Useful Equations - Lishko Lab at Washington University in St.Louis

Calculating molarity

$\textup{Molarity}=\frac{moles_{solute}}{Volume_{solution}}$

Where volume is in liters

Converting between mass and moles

$\textup{moles}_{X}=\frac{\textup{mass}_{X}}{\textup{molecular weight}_{X}}$

Where mass is in grams and molecular weight is in grams per mole

Dilution Equation

$C_{i}\cdot V_{i}=C_{f}\cdot V_{f}$

Where both volumes are in the same units and both concentrations are in the same units.

Going from ratios to amounts

For a solution of a ratio of a:b:c where a, b, and c are coefficients for relative volumes, to calculate the volumes need for a solution of volume $V_{Final}$ :

$V_{A}=\frac{A}{A+B+C} \times V_{Final}$

$V_{B}=\frac{B}{A+B+C} \times V_{Final}$

$V_{C}=\frac{C}{A+B+C} \times V_{Final}$

This is generalizeable for any amount of coefficients

Converting between g/mL and mol/mL

$C_{g/mL}=C_{mol/mL}\times \textup{molar mass}$

Calculate standard error of mean

$SE=\frac{s}{\sqrt{n}}$

where SE is the standard error, s is the sample standard deviation, and n is the sample size.

Reversal Potential

$E=\frac{RT}{zF}ln(\frac{[ion]_{outside}}{[ion]_{inside}})$

Logarithm Rules

Given a number y, which is in log base b ( $log_{b}x=y$ ), to undo the log and find x, use the following equation: $b^{y}=x$

Other logarithm properties:

Addition: $log(a)+log(b)=log(a*b)$

Multiplication: $b\times log(a)=log(a^{b})$

Base Change Formula: $log_{x}(y)=\frac{log_{b}(y)}{log_{b}(x)}$ for any positive numbers b, x, and y.

Note: taking taking the average and then undoing the log is not mathematically equal to undoing the log then taking the average. That is to say: $x^{\frac{log_{x}(a)+log_{x}(b)}{2}}\neq \frac{a+b}{2}$ The right is the arithmetic average and the left is the geometric average which are not equivalent.