Updated April 26, 2018
By Claire Gillespie
Dilution is a common lab technique that most science students encounter when they want to achieve a specific concentration of a solution. But it is also what you do when you add water to your food and drinks at home to make them more to your liking. Dilution affects many properties of a solution, including its pH level.
Dilution makes an acidic solution more alkaline and an alkaline solution more acidic. To work out the pH effect of dilution, you determine the concentration of hydrogen ions and convert it to pH using a simple working formula.
To dilute an aqueous solution, you simply add water to it. This increases the proportion of the solvent or the liquid material for dilution compared to that of the solute or the component dissolved in the solvent. For example, if you dilute saltwater, the solution will contain the same amount of salt, but the amount of water will increase.
The pH scale measures how acidic or alkaline a substance is. It runs from 0 to 14, with a pH of 7 being neutral, a pH lower than 7 being acidic and a pH higher than 7 being alkaline. The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. For example, pH 3 is ten times more acidic than pH 4 and 100 times more acidic than pH 5.
The same is true for pH values above 7. Each value is ten times more alkaline than the next lower whole value. For example, pH 9 is ten times more alkaline than pH 8 and 100 times more alkaline than pH 7. Pure or distilled water has a pH of 7, but when you add chemicals to water, the solution can become either acidic or alkaline. The pH level of a solution is a measure of its hydrogen ion concentration. Solutions with a high concentration of hydrogen ions have a low pH, and solutions with a low concentrations of H+ ions have a high pH.
Acidic substances include black coffee, battery acid and lemon juice. Diluting an acid decreases the concentration of H+(aq) ions, which increases the pH level of the solution towards 7, making it less acidic. However, the pH level of an acidic solution cannot become greater than 7, because the water you add to dilute it is not alkaline.
Alkaline substances include ammonia, baking powder and bleach. Diluting an alkali decreases the concentration of OH-(aq) ions, which decreases the pH level of the solution towards 7, making it less alkaline. However, the pH level of an alkaline solution cannot become lower than 7, because the water you add to dilute it is not acidic.
The pH level of a solution is a measure of its hydrogen ion concentration. Solutions with a high concentration of hydrogen ions have a low pH, and solutions with a low concentrations of H+ ions have a high pH. A simple working definition of pH is pH = - log[H+], where [H+] is the hydrogen ion molarity. A logarithm of a number is simply the exponent when you write that number as a power of ten. The definition of pH solved for hydrogen ion molarity is then [H+] = 10-pH. For example, the molarity of hydrogen ions in a pH 6 solution is 10-6 M. Use this calculation to estimate the hydrogen ion concentration before dilution.
After dilution, measure the solution's new volume. For example, if you dilute the solution to four times its original volume, the concentration will be reduce to one quarter. If the original volume is V1, and the total volume after dilution is V4, the final concentration will be V1/V4 times the original concentration. You can then convert the hydrogen ion concentration back to pH using pH = - log[H+].
Since the amount of substance stays equal, you can calculate the volume of your final solution $V_\mathrm{end}$, form your start concentration $c_\mathrm{start}(\ce{OH-})$ and your initial volume $V_\mathrm{start}$ and your target concentration $c_\mathrm{end}(\ce{OH-})$. Your working equation should be:
\begin{align} c_\mathrm{start}(\ce{OH-})\cdot V_\mathrm{start} &= c_\mathrm{end}(\ce{OH-})\cdot V_\mathrm{end} \\ V_\mathrm{end} &= \frac{c_\mathrm{start}(\ce{OH-})}{c_\mathrm{end}(\ce{OH-})}\cdot V_\mathrm{start} \end{align}
You can work out the start concentration for the initial pH and the target concentration from your final pH. Given (at $T=298.15~\mathrm{K}$, $p=1~\mathrm{atm}$):
\begin{align} \ce{pH}_\mathrm{start} &= 13 \\ c_\mathrm{start}(\ce{OH-}) &= 10^{-(14-\ce{pH})}~\mathrm{mol/L} = 0.1~\mathrm{mol/L} \\ V_\mathrm{start} &= 0.1~\mathrm{L} \\ \ce{pH}_\mathrm{end} &=11 \\ c_\mathrm{end}(\ce{OH-}) &=10^{-(14-\ce{pH})}~\mathrm{mol/L} = 0.001~\mathrm{mol/L} \end{align}
Hence
$$ V_\mathrm{end}= \frac{c_\mathrm{start}(\ce{OH-})}{c_\mathrm{end}(\ce{OH-})}\cdot V_\mathrm{start} = 10~\mathrm{L} $$
and therefore
$$ \Delta V = V_\mathrm{end}-V_\mathrm{start} = 9.9~\mathrm{L}= 9900~\mathrm{mL}. $$
Katherine B.
asked • 04/07/17
It's for a Biology project- I need to have different pH of solutions, with my base point being water with a pH of 7, and then increments down to a pH of 3. I don't know how much HCl to add for each increment (increments of pH of 3, 4, 5, 6, 7)
1 Expert Answer
To get a pH of 3, the [H+] needs to be 10^-3 M. For pH 4, it needs to be 10^-4 M, etc. So, since you are starting with 1 M HCl = 1 M [H+], you can make simple dilutions from that. Of course, the amount of HCl you use will depend on what final volume you desire. Let's assume you want to make 100 mls of pH 3, 4, 5, and 6. For pH 3: (x ml)(1 M) = (100 ml)(1x10^-3 M) x = 0.1 ml. So take 0.1 ml of 1 M HCl and dilute to a final volume of 100 mls For pH 4: (x ml)(1 M) = (100 ml)(1x10^-4 m) x = 0.01 ml. So take 0.01 ml (10 ul) and dilute to a final volume of 100 mls same calculation and x = 0.001 mls. This is too small to really measure, so you can take some of the previously made pH 4 solution and dilute that 1:10. Take 10 mls of pH4 solution and dilute to a final volume of 100 mls. Take 10 mls of pH 5 solution and dilute to 100 mls final volume NOTE: You can start with making the pH3 and then just keep making 1:10 dilutions from that. In other words, make the pH 3 as described, and then 10 mls diluted to 100 mls gives you pH4. Then dilute that 1:10 to get pH, and dilute that to get pH 6. Water will be your pH 7 (assuming it is pure and actually at pH 7).
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We don’t have your requested question, but here is a suggested video that might help.
A solution of $\mathrm{HCl}$ has a $\mathrm{pH}=5$. If one $\mathrm{mL}$ of it is diluted to 1 litre, what will be the $\mathrm{pH}$ of resulting solution?