<u>Answer:</u> The half life of the given radioactive isotope is 43.86 minutes
<u>Explanation:</u>
Rate law expression for first order kinetics is given by the equation:
![k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2.303%7D%7Bt%7D%5Clog%5Cfrac%7B%5BA_o%5D%7D%7B%5BA%5D%7D)
where,
k = rate constant = ?
t = time taken for decay process = 233 minutes
= initial amount of the reactant = 0.500 M
[A] = amount left after decay process = 0.0125 M
Putting values in above equation, we get:

The equation used to calculate half life for first order kinetics:

where,
= half-life of the reaction = ?
k = rate constant = 
Putting values in above equation, we get:

Hence, the half life of the given radioactive isotope is 43.86 minutes
Answer : when a beaker of acid is titrated with a basic solution, the acid becomes neutralized.
Explanation :
The reaction in which an acid reacts with a base forming a salt and water is known as neutralization reaction.
During neutralization reaction, acid and base neutralize each other.
That means they both lose their properties and completely new substances are formed which have different properties
For example, a reaction of acid HCl with base NaOH produces water and salt, NaCl.

Therefore we can say that, when a beaker of acid is titrated with a basic solution, the acid is neutralized.
D. Catalysts get used up in the formation of the product.
Catalysts are never used up in a reaction.
Warm air is lighter than cold air so hot air will rise as cold air sinks