Question

You started off with 12 L of a 3.0 M solution. You diluted it so that now, you have 20 L instead. What is the new molarity?

Answer 1

Answer:

1.8 M

Explanation:

When diluting, the starting molarity multiplied by the starting volume should equal the final molarity multiplied by the final volume.

$\[\boxed{ \begin{minipage}{0.9\textwidth} \[ \textbf{Dilution Formula: }M_1 V_1 = M_2 V_2 \] Where: \begin{itemize} \item \( M_1 \) = initial molarity \item \( V_1 \) = initial volume \item \( M_2 \) = final molarity \item \( V_2 \) = final volume \end{itemize} \end{minipage}}\]$

In this problem:

$M_1 = 3.0~M,~ V_1 = 12~L \\\\M_2 = ~\textbf{?}, V_2 = 20~L$

As you can see, we are solving for the final molarity and all other information is given.

Solving:

$M_1V_1 = M_2V_2 ~ \text{(plug in values from above)}$

$(3.0M)(12L) = (M_2)(20L)$

$M_2 = \frac{(3.0M)(12L)}{(20L)}$

$\therefore\boxed{M_2 = 1.8M}$