Formulas

Combined Gas Law Formula

• Use case:
  • When one of the following variables are desired, while the rest are given:
    • Pressure ($P$)
    • Temperature ($T$)
    • Volume ($V$)
• Variables:
  • $P_1$ - First / Initial Pressure
  • $P_2$ - Second / Final Pressure
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $T_1$ - First / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second / Final Temperature ( $\text{K}$ )
• Formula: $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Ideal Gas Law Formula

• Use case:
  • When one of the following variables are desired, while the rest are given:
    • Pressure ($P$)
    • Temperature ($T$)
    • Volume ($V$)
    • Number of moles ($n$)
• Variables:
  • $P$ - Pressure ( $\text{atm}$ )
  • $V$ - Volume ( $\text{L}$ )
  • $T$ - Temperature ( $\text{K}$ )
  • $n$ - Number of moles ($mol$)
  • $R$ - Gas constant ($0.08206L\cdot atm/mol\cdot K$)
• Formula: $PV=nRT$

Boyle’s Law Formula

• Use Case:
  • Temperature is constant / Isothermal
  • Temperature is not given or will not be used.
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $P_1$ - First / Initial Pressure
  • $P_2$ - Second / Final Pressure
• Formula: $V_1{P}_1=V_2{P}_2$

Gay-Lussac’s Law Formula

• Use case:
  • Volume is constant / Isovolumetric
  • Volume is not given
• Variables:
  • $P_1$ - First Pressure / Initial Pressure
  • $P_2$ - Second Pressure / Final PressurE
  • $T_1$ - First Temperature / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second Temperature / Final Temperature ( $\text{K}$ )
• Formula: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Charles’ Law Formula

• Use case:
  • Pressure is constant / Isobaric
  • Pressure is not given.
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $T_1$ - First / Initial Temperature ( $\text{K}$ )
  • $T_2$ - Second / Final Temperature ( $\text{K}$ )
• Formula: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Avogadro’s Law Formula

• Use case:
  • Pressure and Temperature are constant / Isobaric and Isothermal
• Variables:
  • $V_1$ - First / Initial Volume
  • $V_2$ - Second / Final Volume
  • $n_1$ - First / Initial Number of Moles ( $\text{mol}$ )
  • $n_2$ - Second / Final Number of Moles ( $\text{mol}$ )
• Formula: $\frac{V_1}{n_1}=\frac{V_2}{n_2}$

Van der Waal’s Real Gas Formula

• Use case:
  • When the problem concerns real gases
• Variables:
  • $R$ - Gas Constant ( $0.08206L\cdot atm/mol\cdot K$ )
  • $P$ - Pressure ( $\text{atm}$ )
  • $n$ - Number of moles of the given gas ( $\text{mol}$ )
  • $a{n}^2$ - Internal Pressure per mole ( ${\text{L}}^2\cdot \text{atm}$ )
  • $nb$ - Incompressibility ( $\text{L}/\text{mol}$ )
  • $V$ - Volume ( $\text{L}$ )
  • $T$ - Temperature ( $\text{K}$ )
• Formula: $(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$

Dalton’s Law Formula

• Use case:
  • When asked the partial pressure of a gas
  • Mole fraction is given
  • Total pressure is given
• Variables:
  • $P_T$ - Total Pressure ( $\text{atm}$ )
  • $\chi$ - Mole fraction ( $\frac{n_x}{n_T}$ )
    • $n_x$ - Moles of a particular gas ( $\text{mol}$ )
    • $n_T$ - Total moles within a gas ( $\text{mol}$ )
  • $P_x,P_y,P_z$ - Partial pressure of a particular gas ( $\text{atm}$ )
• Formula for total pressure: $P_T=P_z+P_y+\cdots P_x$
• Formula for partial pressure: $P_x=P_T\chi$

