# Question 16d0c

May 20, 2015

You need 76 mL of your stock silver acetate solution.

The key to doing dilution calculations is to realize that the number of moles of solute, in your case silver acetate, remains unchanged following a dilution.

Diluting a solution decreases its molarity because you're essentially increasing the volume of the solution while keeping the number of moles of solute constant.

{: ("Same number of moles of solute"), ("bigger volume") :}} $\implies \text{smaller molarity}$

This means that you can work backwards from the target solution to determine what volume of the stock solution you need.

Use the molarity and volume of the target solution to determine how many moles of silver acetate are present

$C = \frac{n}{V} \implies n = C \cdot V$

${n}_{\text{silver acetate" = "0.61 M" * 250 * 10^(-3)"L" = "0.1525 moles}}$

This means that you need the stock solution to contain 0.1525 moles of silver acetate, so you can determine its volume by

$C = \frac{n}{V} \implies V = \frac{n}{C}$

${V}_{\text{stock" = (0.1525 cancel("moles"))/(2.0cancel("moles")/"L") = "0.07625 L}}$

Expressed in mL and rounded to two sig figs, the answer will be

V_"stock" = color(green)("76 mL")

This is what the formula used for dilution calculations is all about. Here's how you'd solve using that approach

${C}_{1} {V}_{1} = {C}_{2} {V}_{2}$, where

${C}_{1}$, ${V}_{1}$ - the molarity and volume of the stock solution;
${C}_{2}$, ${V}_{2}$ - the molarity and volume of the target solution.

Solve for ${V}_{1}$ by plugging your values into the equation

V_1 = C_2/C_1 * V_2 = (0.61cancel("M"))/(2.0cancel("M")) * "250 mL" = "76 mL"# $\to$ rounded to two sig figs.