Learn about Half-life and Theoretical Yield

Chemistry is a diverse field of Science that includes a variety of practices, including compositions of elements, properties, reactions, and their subsequent products. For someone who is either naive or well-versed in chemistry, it is necessary to seek the insight of the element’s composition and their attributes.                  

It is obvious from its definition that while doing chemistry, one must have to go through all the aspects mentioned above. So, here we are learning one of many prominent properties of chemical elements of Half-life [t (1/2)].

What exactly Half-life is?

Half-life is actually the time required for a radioactive element in which it loses half of its initial value. Formally, it is half of an isotope’s decay time. Isotopes are such radioactive elements that undergo nuclear fission or fusion reactions. Once in their lifespan, they react at least once and emit radioactive waves into their surroundings. This is when their journey of radioactivity starts and the phenomenon of Half-life acts upon them as well. 

‘Half-life (t1/2) of a radioactive substance is the time or interval required for a quantity of material to decay to its original value’

The term describes how quickly unstable atoms undergo, or how long stable atoms survive decay. The term is commonly used in nuclear physics, but as all the radioactive isotopes also fall in the periodic table of chemistry.

Each atom has a different half-life, from millions of years to fractions of seconds, atoms decay and lost radioactive radiation.

The formula of Half-life:

A Half-life period for the disintegration of a radioactive substance is independent of the amount of that substance.

The rules or the values applicable to the half-life period of the first-order reaction are not the same as in the case of a second-order reaction. The half-life period is inversely proportional to the initial concentration of the reactant. It is not so difficult to calculate half life with online tools. For the third-order reaction, the half-life is inversely proportional to the square of the initial concentration of the reaction 

(t1/2)1 ~ 1/a, since (t1/2)1 = 0.693/ka

(t1/2)2 ~ 1/a1, since (t1/2)2 = 1/ka

(t1/2)3 ~ 1/a2, since (t1/2)3 = 1.5/ka2

Where (t1/2), (t1/2) and (t1/2), are the half-life periods for 1st, 2nd and 3rd order reactions respectively and ‘a’ is the initial concentration of reactants.

In general for the reaction of nth order:

(t1/2)n ~ 1/an-1

Radioactivity decay:

Radioactivity decay is the time interval of any isotope during which it stopped its radioactive emission. 

The quantity of the radioactive falls to half of its initial value in one full half-life. Let’s conclude it with some dose of half-lives in our basic lives, for example, the biological half-life of water in a human being is about 9 to 10 days, though this can be altered by behavior and other environmental conditions. The biological half-life of cesium in human beings is between one and four months.

Theoretical yield

While doing Chemistry, we have encountered many chemical reactions, reactants, products, equations, and a variety of calculations to obtain or to achieve the desired products (reaction) as final results. As far now, we are going to discuss one of many common but basic calculations of chemistry, i.e., Theoretical Yield.

You can calculate chemical equations by using chemical equation balancer free online.

 Learn about Theoretical yield:                              

 Theoretical Yield is actually the quantity of a product obtained from a complete chemical reaction, or you can say, it is the amount of product that results from a theoretical experiment which can't be obtained by the reaction performed at the laboratory as it is a written form of hypothetical calculations which includes the number of reactants participating in the particular chemical reaction to give a certain amount of products. 

Theoretical yield = actual yield/percent yield x 100%

Theoretical yield calculation

To calculate the theoretical yield of any reaction, you must know the reaction. Let’s look at the following reaction where at heating potassium chlorate (KClO3), it produces oxygen gas (O2).

2 KClO3 (s) → 3 O2 (g) + 2 KCl (s)

The balanced reaction shows that 2 moles of KClO3 will produce 3 moles of O2 and 2 moles of KCl. To calculate the theoretical yield, use these ratios as a conversion factor.  Here is a typical example problem.

Step 1. We need to know the amount of KClO3 in moles to use the conversion, so the first step is to convert grams KClO3 to moles KClO3. To make it easier, know the molecular mass of KClO3 is 122.55 g/mol.

6 = x moles KClO3

Step 2: Use the chemical equation to relate moles KClO3 to moles O2.

x moles O2 = 3 x 3 moles O2
x moles O2 = 9 moles O2

6 moles of KClO3 (735.3 grams of KClO3) will produce 9 moles of O2 gas.