Raoult’s Law Formula

• Use case:
  • For calculating the vapor pressure of a solution
  • Solvent pressure is given
  • Solvent mole fraction is given
• Variables:
  • $P_{\text{solution}}$ - Vapor pressure of the solution ( $\text{atm}$ )
  • ${\chi }_{\text{solvent}}$ - Mole fraction of the solvent ( $\frac{n_{\text{solvent}}}{n_{\text{solvent}}+n_{\text{solute}}}$ )
    • $n_{\text{solvent}}$ - Moles of the solvent ( $\text{mol}$ )
    • $n_{\text{solute}}$ - Moles of the solute ( $\text{mol}$ )
  • $P_{\text{solvent}}^0$ - Vapor pressure of the pure solvent ( $\text{atm}$ )
• Formula: $P_{\text{solution}}=({\chi }_{\text{solvent}})(P_{\text{solvent}}^0)$

Graham’s Law Formula

• Use case:
  • To compare the rates of diffusion between two gases
• Variables:
  • ${\text{Rate}}_1$ - Rate of the first gas ( ${\text{m}}^2/\text{s}$ )
  • ${\text{Rate}}_2$ - Rate of the second gas ( ${\text{m}}^2/\text{s}$ )
  • $M{W}_1$ - Molecular weight of the first gas
  • $M{W}_2$ - Molecular weight of the second gas
• Formula: $\frac{{\text{Rate}}_1}{{\text{Rate}}_2}=\sqrt{\frac{M{W}_2}{M{W}_1}}$

Fick’s 1st Law Formula

• Use case:
  • When asked the flux of a given gas
• Variables:
  • $J$ - Flux; amount of substance per unit area per unit of time
  • $D$ - Diffusivity; diffusion coefficient
  • $\phi$ - Concentration gradient; difference in concentration
  • $x$ - Path length
• Formula: $J=-D\frac{d\phi }{dx}$

Formal Charge Formula

• Use case:
  • For determining formal charge
• Variables:
  • $\text{formal charge}$ - The integer charge of the element.
  • ${\text{Ve}}^{-}$ - The valence electron of the element.
  • $\text{bond}$ - The number of bonds of the element.
  • ${\text{unpaired e}}^{-}$ - The number of unpaired electrons of the element
• Formula: $\text{formal charge}={\text{Ve}}^{-}-\text{bond}-{\text{unpaired e}}^{-}$

Calculation of Microscope Magnification

• Use case:
  • For logging the magnification used when conducting microscopy.
• Variables:
  • $M_{\text{Ocular}}$ - Magnification value of the ocular lens ( usually $10\times$ magnification )
  • $M_{\text{Objective}}$ - Magnification value of the objective lens
    • Scanning Lens = $4\times$
    • Low Power Lens = $10\times$
    • High Power Lens = $40\times$
    • Oil Immersion Objective Lens = $100\times$
  • $M_{\text{Total}}$ - Total magnification used in your experiment
• Formula: $M_{\text{Total}}=M_{\text{Ocular}}\times M_{\text{Objective}}$

Mole Conversion Between Different Molecules Formula

• Use case:
  • When converting from the moles of element $x$ to moles of element $y$ and a balanced chemical equation is given.
• Variables:
  • $C{f}_x$ - Coefficient of element $x$ in the balanced chemical equation ( $\text{mol}$ )
  • $C{f}_y$ - Coefficient of element $y$ in the balanced chemical equation ( $\text{mol}$ )
• Formula: $\frac{C{f}_x}{C{f}_y}$

Grams to Moles Conversion Formula

• Use case:
  • When converting from grams of the element $x$ to moles of the element $x$, and the molecular weight of the element $x$ is given.
• Variables:
  • $n_x$ - Moles of element $x$ ( $\text{mol}$ )
  • $M{W}_X$ - Molecular weight of element $x$ ( $\text{g}$ )
  • $g_x$ - Grams of element $x$ ( $\text{g}$ )
• Formula: $n_x=\frac{g_x}{M{W}_x}$

