Question

A volume of \(50 \mathrm{ml}\) of ' 20 vol' \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution is mixed with \(50 \mathrm{ml}\) of ' 10 vol' \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution. The volume strength of resulting solution is (assume neither expansion nor contraction in volume of solution, on mixing) (a) ' 30 vol' (b) '10 vol' (c) '15 vol' (d) \(22.5\) vol'

Short answer

'15 vol'

Step-by-step solution

Understand Volume Strength

Volume strength of hydrogen peroxide (H_2O_2) refers to the amount of oxygen gas, in milliliters, that is released by the decomposition of 1 ml of hydrogen peroxide solution at standard temperature and pressure (STP). For example, '20 vol' solution means 1 ml of this solution will release 20 ml of oxygen gas under STP conditions.

Calculate Total Oxygen Released

To find the combined volume strength of the resulting solution, first calculate the total volume of oxygen released by each solution. For the '20 vol' solution, multiply the volume by the strength: (50 ml) * (20 vol) = 1000 ml of O_2. For the '10 vol' solution, the calculation is (50 ml) * (10 vol) = 500 ml of O_2.

Calculate Total Volume of Solution

The total volume of the mixed solution is the sum of the volumes of the two solutions mixed. This is simply (50 ml + 50 ml) = 100 ml since there is neither expansion nor contraction upon mixing.

Determine Volume Strength of Resulting Solution

The volume strength of the resulting mixture can be determined by dividing the total volume of oxygen released by the total volume of the mixed solution: (total O_2 released) / (total volume of mixture) = (1000 ml + 500 ml) / (100 ml) = 1500 ml / 100 ml = 15 vol.

Key concepts

H2O2 Solution Concentration

Understanding the concentration of a hydrogen peroxide (H2O2) solution is crucial when working with this common chemical reagent. The term 'volume strength' is specific to H2O2 and is a measure of how much oxygen gas a specific volume of hydrogen peroxide can release. This is usually under standard temperature and pressure (STP) conditions, which are 0°C and 1 atmosphere of pressure.

Volume strength is expressed in a unit called 'vol', an abbreviation for volume. For example, '20 vol' hydrogen peroxide means that one milliliter of the hydrogen peroxide solution will release 20 milliliters of oxygen gas under STP conditions. It's a straightforward way to describe the concentration; the higher the 'vol' number, the more concentrated the solution, and the more reactive it is in terms of releasing oxygen.

For students and professionals alike, it's essential to be able to calculate and understand these concentrations, as they impact the outcome in various chemical reactions where H2O2 is used as a reactant or a catalyst. Displaying the concentration as volume strength helps in quickly determining the amount of active oxygen available in a given volume of peroxide solution.

Chemical Solution Mixing

Mixing chemical solutions correctly is an essential skill in chemistry. When combining two or more solutions with differing concentrations, understanding the resulting mixture's concentration is paramount. The process involves careful measurement and understanding that the volume strengths pertain to the amount of gas released under controlled conditions.

When solutions are mixed, the total volume of gas that each can generate is added together to find the combined capacity of the mixture. An essential point to consider, as highlighted in the provided exercise, is the assumption that there is neither expansion nor contraction in the volume of the mixed solutions. This means that the volumes are simply additive, which greatly simplifies calculations. However, in actual lab conditions, factors like temperature, pressure, and the nature of substances can cause volume changes upon mixing, which would need to be considered.

In our example, the isotonic mixing of '20 vol' and '10 vol' H2O2 solutions in equal volumes results in a uniform solution whose strength can be calculated by dividing the total volume of oxygen that can be yielded by the total volume of the mixed solution. Understanding this concept helps in preparing solutions with desired reactive properties for various applications in laboratory and industrial processes.

Standard Temperature and Pressure (STP)

The concept of Standard Temperature and Pressure (STP) is a reference point used to describe the conditions under which a chemical reaction or calculation, such as volume strength of H2O2, is standardized. STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm), which equals to 101.325 kPa.

For students learning about gas laws and solution concentrations, STP is a critical concept because it allows for standardization and comparison between different studies and experiments. When we talk about gases released or absorbed in reactions – like the oxygen from the decomposition of H2O2 – it is measured at these standard conditions, unless stated otherwise.

This standardization becomes particularly important when considering gas volumes since gases are highly affected by changes in temperature and pressure. By using STP, chemists and students can ensure consistent calculations and communication of volume strength when discussing concentrations, as seen in the exercise's context. The STP assumption allows us to calculate the volume strength of mixed H2O2 solutions without the need to correct for temperature or pressure variances.