Question

A 3.25 liter flask contains a 9.0 molar solution. What will be the final volume if the molarity is cut in half?

Answer 1

To find the final volume when the molarity is cut in half, we start with the initial conditions.

We have:
- Initial volume (V1) = 3.25 liters
- Initial molarity (M1) = 9.0 M

The number of moles of solute (n) can be calculated using the formula:

\[
n = M \times V
\]

Substituting the values we have:

\[
n = 9.0 \, \text{M} \times 3.25 \, \text{L} = 29.25 \, \text{moles}
\]

Now, if the molarity is cut in half, the new molarity (M2) will be:

\[
M2 = \frac{M1}{2} = \frac{9.0 \, \text{M}}{2} = 4.5 \, \text{M}
\]

Next, we want to find the final volume (V2) such that the number of moles of solute remains the same (29.25 moles) but the new molarity is 4.5 M. We can use the formula again:

\[
n = M2 \times V2
\]

Setting this equal to the moles we calculated:

\[
29.25 \, \text{moles} = 4.5 \, \text{M} \times V2
\]

Now we solve for \( V2 \):

\[
V2 = \frac{29.25 \, \text{moles}}{4.5 \, \text{M}} \approx 6.5 \, \text{liters}
\]

Therefore, the final volume when the molarity is cut in half will be approximately **6.5 liters**.