Moles to Grams Conversion Formula

• Use case:
  • When converting from moles of the element $x$ to grams of the element $x$, and the molecular weight of the element $x$ is given.
• Variables:
  • $g_x$ - Grams of element $x$ ( $\text{g}$ )
  • $n_x$ - Moles of element $x$ ( $\text{mol}$ )
  • $M{W}_X$ - Molecular weight of element $x$ ( $\text{g}$ )
• Formula: $g_x=n_{x}M{W}_x$

Moles to Volume Conversion Formula

• Use case:
  • When converting from moles of the element $x$ to volume of the element $x$, and the temperature and pressure is given or is assumed as STP.
• Variables:
  • $V_x$ - Volume of element $x$ ( $\text{L}$ )
  • $n_x$ - Moles of element $x$ ( $\text{mol}$ )
  • $R$ - Gas constant ( $0.08206\text{L}\cdot \text{atm}/\text{mol}\cdot \text{K}$ )
  • $T$ - Temperature ( $\text{K}$ ) { STP: $273.15\text{K}$ }
  • $P$ - Pressure ( $\text{atm}$ ) { STP: $1\text{atm}$ }
• Formula: $V_x=\frac{n_{x}RT}{P}$

Volume to Moles Conversion Formula

• Use case:
  • When converting from volume of the element $x$ to moles of the element $x$, and the temperature and pressure is given or is assumed as STP.
• Variables:
  • $n_x$ - Moles of element $x$ ( $\text{mol}$ )
  • $P$ - Pressure ( $\text{atm}$ ) { STP: $1\text{atm}$ }
  • $V_x$ - Volume of element $x$ ( $\text{L}$ )
  • $R$ - Gas constant ( $0.08206\text{L}\cdot \text{atm}/\text{mol}\cdot \text{K}$ )
  • $T$ - Temperature ( $\text{K}$ ) { STP: $273.15\text{K}$ }
• Formula: $n_x=\frac{P{V}_x}{RT}$

Number of Particles to Moles Conversion Formula

• Use case:
  • When converting from number of particles of the element $x$ to moles of the element $x$, and the temperature and pressure is given or is assumed as STP.
• Variables:
  • $n_x$ - Number of moles of element $x$ ( $\text{mol}$ )
  • $a_x$ - Number of atoms of a given element $x$
  • $N_A$ - Avogadro’s Number ($6.022\times 10^{23}{\text{mol}}^{-1}$).
• Formula: $n_x=\frac{a_x}{N_A}$

Moles to Number of Particles Conversion Formula

• Use case:
  • When converting from number of particles of the element $x$ to moles of the element $x$, and the temperature and pressure is given or is assumed as STP.
• Variables:
  • $a_x$ - Number of atoms of a given element $x$
  • $n_x$ - Number of moles of element $x$ ( $\text{mol}$ )
  • $N_A$ - Avogadro’s Number ($6.022\times 10^{23}{\text{mol}}^{-1}$).
• Formula: $a_x=n_x{N}_A$

The Number of Subsets in a Set

• Use case:
  • When calculating the number of subsets in a set
• Variables:
  • $|A|$ - Number of elements in a set
• Formula: $\text{Number of subsets}=2^{|A|}$

Calculating the Change of Variable formula

• Use case:
  • When calculating the value of a variable with a leading capital delta symbol ( $\Delta$ ).
• Variables:
  • $\Delta a$ - The change in variable $a$;
  • $a_{\text{final}}$ - The final value of variable $a$; the last value;
  • $a_{\text{initial}}$ - The initial value of variable $a$; the starting value;
• Formula: $\Delta a=a_{\text{final}}-a_{\text{initial}}$

