Chemistry, 04.10.2019 23:00 natalieburnett82

The table shows the amount of radioactive element remaining in a sample over a period of time.

radioactive decay rate

amount of radioactive sample

(grams) time

(years)

56.0 0

47.1 400

39.6 800

33.3 1,200

28 1,600

part 1: what is the half-life of the element? explain how you determined this.

part 2: how long would it take 312 g of the sample to decay to 9.75 grams? show your work or explain your answer.

Answers: 1

Show answers

Answers

Answer from: xxhighwolfxx7508

8,000 year.

Explanation:

It is known that the decay of a radioactive isotope isotope obeys first order kinetics.Half-life time is the time needed for the reactants to be in its half concentration.If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).Also, it is clear that in first order decay the half-life time is independent of the initial concentration.

Part 1: What is the half-life of the element? Explain how you determined this.

The half-life of the element is 1,600 years.

Half-life time is the time needed for the reactants to be in its half concentration.

The sample stats with 56.0 g and reaches its half concentration (28.0 g) after 1,600 years.

So, the half-life of the sample is 1,600 years.

Part 2: How long would it take 312 g of the sample to decay to 9.75 grams? Show your work or explain your answer.

For, first order reactions:

k = ln(2)/(t1/2) = 0.693/(t1/2).

Where, k is the rate constant of the reaction.

t1/2 is the half-life of the reaction.

∴ k =0.693/(t1/2) = 0.693/(1,600 years) = 4.33 x 10⁻⁴ year⁻¹.

Also, we have the integral law of first order reaction:

kt = ln([A₀]/[A]),

where, k is the rate constant of the reaction (k = 4.33 x 10⁻⁴ year⁻¹).

t is the time of the reaction (t = ??? year).

[A₀] is the initial concentration of the sample ([A₀] = 312.0 g).

[A] is the remaining concentration of the sample ([A] = 9.75 g).

∴ t = (1/k) ln([A₀]/[A]) = (1/4.33 x 10⁻⁴ year⁻¹) ln(312.0 g/9.75 g) = 8,000 year.

Answer from: whiteshawn02

Half life of the sample= 1600 years

Part 2: 8000 years

Explanation:

The half life of a radioactive substance is the time taken for the substance to decay to half its initial amount.

Since 56.0g of radioactive material was present at t= 0 years. Half of 56.0g is 28.0g hence the time taken to have 28.0g of the sample left is the half life of the material.

If the original sample contained 312g of radioactive material

First half life. 156g left

Second half life. 78 g left

Third half life. 39gleft

Fourth half life. 19.5 g left

Fifth half life. 9.75 g

If each half life takes 1600 years then five half life will take 5×1600= 8000 years

Answer from: Quest

i believe the answer is a.

An object is transported from the earth to the moon which statement is true about the object

Answer from: Quest

29.1-12=17.1the answer is this one

Another question on Chemistry

Chemistry, 22.06.2019 07:10

Provide a stepwise curved arrow mechanism that fully explains the outcome of the reaction shown below. oh нао* heat он

Answers: 2

Answer

Chemistry, 22.06.2019 16:00

Which of the following is the correct definition of chemical energy? a. energy an object has because of its motion or position b. energy resulting from the flow of charged particles, such as electrons or ions c. energy produced from the splitting of atoms d. energy stored in chemical bonds of molecules

Answers: 1

Answer

Chemistry, 22.06.2019 16:10

Given the following equation: 2a1 + 3mgcl2 --> 2alcl3 + 3mg how many moles of aluminum chloride are produced from 2.5 moles of magnesium chloride?

Answers: 1

Answer

Chemistry, 22.06.2019 22:30

Which of the following is true about the speed of light? it depends on the wavelength.

Answers: 3

Answer

You know the right answer?

The table shows the amount of radioactive element remaining in a sample over a period of time.
...