## How to Prepare 1x TAE Buffer from 50x TAE using C_{1}V_{1} = C_{2}V_{2}

Tris-acetate-EDTA – commonly referred to as **TAE **–** **is a buffer is a conductive solution that is used in gel electrophoresis experiments. It’s typical made in a 50 times concentrated (50x) stock solution that needs to be diluted to 1x before use. Depending on how much volume of this 1x buffer you need, you can easily calculate how to dilute a small volume of your stock using the equation C_{1}V_{1} = C_{2}V_{2}.

TL; DR

- → C1V1 = C2V2 can be used to calculate how to dilute concentrated buffers.

### Use C_{1}V_{1} = C_{2}V_{2} to Calculate Your Dilution

Whenever we want to make a dilution from a concentrated solution, we should consider the equation

- $ \large (C_1 \cdot V_1) = (C_2 \cdot V_2)$

- $ \large (C_1 \cdot V_1) = (C_2 \cdot V_2)$

Where:

- $C_1$ = the concentration of the solution we currently have – or stock solution.
- $V_1$ = the volume of we need to dilute.
- $C_2$ = the concentration of the solution we want to make.
- $V_2$ = the total volume of the diluted solution we want.

This equation tells you that the concentration of our starting solution (C1) multiplied by the volume of our stock solution that we add during the dilution (V1) is each to the concentration of the diluted solution (C2) multiplied by the volume that we choose for the dilution (V2). Since these values are in proportion to each other, we can easily manipulate the equation to calculate how much volume of our stock solution (V1) we need to add to create desired solution.

### Calculate a 50x TAE Dilution using C_{1}V_{1} = C_{2}V_{2}

Let’s try the following example. Say we have a 50x stock solution of TAE buffer and we need to make 2000mL of 1x TAE. How can we make this solution? Let’s use

- $\large (C_1 \cdot V_1) = (C_2 \cdot V_2)$.

**Step 1**: Plug in the numbers and don’t forget units!

- $\large (50x \cdot V_1) = (1x \cdot 2000mL)$
- ✔ Stock Concentration ($C_1$) = 50x TAE.
- ✘ Volume of Stock to Dilute ($V_1$) = ?
- ✔ Final Concentration ($C_2$) = 1x TAE
- ✔ Final Volume ($V_2$) = 2000mL of 1x TAE

- $\large (50x \cdot V_1) = (1x \cdot 2000mL)$

**Step 2**: Solve for $V_1$ by multiplying both sides by $C_1$

- $ \Large \frac {( \bcancel{50x} \cdot \, V_1)} {\bcancel{50x}} = \frac{(1x \,\cdot \, 2000mL)}{50x}$

- $ \Large \frac {( \bcancel{50x} \cdot \, V_1)} {\bcancel{50x}} = \frac{(1x \,\cdot \, 2000mL)}{50x}$
- Simplifies to:
- $ \Large V_1 = \frac{(1x \, \cdot \, 2000mL)}{50x} = \frac{( 2000mL\, \cdot \, \bcancel x)}{50\bcancel x}\frac{(2000mL)}{50} = 40 mL $

- $ \Large V_1 = \frac{(1x \, \cdot \, 2000mL)}{50x} = \frac{( 2000mL\, \cdot \, \bcancel x)}{50\bcancel x}\frac{(2000mL)}{50} = 40 mL $

Note that ‘x’ here is actually a unit of measure meaning ‘times concentrated’ and not meaning ‘x the variable’. Great, so we have $V_1 = 40mL$ but we’re not finished yet. That’s how much volume of 50x TAE that we need to dilute into a total volume of 2000mL. So we take our 40mL of 50x TAE and we mix it into 1960mL of deionized $H_2O$ and violà: we’ve made our 1x TAE buffer.