Reaction Rate of a Reactant Formula

• Use case:
  • when determining the reaction rate of a reactant $\text{A}$ in terms of molars per second ( $\text{M}/\text{s}$ )
• Variables:
  • $\Delta \left[\text{A}\right]$ - the change in concentration of the reactant $\text{A}$. ( $\text{M}$ )
  • $\Delta t$ - the change in time; the time elapsed. ( $\text{s}$ )
• Formula: $-\frac{\Delta \left[\text{A}\right]}{\Delta t}$

Reaction Rate of a Product Formula

• Use case:
  • when determining the reaction rate of a product $\text{B}$ in terms of molars per second ( $\text{M}/\text{s}$ )
• Variables:
  • $\Delta \left[\text{B}\right]$ - the change in concentration of the product $\text{B}$. ( $\text{M}$ )
  • $\Delta t$ - the change in time; the time elapsed. ( $\text{s}$ )
• Formula: $\frac{\Delta \left[\text{B}\right]}{\Delta t}$

Overall Reaction Rate with a Reactant Formula

• Use case:
  • When determining the overall reaction rate ( $\text{M}/\text{s}$ ), given the full balanced equation or the coefficient of one of the reactants;
• Variables:
  • $C{f}_{\text{A}}$ - The coefficient of reactant $\text{A}$ in the balanced equation
  • $\Delta \left[\text{A}\right]$ - The change in concentration of the reactant $\text{A}$. ( $\text{M}$ )
  • $\Delta t$ - The change in time; the time elapsed. ( $\text{s}$ )
• Formula: ${\text{R}}_{\text{OA}}=-\frac{1}{C{f}_{\text{A}}}\frac{\Delta \left[\text{A}\right]}{\Delta t}$

Overall Reaction Rate with a Product Formula

• Use case:
  • When determining the overall reaction rate ( $\text{M}/\text{s}$ ), given the full balanced equation or the coefficient of one of the products;
• Variables:
  • $C{f}_{\text{B}}$ - The coefficient of product $\text{B}$ in the balanced equation.
  • $\Delta \left[\text{B}\right]$ - The change in concentration of the product $\text{B}$. ( $\text{M}$ )
  • $\Delta t$ - The change in time; the time elapsed. ( $\text{s}$ )
• Formula: ${\text{R}}_{\text{OA}}=\frac{1}{C{f}_{\text{B}}}\frac{\Delta \left[\text{B}\right]}{\Delta t}$

Modified Ideal Gas Law using Molarity

• Use case:
  • For determining Ideal Gas Law variables with molarity as a given or desired value;
• Variables:
  • $P$ - Pressure ( $\text{atm}$ ) { STP: $1\text{atm}$ }
  • $M$ - Concentration; molarity ( $\text{M}$ );
  • $R$ - Gas Constant ( $0.08206\text{L}\cdot \text{atm}/\text{mol}\cdot \text{K}$ )
  • $T$ - Temperature ( $\text{K}$ ) {STP: $273.15\text{K}$ }
• Formula: $P=MRT$

Modified Ideal Gas Law for Determining Pressure Change Rate

• Use case:
  • For determining the change in pressure per change of $\text{A}$ in time when given the reaction rate.
  • For determining the reaction rate of $\text{A}$ when given the change in pressure per change in time.
• Variables:
  • $\frac{\Delta P}{\Delta t}$ - The change in pressure per change in time ( $\text{atm}/\text{s}$ )
  • $\frac{\Delta \left[\text{A}\right]}{\Delta t}$ - The reaction rate; the change in concentration per change in time ( $\text{M}/\text{s}$ )
  • $R$ - Gas Constant ( $0.08206\text{L}\cdot \text{atm}/\text{mol}\cdot \text{K}$ );
  • $T$ - Temperature ( $\text{K}$ ) { STP: $273.15K$ }
• Formula: $\frac{\Delta P}{\Delta t}=\frac{\Delta \left[\text{A}\right]}{\Delta t}RT$

