Useful Equations

Calculating molarity


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


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

Reversal Potential


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.