Question

A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage strength is nearly (a) \(3 \%\) (b) \(1 \%\) (c) \(90 \%\) (d) \(10 \%\)

Short answer

10 volume hydrogen peroxide has approximately a percentage strength of 3%.

Step-by-step solution

Understanding '10 volume' hydrogen peroxide

The term '10 volume' means that 1 mL of this hydrogen peroxide solution will produce 10 mL of oxygen gas at standard temperature and pressure when it decomposes.

Calculating percentage strength

2 moles of hydrogen peroxide (H_2O_2) decompose to form 1 mole of dioxygen (O_2) and 2 moles of water (H_2O). The reaction is: 2H_2O_2 -> 2H_2O + O_2. From the molar volume concept (1 mole of gas occupies 22.4 L at STP), 1 mole of O_2 will occupy 22.4 L. Therefore, 10 volumes of O_2 would be 10 mL, which comes from 1/2240 moles of hydrogen peroxide.

Deducing the mass of hydrogen peroxide

Calculate the mass of 1/2240 moles ofH_2O_2using its molar mass (34 g/mol). Mass = (1/2240) * 34 g.

Finding the percentage strength

Percentage strength is calculated using the mass ofH_2O_2and assuming a density of the solution close to that of water, thus 1 mL ~ 1 g. To get the percentage strength, divide the mass ofH_2O_2by the mass of the solution (which is 1 g/mL for 1 mL of solution) and multiply by 100.

Key concepts

10 Volume Hydrogen Peroxide

The term '10 volume hydrogen peroxide' is a way of measuring the concentration of hydrogen peroxide solution. This term indicates the amount of oxygen gas released when hydrogen peroxide goes through chemical decomposition. Specifically, '10 volume' means that 1 milliliter (mL) of the hydrogen peroxide solution can produce 10 mL of oxygen gas under standard temperature and pressure conditions (STP).
This concept is crucial for a variety of applications such as hair coloring, disinfecting, and in science experiments. In the context of the problem at hand, understanding this measurement helps us calculate the percentage strength of the hydrogen peroxide solution, which will further aid in scientific calculations and experimental setups.

Molar Volume

The molar volume of a substance is the volume occupied by one mole of it at a given temperature and pressure, typically standard temperature and pressure (STP). At STP, which is defined as 0 degrees Celsius and 1 atmosphere of pressure, the molar volume of any ideal gas is considered to be 22.4 liters (L).
This concept is fundamental for understanding the relationship between the physical quantity of the gas—like volume—and its chemical quantity—like the number of moles. The direct application of molar volume in calculations allows chemists and students to convert between the amount of substance and volume for gases, leading to solutions to problems like the one posed about hydrogen peroxide's concentration.

STP (Standard Temperature and Pressure)

Standard Temperature and Pressure (STP) is a set of conditions for experimental measurements established to allow comparisons to be made between different sets of data. At STP, the temperature is 273.15 Kelvin (0 degrees Celsius), and the pressure is 1 atmosphere (atm). It is at these conditions that one mole of a gas occupies 22.4 L, which is known as the molar volume of a gas.
In practical situations like our textbook problem, STP is used to calculate the volume of gas produced or consumed in chemical reactions. This is essential for scientists and engineers to design reactions, calculate yields, and scale up processes from laboratory to industrial scales.

Chemical Decomposition

Chemical decomposition, also known as chemical breakdown or analysis, is a chemical reaction where a single compound breaks down into two or more simpler substances. The decomposition of hydrogen peroxide (H_2O_2) into water (H_2O) and oxygen (O_2) is a common example of such a reaction and can be represented by the equation:
2H_2O_2 -> 2H_2O + O_2
This type of reaction is integral to understanding the behavior of hydrogen peroxide, especially given its wide range of applications from antiseptics to rocket fuel. In the case of our exercise, the decomposition of hydrogen peroxide helps in calculating the volume of oxygen produced, which is then used to deduce the concentration of the initial hydrogen peroxide solution.