N₂CH₃] (mol L⁻¹)
0 2.00 × 10⁻²
500 1.00 × 10⁻²
1000 5.00 × 10⁻³

(a) Show that the above reaction is of first order.
(b) Calculate the rate constant for this reaction.
(c) State the units of the rate constant and write the expression for the half-life of a first-order reaction.

A food scientist is studying the spoilage of a fruit juice at different storage temperatures. The spoilage follows first-order kinetics with respect to the concentration of a key degradable compound. The rate constant k is found to obey the following relationship:

log k = 14.80 − 4200 / T

where T is the temperature in Kelvin and k is in s⁻¹.

(a) Calculate the activation energy Eₐ for the spoilage reaction. [R = 8.314 J K⁻¹ mol⁻¹] (2 marks)

(b) The juice is stored at 27°C. Calculate the rate constant k at this temperature. Also state the unit of k. (1 mark)

(c) The food scientist claims: 'Storing the juice at a lower temperature slows spoilage because the fraction of molecules with energy equal to or greater than Eₐ decreases significantly.' Justify this claim using the Arrhenius equation. (1 mark)

The initial concentration of a substance A in the first order reaction A(g) → B(g) + C(g) was 0·80 mol L⁻¹. After 40 minutes the concentration of A was 0·10 mol L⁻¹. Calculate: (i) the rate constant of the reaction, and (ii) the half-life of the reaction. [log 2 = 0·301]

The following data were obtained for the reaction: P + Q → Products

| Experiment | [P] / mol L⁻¹ | [Q] / mol L⁻¹ | Initial Rate / mol L⁻¹ s⁻¹ |
|---|---|---|---|
| 1 | 0·10 | 0·10 | 2·0 × 10⁻² |
| 2 | 0·20 | 0·10 | 4·0 × 10⁻² |
| 3 | 0·10 | 0·30 | 1·8 × 10⁻¹ |

(a) Determine the order of reaction with respect to P and with respect to Q.
(b) Write the rate law for the reaction.
(c) Calculate the rate constant, k, giving its units.

The decomposition of azomethane, CH₃N₂CH₃(g) → C₂H₆(g) + N₂(g), follows first-order kinetics. At 600 K, the initial partial pressure of azomethane was 3.6 × 10⁻² atm. After 40 minutes, the partial pressure fell to 0.6 × 10⁻² atm.
(a) Calculate the rate constant k at 600 K. [Given: log 6 = 0.778]
(b) Calculate the half-life of the reaction at 600 K.
(c) State one characteristic feature that distinguishes a first-order reaction from a zero-order reaction with respect to half-life.

The following data were obtained during the first order thermal decomposition of SO₂Cl₂ at constant volume:

SO₂Cl₂(g) → SO₂(g) + Cl₂(g)

| S. No. | Time (s) | Total Pressure (atm) |
|--------|----------|----------------------|
| 1 | 0 | 0.40 |
| 2 | 60 | 0.60 |

Calculate the rate constant for this reaction.
[Given: log 2 = 0.3010, log 4 = 0.6021]

(a) The rate constant of a first order reaction is 2.303 × 10⁻³ s⁻¹. Calculate the time required for 75% of the reactant to decompose.
(b) How does the rate constant of a reaction change with temperature? Name the equation used.
(c) Write the unit of rate constant for a second order reaction.

A pharmaceutical company is studying the degradation of a drug in a patient's bloodstream. The drug follows first-order kinetics. A doctor administers a dose such that the initial concentration of the drug in the blood is 200 mg L⁻¹. Clinical records show that the drug concentration falls to 25 mg L⁻¹ in 120 minutes.

(a) Calculate the rate constant (k) for the degradation of the drug. [log 2 = 0.3010]

(b) The drug is therapeutically effective only when its concentration is above 50 mg L⁻¹. Using your answer from part (a), calculate the time window during which the drug remains effective after administration.

(c) A trainee pharmacist claims: 'Since the drug follows first-order kinetics, doubling the initial dose will double the time the drug remains effective.' Evaluate this claim with a suitable calculation. [log 2 = 0.3010]

A food scientist is studying the spoilage of a packaged fruit juice. She finds that the degradation of Vitamin C (ascorbic acid) in the juice follows first-order kinetics. At 25°C, the rate constant for degradation is 1.386 × 10⁻² day⁻¹. The juice is considered unfit for consumption when 75% of the original Vitamin C has degraded.

A food scientist is studying the spoilage of a packaged fruit juice. She finds that the degradation of Vitamin C (ascorbic acid) in the juice follows first-order kinetics. At 25°C, the rate constant for degradation is 1.386 × 10⁻² day⁻¹. The juice is considered unfit for consumption when 75% of the original Vitamin C has degraded.

(a) Calculate the half-life of Vitamin C degradation at 25°C. [1]

(b) Calculate the time (in days) after which the juice becomes unfit for consumption. [2]

(c) The scientist also observes that storing the juice at 5°C instead of 25°C significantly slows the degradation. Identify the factor responsible for this observation and state how it affects the rate constant. [1]

A food scientist is studying the spoilage of a fruit juice at different storage temperatures. The decomposition of ascorbic acid (Vitamin C) in the juice follows first-order kinetics. The scientist records the following data:

| Experiment | Temperature (K) | Rate constant, k (s⁻¹) |
|---|---|---|
| 1 | 300 | 2.0 × 10⁻³ |
| 2 | 320 | 8.0 × 10⁻³ |

(Given: R = 8.314 J K⁻¹ mol⁻¹, log 4 = 0.602, log 2 = 0.301)

