Sure! Let's break down the problem step-by-step to understand the correct answer.
The equation [tex]\( C_1 V_1 = C_2 V_2 \)[/tex] is actually a very common equation used in chemistry, specifically for situations involving solutions. It is used to understand how the concentration of a solution changes when it is diluted, or to find out how much of a concentrated solution is needed to achieve a certain concentration.
Here’s a detailed explanation of each component of the equation:
- [tex]\( C_1 \)[/tex]: This represents the initial concentration of the solution before dilution.
- [tex]\( V_1 \)[/tex]: This is the initial volume of the solution before dilution.
- [tex]\( C_2 \)[/tex]: This denotes the final concentration of the solution after dilution.
- [tex]\( V_2 \)[/tex]: This stands for the final volume of the solution after dilution.
When we mix or dilute a solution, the quantity of solute that was present initially is spread out into a new total volume. The equation [tex]\( C_1 V_1 = C_2 V_2 \)[/tex] states that the product of the initial concentration and volume is equal to the product of the final concentration and volume.
Here is how this equation works in practice:
1. To Find Initial or Final Concentration: Suppose you know the volumes and need to find out the concentration after dilution (or vice-versa):
[tex]\[
C_2 = \frac{C_1 V_1}{V_2}
\][/tex]
or
[tex]\[
C_1 = \frac{C_2 V_2}{V_1}
\][/tex]
2. To Find Initial or Final Volume: If you need to find out the volume required to achieve a particular concentration:
[tex]\[
V_2 = \frac{C_1 V_1}{C_2}
\][/tex]
or
[tex]\[
V_1 = \frac{C_2 V_2}{C_1}
\][/tex]
From these interpretations, it is clear that the equation [tex]\( C_1 V_1 = C_2 V_2 \)[/tex] is specifically used to relate the concentration and volume of a solution before and after dilution.
Therefore, the correct answer to the question is:
The equation [tex]\( C_1 V_1 = C_2 V_2 \)[/tex] is used to relate concentration and volume before/after dilution.
