Half-Life - Online Tutor, Practice Problems & Exam Prep

The thermal dehydrogenation of propane is a first-order process and has a rate constant of 4.86×10⁻² s⁻¹ at 873 K:

C₃H₈(g) → C₃H₆(g) + H₂(g)

Calculate the half-life of propane at 873 K.

The thermal cracking of ethane is a first-order process and has a half-life of 2.11×10⁻² s at 900°C:

C₂H₆(g) → C₂H₄(g) + H₂(g)

Determine the rate constant at 900°C.

X molecules (gray spheres) are converted to Y molecules (red spheres) in the first-order reaction, X → Y.

Determine the number of X and Y molecules present at t = 60 s and t = 90 s given that the images below are at t = 0 and t = 30 s.

The first-order reaction of A molecules (gray spheres) occurs in three vessels, 1, 2, and 3, of equal volume.

If the volume of each vessel is increased by a factor of 2, what will happen to the rates and half-lives of the reaction?

Methane and propylene are produced when butane undergoes gas-phase thermal decomposition.

C₄H₁₀(g) → C₃H₆(g) + CH₄(g)

Butane is introduced into a furnace at a pressure of 30 torr. How many seconds are required for the pressure of CH₄ to reach 6.5 torr? The half-life for this reaction is 3.0×10³ s. Assume a first-order reaction.

Determine the relative half-lives of the decomposition of X molecules (green spheres) in three vessels, A, B, and C, of equal volume. Assume a first-order reaction.

When A reacts with itself, product B is formed. If the initial concentration of A is 0.0500 M, determine the half-life of the reaction. How long does it take for the concentration of A to drop from 0.0250 M to 0.0125 M? Assume the rate constant is 8.00×10⁻² M⁻¹•s⁻¹.

The first-order rate constant for the radioactive decay of Berkelium-248 (²⁴⁸Bk) and Seaborgium-260 (²⁶⁰Sg) is 0.0292 h⁻¹ and 0.173 ms⁻¹, respectively. Which sample decays at a faster rate?

Two reactions were observed. The first reaction has a half-life that is twice as long as the last one. The second reaction has a half-life that is not affected by the concentration of the reactant and is constant over time. Identify the order of the rate law for each reaction based on the observations.

Using spectroscopy, a first-order reaction was observed at 380 nm. The reaction was allowed to occur in a 1.00 cm sample cell. The only colored species in the reaction at the specified wavelength had a 4.73x10³ M^-1 cm^-1 extinction coefficient and 3.89x10^-4 s^-1 decay rate. Based on this, what is the half-life of the reaction?

The rate constant for the radioactive decay of Berkelium-248 (²⁴⁸Bk) and Seaborgium-260 (²⁶⁰Sg) is 0.0292 h^-1 and 0.173 ms^-1, respectively. How much of a 1.25-mg sample of each isotope remains after four half-lives?

The gas-phase reaction of a solution created by dissolving 0.045 mol of C in a total volume of 250 mL was observed. 

C (g) → D (g)

What is the half-life for the reaction?

The hypothetical gas-phase isomerization of AB → BA at 425 °C was observed.

What are its rate constant and half-life if the reaction is first-order?

The components of a reaction after 0 mins and 20 mins are shown below. 

After 7 half-life periods, what fraction of reactant is still present if the reaction is first-order?

The decomposition of NH₃ over hot tungsten is a zero-order reaction. The rate constant of the reaction at a certain temperature is 1.31×10^–6 mol/L•s. Initially, the amount NH₃ is 0.00475 M. Calculate the time when the concentration of NH₃ is half of its original amount.

Americium-243 has a half-life of over 7500 years and decays in first-order kinetics. Calculate the time it will take for one mole of Am-243 to decay until only 25 atoms remain.

An archeologist wants to determine the age of a shell using carbon dating. Carbon-14 decays with first-order kinetics and has a half-life of 5730 years. A fossilized shell contains 26.3% of the C-14 found in a living shell. Determine the age of the shell.

Consider the hypothetical decomposition reaction: AB → A + B. The following data were collected at 423.15 K:

t (s)           [AB] (M)
0.0           2.500
20.0         2.099
40.0         1.762
60.0         1.479
80.0         1.241
100.0        1.042

Calculate the half-life of the reaction at the initial concentration.

A reaction of a hypothetical compound AB occurs in second-order kinetics. At a certain temperature, the reaction has a rate constant of 3.54×10^–3 M^–1•s^–1. Determine the half-life of the reaction when the initial concentration of 0.250 M.

The half-life of Plutonium-239 is independent of the initial concentration and has a value of 24110 years. Assuming you start with 100% of Pu-239, calculate the time it will take for 38% of a Pu-239 sample to decay.

The hydrolysis of the anticancer drug cisplatin occurs in first-order kinetics with a rate constant of 5.33 × 10⁻³ min⁻¹ at 310.15 K. Determine the half-life of the reaction.

The hydrolysis of the anticancer drug cisplatin occurs in first-order kinetics with a rate constant of 5.33 × 10⁻³ min⁻¹ at 310.15 K. Assuming we start with 100% cisplatin, determine the time it will take for 35.0% of cisplatin to react? How about 50.0% of the cisplatin?

Tritium (³H) has a half-life of 12.32 years which is independent of the initial concentration. Calculate the number of millimoles present in a sample after 26.45 years if the sample initially contains 6.4 mmol of ³H.

The synthetic isotope ¹⁸⁵W has a half-life of 75.1 days that does not depend on the initial concentration. A sample of ¹⁸⁵W contains 1.38 × 10¹⁹ atoms. Calculate the number of ¹⁸⁵W atoms present after 3 years.

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 19.5% of the C-14 found in living organisms. How old is the bone?

The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 18% of the U-238 atoms in a sample of U-238 to decay?