Peroxide content in an aqueous solution

The input data consists of the mass fraction and the volume of the solution (when you buy a bottle of peroxide at a pharmacy, the insert usually specifies something like "Hydrogen peroxide mass fraction, %: 2.7–3.3," while the bottle itself indicates the volume—100 ml). In addition to volumetric concentration, the calculator determines the masses and volumes of the pure substances—hydrogen peroxide and water—as well as the contraction value, which characterizes the non-additive change in the volume (and, consequently, the density) of the liquid mixture. You can read more about contraction and the calculation formulas below the calculator.

Note: All calculations are based on reference data for 18°C.

Peroxide content in an aqueous solution

Mass fraction of hydrogen peroxide, %

Volume of hydrogen peroxide solution, ml

Calculate

Mass of hydrogen peroxide, g

 

Mass of water, g

 

Mass of solution, g

 

Volumetric concentration, %

 

Volume of hydrogen peroxide before mixing, ml

 

Volume of water before mixing, ml

 

Total volume of pure substances, ml

 

Contraction, %

 

Calculation precision

Digits after the decimal point: 2

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Contraction and converting from mass percentage to volume percentage

The phenomenon of contraction has been known for quite some time. Mendeleev’s doctoral dissertation was dedicated to the reduction in the total volume of an alcohol solution compared to the initial volumes of water and ethyl alcohol; in it, he investigated how the specific gravity of alcohol solutions varied with concentration and temperature. This phenomenon is believed to be caused by the formation of compounds—solvates or hydrates (in the case of water)—comprising solute and solvent molecules, driven by electrostatic interactions (for polar substances) or hydrogen bonding (for non-polar substances).

Incidentally, the volume of an ideal solution is exactly equal to the sum of the initial volumes of its components, and its density is simply the ratio of the total mass to the total volume. The density of a real solution is, therefore, higher than that of an ideal solution, owing to its smaller volume for the same total mass. Moreover, solution density depends non-linearly on the concentration of the dissolved substance. This is due to the composition of the hydrates formed within the solution. For instance, depending on the concentration, ethyl alcohol can form three types of hydrates: those with 12, 3, or 1 attached water molecule(s)¹.

Converting from the mass fraction of a substance in a solution to its volumetric concentration requires knowledge of the solution's density (since volume and mass are linked by density). In this case, we must rely on empirical data regarding the relationship between solution density and solute concentration. Chemical reference books come in handy here—specifically, the Handbook for the Young Chemical Process Operator (1991)², page 144, Table 7.6. The graph below shows how the density of a hydrogen peroxide solution depends on its mass concentration (or mass fraction). As we can see, the relationship is non-linear.

Densities of hydrogen peroxide (H₂O₂) solutions at 18°C

Densities of hydrogen peroxide (H₂O₂) solutions at 18°C

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Once the density value is known, it is possible to convert from mass percentage to volume percentage, though there is a nuance involved. We can confidently calculate the volumetric concentration, but not the volume fraction. This is because volumetric concentration is the ratio of the volume of the pure component before mixing to the volume of the resulting mixture, whereas volume fraction is the ratio of the volume of the component within the mixture to the sum of the volumes of all components. The latter is obviously difficult to determine if only the mass fraction is known. However, dealing with the volumes of pure components prior to mixing is quite straightforward: we simply use the density values ​​of the pure substances at the corresponding temperature (since our data on peroxide solution density is available only for 18°C). For reference, at 18°C, the density of water is 0.9986 g/mL, and the density of hydrogen peroxide is 1.450 g/mL.

The rest is fairly straightforward. The fundamental formula is the density formula:

The sequence of steps is as follows:

• look up the solution density corresponding to the specific mass fraction in a reference table (if the table lacks an entry for the specific value, the calculator computes it via linear interpolation between the two nearest values)
• determine the mass of the solution using its volume and density
• calculate the mass of the peroxide and the mass of water (the latter being the difference between the solution mass and the peroxide mass, based on the law of conservation of mass) using the solution mass and the peroxide mass fraction
• determine the volumes of the pure substances—water and peroxide—using their respective masses and densities (of the pure substances)
• determine the volumetric concentration as the ratio of the pure peroxide volume (before mixing) to the solution volume
• calculate the contraction based on the sum of the pure volumes and the solution volume.