Certainly! Let's work through the problem step-by-step using the provided equation [tex]\( M_1 V_1 = M_2 V_2 \)[/tex], which relates the molarity (concentration) and volume of two solutions.
Given:
- Molarity of solution 1 ([tex]\(M_1\)[/tex]) = 0.5 M
- Volume of solution 1 ([tex]\(V_1\)[/tex]) = 10 L
- Volume of solution 2 ([tex]\(V_2\)[/tex]) = 20 L
- Molarity of solution 2 ([tex]\(M_2\)[/tex]) is unknown
Step-by-Step Solution:
1. Identify the given values: From the information provided:
- [tex]\(M_1 = 0.5 \text{ M}\)[/tex]
- [tex]\(V_1 = 10 \text{ L}\)[/tex]
- [tex]\(V_2 = 20 \text{ L}\)[/tex]
2. Set up the equation: We have the equation [tex]\( M_1 V_1 = M_2 V_2 \)[/tex].
3. Substitute the known values into the equation:
[tex]\[
0.5 \text{ M} \times 10 \text{ L} = M_2 \times 20 \text{ L}
\][/tex]
4. Solve for [tex]\(M_2\)[/tex]:
[tex]\[
5 \text{ M} \cdot \text{L} = M_2 \times 20 \text{ L}
\][/tex]
To isolate [tex]\(M_2\)[/tex], divide both sides of the equation by 20 L:
[tex]\[
M_2 = \frac{5 \text{ M} \cdot \text{L}}{20 \text{ L}}
\][/tex]
[tex]\[
M_2 = \frac{5}{20} \text{ M}
\][/tex]
[tex]\[
M_2 = 0.25 \text{ M}
\][/tex]
Conclusion:
The molarity of solution 2 ([tex]\(M_2\)[/tex]) is 0.25 M.
Thus, the values are:
- [tex]\(M_1 = 0.5 \text{ M}\)[/tex]
- [tex]\(V_1 = 10 \text{ L}\)[/tex]
- [tex]\(V_2 = 20 \text{ L}\)[/tex]
- [tex]\(M_2 = 0.25 \text{ M}\)[/tex]
This satisfies the equation [tex]\( M_1 V_1 = M_2 V_2 \)[/tex].
