# Diluting topical cream (10%)

I need to dilute a face cream with 10 % active ingredient to 2.5 % and 5 % but I am confused as to how. I looked into the $$c_1V_1=c_2V_2$$ and $$\text{concentration of a solution}=(\text{amount of solute}/\text{amount of solvent})\times100$$ but not sure which would work.

Would I have to make a standard solution first and place 10 g of the cream into 100 ml of water?

To practically dilute this cream from $$10\ \%$$ to $$5\ \%$$, you would need to dilute it to a by a factor of $$2$$. You can see this by assuming an initial volume for your cream, in this case, $$100\ \mathrm{ml}$$,
and plugging into the $$c_1V_1=c_2V_2$$ equation. In this case that means $$c_1:=10~\%~~~~~\\V_1:=100~\text{mL}\\c_2:=5~\%~~~~~~~$$ Solving for $$V_2$$ renders $$~~~~~~~~\frac{c_1V_1}{c_2}=V_2$$ $$\frac{10\ \% \cdot 100~\text{mL}}{5\ \%}=V_2~~~~~~~~~~$$ $$\frac{10\ \% \cdot 100~\text{mL}}{5\ \%}=200~\text{mL}$$ Which means that the volume needed in the final solution needs to be $$200~\text{mL}$$. It is however, important to note that this does not mean that you need to add $$200~\text{mL}$$, but rather you need to add $$100~\text{mL}$$ of solvent to your $$100~\text{mL}$$ of cream for a final solution volume of $$200~\text{mL}$$.

Further you may calculate the dilution factor that this correlates to by using the equation

$$DF=\frac{V_\text{final}}{V_\text{initial}}$$

In this case $$V_\text{final}=V_2$$ and $$V_\text{initial}=V_1$$, so plugging into this equation renders

$$DF=\frac{200~\text{mL}}{100~\text{mL}}=2$$

You may apply these same equations to making a cream at $$2.5~\%$$ active ingrediant concentration and should find that if you start with the $$100~\text{mL}$$ of the $$10~\%$$ stock, you would need to dilute to a final volume of $$400~\text{mL}$$, which correlates to a dilution factor of $$4$$. If you start with $$100~\text{mL}$$ of the $$5~\%$$ solution you just made, you would need to dilute to a final volume of $$200~\text{mL}$$, which correlates to a dilution factor of $$2$$.

If you want to do this practically, then water may not be the best solvent – to continue to be able to use this as a cream, you may consider using a cream without any active ingrediant in it as your solvent – maybe something like a hand cream?

• I once learned that "%" denotes mass-percentage. volume-percentages were indicated as "Vol%". Is that not true anymore? Nov 5, 2018 at 15:18