A food scientist is studying the spoilage of a fruit juice at different storage temperatures. The decomposition of ascorbic acid (Vitamin C) in the juice follows first-order kinetics. The scientist records the following data:

| Experiment | Temperature (K) | Rate constant, k (s⁻¹) |
|---|---|---|
| 1 | 300 | 2.0 × 10⁻³ |
| 2 | 320 | 8.0 × 10⁻³ |

(a) Using the Arrhenius equation, calculate the activation energy (E_a) for the decomposition of ascorbic acid. (Given: R = 8.314 J K⁻¹ mol⁻¹, log 4 = 0.602)

(b) The scientist finds that at 300 K, the initial concentration of ascorbic acid is 0.80 mol L⁻¹. How long will it take for the concentration to drop to 0.10 mol L⁻¹? (Given: log 2 = 0.301)

(c) If the juice is stored at 280 K instead of 300 K, predict qualitatively — with a reason — whether the juice will stay fresh for a longer or shorter time.

A food-processing company studies the decomposition of a preservative P in canned food at 300 K. The reaction P(aq) → Products is monitored and the following initial rate data are recorded:

| Experiment | [P] / mol L⁻¹ | Initial Rate / mol L⁻¹ s⁻¹ |
|---|---|---|
| 1 | 0.10 | 2.0 × 10⁻³ |
| 2 | 0.20 | 4.0 × 10⁻³ |
| 3 | 0.40 | 8.0 × 10⁻³ |

A food-processing company studies the decomposition of a preservative P in canned food. The reaction is: P(aq) → Products. The technician records the following initial rate data at 300 K:

| Experiment | [P] / mol L⁻¹ | Initial Rate / mol L⁻¹ s⁻¹ |
|---|---|---|
| 1 | 0.10 | 2.0 × 10⁻³ |
| 2 | 0.20 | 4.0 × 10⁻³ |
| 3 | 0.40 | 8.0 × 10⁻³ |

(a) Determine the order of the reaction with respect to P and write the rate law. (1 mark)
(b) Calculate the value of the rate constant k, stating its units. (1 mark)
(c) The company needs the preservative to drop to 25% of its initial concentration. Using the first-order integrated rate law, calculate the time required if k = 2.0 × 10⁻² s⁻¹. (2 marks)

A food scientist is studying the spoilage of a packaged fruit juice. The spoilage reaction follows first-order kinetics. Rate constants: k₁ = 2.0 × 10⁻³ min⁻¹ at 300 K; k₂ = 8.0 × 10⁻³ min⁻¹ at 320 K.

A food scientist is studying the spoilage of a packaged fruit juice. The spoilage reaction follows first-order kinetics with respect to the concentration of a key reactant (vitamin C degradation). The following data were collected at two different storage temperatures:

| Storage Temperature | Rate constant (k) |
|---|---|
| 27°C (300 K) | 2.0 × 10⁻³ min⁻¹ |
| 47°C (320 K) | 8.0 × 10⁻³ min⁻¹ |

(a) Calculate the activation energy (Eₐ) for the vitamin C degradation reaction. (Given: R = 8.314 J K⁻¹ mol⁻¹, log 2 = 0.301)

(b) The juice manufacturer wants to ensure that at 27°C, at least 50% of the original vitamin C remains. Calculate the shelf life of the juice (in minutes) at 27°C.

(c) Based on your answer to (a), explain briefly whether the spoilage reaction is more sensitive to temperature change compared to a reaction with Eₐ = 30 kJ mol⁻¹, and what practical recommendation you would give the manufacturer.

A food scientist is studying the degradation of Vitamin C (ascorbic acid) in a packaged fruit juice. She finds that the degradation follows first order kinetics. At 27°C, the concentration of Vitamin C drops from 200 mg/L to 25 mg/L in 60 minutes. At 47°C, the same drop (200 mg/L to 25 mg/L) occurs in only 15 minutes.

A food scientist is studying the degradation of Vitamin C (ascorbic acid) in a packaged fruit juice. She finds that the degradation follows first order kinetics. At 27°C, the concentration of Vitamin C drops from 200 mg/L to 25 mg/L in 60 minutes. At 47°C, the same drop (200 mg/L to 25 mg/L) occurs in only 15 minutes.

(a) Calculate the rate constant (k) for the degradation of Vitamin C at 27°C. [log 2 = 0.301]

(b) Calculate the activation energy (Eₐ) for this degradation process.
[R = 8.314 J K⁻¹ mol⁻¹; log 4 = 0.602]

A food scientist is studying the degradation of Vitamin C (ascorbic acid) in a bottled juice under controlled storage conditions. She monitors the concentration of Vitamin C at regular intervals and records the following data at 300 K:

| Time (min) | [Vitamin C] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 10 | 0.400 |
| 20 | 0.200 |
| 30 | 0.100 |

She also finds that when the storage temperature is raised from 300 K to 310 K, the rate constant doubles.

A food scientist is studying the degradation of Vitamin C (ascorbic acid) in a bottled juice under controlled storage conditions. She monitors the concentration of Vitamin C at regular intervals and records the following data at 300 K:

| Time (min) | [Vitamin C] (mol L⁻¹) |
|---|---|
| 0 | 0.800 |
| 10 | 0.400 |
| 20 | 0.200 |
| 30 | 0.100 |

She also finds that when the storage temperature is raised from 300 K to 310 K, the rate constant doubles.

(a) Identify the order of this degradation reaction. Justify your answer using the data given. (2 marks)
(b) Calculate the rate constant at 300 K. State its unit. (1 mark)
(c) Calculate the activation energy (Eₐ) for the degradation process. (Given: R = 8.314 J K⁻¹ mol⁻¹, log 2 = 0.301) (1 mark)