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1 month ago

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

Chemistry

1 answer:

VMariaS [2.8K]1 month ago

6 0

Answer:

8,000 years.

Clarification:

Radioactive isotopes are known to decay following first-order kinetics.

The half-life is defined as the duration required for a reactant's concentration to halve.

When a reactant starts with an initial concentration of [A₀], at the half-life it will reach a concentration of ([A₀]/2).

Furthermore, for first-order decay, the half-life does not depend on the starting concentration.

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

The half-life of this element equals 1,600 years.

This means the reactant reduces from 56.0 g to its half (28.0 g) in 1,600 years.

Thus, the half-life for this sample is 1,600 years.

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

Using the equations for first-order reactions:

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

Where k is the reaction's rate constant.

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

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

Utilizing the integral formula for first-order reaction:

kt = ln([A₀]/[A]),

with k being the reaction's rate constant (k = 4.33 x 10⁻⁴ year⁻¹).

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

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

[A] shows the concentration left after decay ([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 years.

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22 days ago

What types of compounds are CaCl2, Cu, C2H6, respectively.

KiRa [2853]

Response:

Ionic, metal, organic

Clarification:

For this scenario, we should examine each compound:

-) $CaCl_2$

In this compound, there is a non-metal atom (Cl) paired with a metal atom (Ca). This leads to a significant difference in electronegativity, indicating that an ionic bond will form. Ions can be generated:

$CaCl_2~->~Ca^+^2~+~2Cl^-$

The positive ion would be $Ca^+^2$ while the negative ion is $Cl^-$ . Thus, we have an ionic compound.

-) $Cu$

Here, we are looking at a single atom. Consulting the periodic table shows that this atom belongs to the transition metals section (central part of the periodic table). Hence, Cu (Copper) is identified as a metal.

-) $C_2H_6$

Within this molecule, carbon and hydrogen are linked by single bonds. The difference in electronegativity between C and H is insufficient to lead to ion formation. Therefore, we have covalent bonds. This property is typical of organic compounds. (Refer to figure 1)