It would take 147 hours for 320 g of the sample to decay to 2.5 grams from the information provided.
Radioactivity refers to the decay of a nucleus leading to the spontaneous emission of radiation. The half life of a radioactive nucleus refers to the time required for the nucleus to decay to half of its initial amount.
Looking at the table, we can see that the initial mass of radioactive material present is 186 grams, within 21 hours, the radioactive substance decayed to half of its initial mass (93 g). Hence, the half life is 21 hours.
Using the formula;
k = 0.693/t1/2
k = 0.693/21 hours = 0.033 hr-1
Using;
N=Noe^-kt
N = mass of radioactive sample at time t
No = mass of radioactive sample initially present
k = decay constant
t = time taken
Substituting values;
2.5/320= e^- 0.033 t
0.0078 = e^- 0.033 t
ln (0.0078) = 0.033 t
t = ln (0.0078)/-0.033
t = 147 hours
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Answer: The increase in solubility or the rate of dissolving process of a gaseous solute in a liquid solvent is due to following:
- Increasing agitation
- Increasing temperature
- Increasing solute's partial pressure over the solvent
- Increasing solute's surface area
Explanation:
When agitation is increased then there will occur an increase in kinetic energy of the molecules of a substance. As a result, more number of collisions will take place due to which more amount of solute will dissolve into the solvent.
Similarly, increasing the temperature will further increase the kinetic energy of molecules. Hence, this will lead to more solubility of gaseous solute into the liquid solvent.
As solubility of a gas is directly proportional to the pressure of the gas above surface of the solution. So, an increase in solute's partial pressure over solvent will also lead to an increase in solubility of gaseous solute into liquid solvent.
When surface area of solute is increased then there will be more solute particles available for reaction. Hence, more collisions will take place. As a result, rate of reaction is more due to which there will be an increase in solubility.
Thus, we can conclude that the increase in solubility or the rate of dissolving process of a gaseous solute in a liquid solvent is due to following:
- Increasing agitation
- Increasing temperature
- Increasing solute's partial pressure over the solvent
- Increasing solute's surface area