Generic Rate Law Formula

• Use case:
  • For calculating the rate of a reaction ( $\text{M}/\text{s}$ ) using rate constant and the given reactant’s concentrations and reaction orders;
  • This formula is applicable for reactions any one or more reactants
• Variables:
  • $\text{rate}$ - Reaction rate ( $\text{M}/\text{s}$ );
  • $k$ - Rate constant ( value varies per reaction );
  • $\left[\text{A}\right]$ - Concentration of first reactant ( $\text{M}$ );
  • $\left[\text{B}\right]$ - Concentration of second reactant ( $\text{M}$ );
  • $\left[\text{N}\right]$ - Concentration of nth reactant ( $\text{M}$ );
  • $x$ - Reaction order of your first reactant;
  • $y$ - Reaction order of your second reactant;
  • $n$ - Reaction order of your nth reactant;
• Formula: $\text{rate}=k{\left[\text{A}\right]}^x{\left[\text{B}\right]}^y\cdots {\left[\text{N}\right]}^n$

Generic Rate Law - Reaction Order Formula

• Use case:
  • For calculating the reaction order of a reaction using the generic rate law;
  • Use two sets of experimental data where the values of the other reactants are equal on both experiments.
• Variables:
  • $x$ - Reaction order of reactant;
  • ${\text{rate}}_1$ - Reaction rate of your first experiment ( $\text{M}/\text{s}$ )
  • ${\text{rate}}_2$ - Reaction rate of your second experiment ( $\text{M}/\text{s}$ )
  • ${\left[\text{A}\right]}_1$ - Concentration of your reactant in the first experiment ( $\text{M}$ )
  • ${\left[\text{A}\right]}_2$ - Concentration of your reactant in the second experiment ( $\text{M}$ )
• Formula: $x=\frac{\log \left(\frac{{\text{rate}}_1}{{\text{rate}}_2}\right)}{\log \left(\frac{{\left[\text{A}\right]}_1}{{\left[\text{A}\right]}_2}\right)}$

Generic Rate Law - Rate Constant Formula

• Use case:
  • For calculating the rate constant of a reaction using the generic rate law;
  • use one set of experimental data;
• Variables:
  • $k$ - Reaction rate constant;
  • $\text{rate}$ - Reaction rate ( $\text{M}/\text{s}$ )
  • $\left[\text{A}\right]$ - Concentration of first reactant ( $\text{M}$ )
  • $\left[\text{B}\right]$ - Concentration of second reactant ( $\text{M}$ )
  • $\left[\text{N}\right]$ - Concentration of nth reactant ( $\text{M}$ )
  • $x$ - Reaction order of your first reactant ( $\text{M}$ )
  • $y$ - Reaction order of your second reactant ( $\text{M}$ )
  • $n$ - Reaction order of your nth reactant ( $\text{M}$ )
• Formula: $k=\frac{\text{rate}}{{\left[\text{A}\right]}^x{\left[\text{B}\right]}^y\cdots {\left[\text{N}\right]}^n}$

Overall Reaction Order Formula

• Use case:
  • For calculating the overall reaction order when all reaction orders are known.
• Variables:
  • ${\text{RO}}_{\text{OA}}$ - Overall Reaction Order;
  • $\sum$ - “the sum of all—”;
  • $x$ - reaction order; the exponent of your reactant’s concentration
    • $x_1$ - first reactant’s reaction order;
    • $x_2$ - second reactant’s reaction order;
    • $x_n$ - nth reactant’s reaction order;
• Formula: ${\text{RO}}_{\text{OA}}=\sum x\text{or}{\text{RO}}_{\text{OA}}=x_1+x_2+\cdots +x_n$

Rate Constant Unit Formula

• Use case:
  • For determining the unit of your rate constant ( $k$ ).
• Variables:
  • ${\text{RO}}_{\text{OA}}$ - Overall reaction rate;
• Formula: $\text{unit}={\text{M}}^{1-{\text{RO}}_{\text{OA}}}{\text{s}}^{-1}$

