Calculating the sum formula
Molecular weight
1. Calculating the molecular weight
Molecular mass
1. Monoisotopic mass
2. Mass spectrometry
Comparing molecular weight and molecular mass

Molecular weight and mass

Calculating the sum formula

Various properties can be derived from the sum formula. The simplest way of calculating the sum formula is to type the sequence (e.g. AGCT) into an online calculator such as this one.

If this kind of tool is not available or does not include the modifications (non-standard nucleotides) present in the molecule of interest, it is also possible to add the unit formulae of each base, then subtract PO₃H (because there is no phosphate linkage at the 3'-end), and add H₂O (to account for the ends) to give the formula of the oligonucleotide:

\footnotesize\begin{equation*} \textrm{Sum formula} = \sum\limits_i n_i \times i - \textrm{PO}_3\textrm H + \textrm H_2\textrm O = n_\textrm{A} \times \textrm A + n_\textrm G \times G + ... - \textrm{PO}_3\textrm H + \textrm H_2\textrm O, \end{equation*}

where $\footnotesize\sum\limits_i$ indicates a sum over the unit sum formulae of nucleotides i. These are given in Table 1.

Base	Formula (DNA)	Formula (RNA)
A	C_{10_H12_O5_N5}P	C_{10_H12_O6_N5}P
G	C_{10_H12_O6_N5}P	C_{10_H12_O7_N5}P
C	C₉H_{12_O6_N3}P	C₉H_{12_O7_N3}P
T	C_{10_H13_O7_N2}P	(C_{10_H13_O8_N2}P)
U	(C₉H_{11_O7_N2}P)	C₉H_{11_O8_N2}P

The structures of the DNA molecule dAGCT and the RNA molecule AGCU are shown in Fig. 1. Under physiological conditions, the phosphate oxygen atoms are deprotonated; as shown for AGCU.

Figure 1

Chemical structure of the DNA oligonucleotide dAGCT (left) and the RNA oligonucleotide AGCU (right)

For dAGCT, Eqn. (1) becomes

\footnotesize{ \textrm{Sum formula} = n_\textrm{A} \times \textrm A + n_\textrm G \times \textrm G + ... - \textrm{PO}_3\textrm H + \textrm H_2\textrm O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }

\footnotesize{ = 1 \times \textrm A + 1 \times \textrm G + 1 \times \textrm C + 1 \times \textrm T - \textrm{PO}_3\textrm H + \textrm H_2\textrm O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }

\footnotesize{ = \textrm C_{10}\textrm H_{12}\textrm O_5\textrm N_5\textrm P + \textrm C_{10}\textrm H_{12}\textrm O_6\textrm N_5\textrm P + \textrm C_9\textrm H_{12}\textrm O_6\textrm N_3\textrm P + \textrm C_{10}\textrm H_{13}\textrm O_7\textrm N_2\textrm P - \textrm{PO}_3\textrm H + \textrm H_2\textrm O }

\footnotesize{ = \textrm C_{39}\textrm H_{50}\textrm O_{22}\textrm N_{15}\textrm P_3.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }

The sum formula of AGCU is C_{38_H48_O26_N15_P3}. The deprotonated formulae are C_{39_H47_O22_N15_P3}³⁻ (dAGCT) and C_{38_H45_O26_N15_P3}³⁻ (AGCU).

Molecular weight

The molecular weight (MW), or, more correctly, molar weight (see the IUPAC Gold Book for commonly accepted definitions), is defined as the average weight of one mole (6.0221 $\footnotesize\times$ 10²³ particles) of a given atom or molecule relative to ¹²C, the weight of which is defined as exactly 12 grams per mole (g/mol).

Calculating the molecular weight

The molecular weight can be calculated from the sum formula by using standard values of the molar weight of each atom. For example, each chlorine atom contributes approximately 35.5 to the molecular weight. These values are typically not whole numbers, partly because of isotopes (chlorine occurs naturally as roughly 75% ³⁵Cl and 25% ³⁷Cl).

There are online calculators that convert sum formulae to molecular weights, such as this one from Lenntech.

Molecular weight can be used to calculate concentration and yield, as well as convert between masses and amounts:

\footnotesize\begin{equation*} c = \frac{n}{V}, \end{equation*}

where c is the concentration, n is the amount and V is the volume;

\footnotesize\begin{equation*} m = n \times \textrm{MW}, \end{equation*}

where m is the mass. A reaction yield is calculated via

\footnotesize\begin{equation*} \textrm{Yield} = \frac{n_\textrm{product}}{n_\textrm{starting material}} \times 100\%, \end{equation*}

and n can be obtained from the experimentally measurable mass via Eqn. (3).

Molecular mass

The molecular mass is defined as the weight of a molecule relative to ¹²C, which is defined as exactly 12 Dalton (Da) or atomic mass units (amu). (The analogous property of an atom is called mass number.)

Monoisotopic mass

When calculating the molecular mass, individual isotopes are considered separately. The monoisotopic mass is calculated using the mass of the most common isotope of each element. This is often also the lightest isotope.

Mass spectrometry

Mass spectrometry is the only experimental technique that can distinguish between isotopes, and therefore the only technique with which the mass is more important than the molecular weight.

Comparing molecular weight and molecular mass

For small molecules, the molecular weight is often the same as the monoisotopic mass (when rounded to the nearest integer). As the molecule gets larger, the two properties diverge.

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