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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?

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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?

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  • $\begingroup$ I once learned that "%" denotes mass-percentage. volume-percentages were indicated as "Vol%". Is that not true anymore? $\endgroup$ – Arsak Nov 5 '18 at 15:18

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