Question

What molarity of sugar water would be made if you diluted 100.0 mL of 7.0 M sugar water solution to a total volume of 300.0 mL?

Answer 1

To find the molarity of the diluted sugar water solution, you can use the dilution formula:

\[
M_1 V_1 = M_2 V_2
\]

where:
- \(M_1\) is the initial molarity (7.0 M),
- \(V_1\) is the initial volume (100.0 mL),
- \(M_2\) is the molarity after dilution (which we want to find),
- \(V_2\) is the final total volume (300.0 mL).

First, let's convert the volumes from mL to L:
- \(V_1 = 100.0 \, \text{mL} = 0.1000 \, \text{L}\)
- \(V_2 = 300.0 \, \text{mL} = 0.3000 \, \text{L}\)

Now, we can plug in the values into the dilution equation:

\[
7.0 \, \text{M} \times 0.1000 \, \text{L} = M_2 \times 0.3000 \, \text{L}
\]

Calculating the left side:

\[
7.0 \times 0.1000 = 0.700 \, \text{mol}
\]

Now we have:

\[
0.700 \, \text{mol} = M_2 \times 0.3000 \, \text{L}
\]

To find \(M_2\), divide both sides by \(0.3000 \, \text{L}\):

\[
M_2 = \frac{0.700 \, \text{mol}}{0.3000 \, \text{L}} = 2.33 \, \text{M}
\]

Thus, the molarity of the diluted sugar water solution is **2.33 M**.