Balance the chemical equation: Al(OH)3 + H3PO4 -> AlPO4 + H2O. What is the branch of chemistry for analyzing substances?

There is 1 Al atom on the left in $\text{Al(OH)}_3$ and 1 Al atom on the right in $\text{AlPO}_4$. Aluminum is balanced.

There is 1 P atom on the left in $\text{H}_3\text{PO}_4$ and 1 P atom on the right in $\text{AlPO}_4$. Phosphorus is balanced.

On the left, there are 3 H atoms in $\text{Al(OH)}_3$ and 3 H atoms in $\text{H}_3\text{PO}_4$, totaling $3 + 3 = 6$ H atoms.
On the right, there are 2 H atoms in $\text{H}_2\text{O}$. To balance the 6 H atoms on the left, we need 3 molecules of $\text{H}_2\text{O}$ on the right ($3 \times 2 = 6$).

On the left, there are 3 O atoms in $\text{Al(OH)}_3$ and 4 O atoms in $\text{H}_3\text{PO}_4$, totaling $3 + 4 = 7$ O atoms.
On the right, there are 4 O atoms in $\text{AlPO}_4$ and $3 \times 1 = 3$ O atoms in $3\text{H}_2\text{O}$, totaling $4 + 3 = 7$ O atoms.
Oxygen is balanced.

The balanced equation is:

a)
The specific branch of Chemistry that deals with identifying the components and purity of substances, such as medicines, is Analytical Chemistry.

b)
The systematic nature of Chemistry provides standardized analytical techniques (e.g., chromatography, spectroscopy) to determine the exact chemical composition and purity of the medicine. By comparing the results from the suspected medicine to the known chemical profile of genuine Amoxicillin, the investigator can objectively identify the presence of impurities like chalk and the absence of the active drug. This reproducible and verifiable evidence can then be presented in court to prove the medicine is counterfeit.

a)

• Prescription: This is the official instruction from a healthcare professional detailing the specific medicine, its strength, and the exact amount to be taken per dose (e.g., $5\text{ml}$) along with frequency and duration.
• Dosage: This refers to the actual quantity of medicine administered to the patient at one time. In this scenario, the prescription indicated a dosage of $5\text{ml}$, but the patient misread the label and took a triple dose, resulting in an actual dosage of $15\text{ml}$. The error was in the patient taking an incorrect dosage, deviating from the prescribed amount.