Least Weighable Quantity Formula

• Use case:
  • For calculating the least weighable quantity.
• Variables:
  • $\text{LWQ}$ - Least weighable quantity.
  • $\text{sens req}$ - Sensitivity requirement of weighing device.
  • $\text{err\%}$ - Acceptable percentage of errors.
• Formula: $\text{LWQ}=\frac{100\times \text{sens req}}{\text{err\%}}$

Aliquot Amount Formula

• Use case:
  • Calculating amount of aliquot.
• Variables:
  • ${\text{a}}_{\text{aliqot}}$ - amount of aliquot.
  • ${\text{a}}_{\text{desired}}$ - desired amount.
  • $\text{f}$ - aliquot factor
• Formula: ${\text{a}}_{\text{aliquot}}={\text{a}}_{\text{desired}}\times f$

Total Aliquot Mixture Formula

• Use case:
  • Calculating amount of total aliquot mixture.
• Variables:
  • ${\text{a}}_{\text{total}}$ - Total amount of mixture.
  • ${\text{a}}_{\text{aliquot}}$ - amount of aliquot.
  • $\text{f}$ - aliquot factor
• Formula: ${\text{a}}_{\text{total}}={\text{a}}_{\text{aliquot}}\times f$

Aliquot Diluent Formula

• Use case:
  • Calculating amount of total aliquot mixture.
• Variables:
  • ${\text{a}}_{\text{diluent}}$ - amount of diluent.
  • ${\text{a}}_{\text{total}}$ - total amount of mixture.
  • ${\text{a}}_{\text{aliquot}}$ - amount of aliquot
• Formula: ${\text{a}}_{\text{diluent}}={\text{a}}_{\text{total}}-{\text{a}}_{\text{aliquot}}$

Aliquot Ratio Formula

• Use case:
  • Calculating the fraction of the total mixture that contains the desired amount of substance.
• Variables:
  • $a_{\text{weighed}}$ - amount of total mixture to be weighed that contains desired amount of substance.
  • $a_{\text{desired}}$ - desired amount of substance
  • $a_{\text{total}}$ - total amount of mixture
  • $a_{\text{aliquot}}$ - amount of aliquot.
• Formula: $\frac{a_{\text{weighed}}}{a_{\text{desired}}}=\frac{a_{\text{total}}}{a_{\text{aliquot}}}$

Percentage Error Formula

• Use case:
  • for calculating the percentage of error in a measurement.
• Variables:
  • $\text{err\%}$ - percentage of error.
  • ${\text{err}}_{\text{measurement}}$ - the amount of error in a measurement
  • $q_{\text{desired}}$ - desired or expected quantity.
• Formula: $\text{err\%}=\frac{{\text{err}}_{\text{measurement}}}{q_{\text{desired}}}\times 100\%$

Density Formula

• Use case:
  • for calculating the density of a substance.
• Variables:
  • $\rho$ - density of a substance
  • $m$ - mass of a substance
  • $V$ - volume of a substance
• Formula: $\rho =\frac{m}{V}$

Specific Gravity Formula

• Use case:
  • for calculating specific gravity of a substance
• Variables:
  • $\text{sp gr}$ - specific gravity of a substance
  • $m_{\text{substance}}$ - weight of a volume of substance
  • $m_{\text{water}}$ - weight of equal volumes of water
• Formula: $\text{sp gr}=\frac{m_{\text{substance}}}{m_{\text{water}}}$

Specific Volume Formula

• Use case:
  • for calculating specific volume of a substance
• Variables:
  • $\text{sp vol}$ - specific volume of a substance
  • $v_{\text{substance}}$ - volume of a weight of substance
  • $v_{\text{water}}$ - volume of equal weight of water
• Formula: $\text{sp vol}=\frac{v_{\text{substance}}}{v_{\text{volume}}}$