Dilution terminology

For thing like 8× dilution, that would be like 1 ml of a solution and then 7 ml of something like water to dilute right? Would 50 ml solution and 50 ml water be a 2× dilution? I’m a bit unsure about the terminology. If I an OD of 0.123 from a sample diluted 5×, would multiply 0.123 by 5 to get the real OD?




You are right. The × in 8× refers to the fold-change in concentration between the concentrated source and diluted solution.


$$\mathrm{DF = \frac{C\_{stock}}{C\_{working}}}$$ where $\mathrm{C\_{stock}}$ and $\mathrm{C\_{working}}$ are the concentrations of a stock solution and the desired final concentration, respectively.


The concentration of the working solution can be expanded:


$$\mathrm{C\_{working} = \frac{C\_{stock} V\_{stock}}{V\_{working}} = \frac{C\_{stock} V\_{stock}}{V\_{stock}+V\_{diluent}}}$$ where $\mathrm{V\_{stock}}$ is the volume of the stock solution and $\mathrm{V\_{diluent}}$ is the volume of diluent (e.g. pure water) added.


Plugging back into the DF equation:


$$\mathrm{DF = \frac{C\_{stock}}{\frac{C\_{stock} V\_{stock}}{V\_{stock}+V\_{diluent}}} = \frac{V\_{stock}+V\_{diluent}}{V\_{stock}}}$$


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