25 mL of a #"10% m/v"# #NH_4Cl# solution is diluted to 250 mL. What is the final concentration of the #NH_4Cl#?

Question

Caleb Adams · Accepted Answer

#"1% m/v"#

Actually, if you know exactly what it means to dilute a solution, you can solve this problem without using any formulas.

The fundamental idea of a dilution is that the mass of the solute, or the number of moles of solute, stays constant.

After a dilution, the concentration of the original solution drops because adding more solvent increases the volume of the solution.

Now, your original solution is #"10% m/v"# ammonium chloride. This essentially means that you get #"10 g"# of ammonium chloride per #"100 mL"# of solution.

In other words, you get one part solute for every #"10 mL"# of solution.

You will see that the volume of this solution after diluting it is ten times greater than the original volume.

Since the mass of solute remained constant, you can say that the diluted solution contains one part solute for every #"100 mL"# of solution.

This means that the concentration of the solution decreased by a factor of #10#. As a result, the new concentration will be

#"% m/v" = 1/10 * "10%" = color(green)(|bar(ul(color(white)(a/a)1%color(white)(a/a)|)))#

The dilution factor is the ratio that exists between the solution's final volume and its initial volume.

#color(blue)(|bar(ul(color(white)(a/a)"D.F." = V_"final"/V_"initial"color(white)(a/a)|)))#

As you can see, by merely comparing the two volumes, you can determine the concentration of the diluted solution thanks to the dilution factor.

Axel Alvarado · Answer

undefined To find the final concentration of NH₄Cl after dilution, we can use the formula for dilution:

C1V1 = C2V2

Where:
C1 = initial concentration
V1 = initial volume
C2 = final concentration
V2 = final volume

Given:
Initial concentration (C1) = 10% m/v = 10 g/100 mL = 0.10 g/mL
Initial volume (V1) = 25 mL
Final volume (V2) = 250 mL

Substituting into the dilution formula:

(0.10 g/mL)(25 mL) = C2(250 mL)

Solving for C2:

C2 = (0.10 g/mL * 25 mL) / 250 mL
C2 = 0.01 g/mL

Therefore, the final concentration of NH₄Cl after dilution is 0.01 g/mL or 1% m/v.