Question

Liquid hydrogen peroxide, an oxidizing agent in many rocket fuel mixtures, releases oxygen gas on decomposition: $$2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) \quad \Delta H=-196.1 \mathrm{~kJ}$$ How much heat is released when \(652 \mathrm{~kg}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}\) decomposes?

Short answer

Approximately \(-1880037.8 \text{ kJ}\) of heat is released.

Step-by-step solution

- Write the Balanced Chemical Equation

Start by writing down the balanced chemical equation:\[2 \text{H}_2\text{O}_2 (l) \rightarrow 2 \text{H}_2\text{O} (l) + \text{O}_2 (g) \] This indicates that 2 moles of hydrogen peroxide decompose to form 2 moles of water and 1 mole of oxygen gas, with a heat release of \(-196.1 \text{ kJ}\).

- Determine Molar Mass of \text{H}_2\text{O}_2

Calculate the molar mass of hydrogen peroxide (\(\text{H}_2\text{O}_2\)). Using atomic masses (H: 1 g/mol, O: 16 g/mol):\[\text{Molar mass of H}_2\text{O}_2 = (2 \times 1) + (2 \times 16) = 34 \text{ g/mol} \]

- Convert Mass to Moles

Convert the given mass of hydrogen peroxide (652 kg) to grams and then to moles:\[652 \text{ kg} \times 1000 \text{ g/kg} = 652000 \text{ g} \]\[\text{Moles of H}_2\text{O}_2 = \frac{652000 \text{ g}}{34 \text{ g/mol}} \approx 19176 \text{ moles} \]

- Calculate Heat Released

Use the heat released per 2 moles of \(\text{H}_2\text{O}_2\) to find the total heat released.For every 2 moles of \(\text{H}_2\text{O}_2\), \(-196.1 \text{ kJ}\) is released:\[\text{Heat released} = 19176 \text{ moles} \times \frac{-196.1 \text{ kJ}}{2 \text{ moles}} \approx -1880037.8 \text{ kJ} \]Thus, the total heat released is approximately \(-1880037.8 \text{ kJ}\).

Key concepts

chemical decomposition

Chemical decomposition is a process where a single compound breaks down into two or more simpler substances. In the context of the given problem, hydrogen peroxide (\text{H}_2\text{O}_2\text{(l)}) undergoes decomposition to form water (\text{H}_2\text{O}\text{(l)}) and oxygen gas (\text{O}_2\text{(g)}). This reaction can be described using the balanced chemical equation: \[2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \] This means that two moles of hydrogen peroxide decompose into two moles of water and one mole of oxygen gas. Decomposition reactions often involve the release or absorption of energy. In this case, energy is released as heat, making the reaction exothermic.

molar mass calculation

To solve for the heat released in the decomposition reaction, we first need to understand the concept of molar mass. Molar mass is the mass of one mole of a substance. It is calculated as the sum of the atomic masses of all atoms in a molecule. For hydrogen peroxide (\text{H}_2\text{O}_2): \ \[ \text{Molar mass} = (2 \times 1) + (2 \times 16) = 34 \text{ g/mol} \] Here, we used the atomic masses of hydrogen (1 g/mol) and oxygen (16 g/mol). This tells us that one mole of \text{H}_2\text{O}_2\text{(l)} weighs 34 grams.

heat released in reaction

Once we know the molar mass, we can calculate the number of moles of hydrogen peroxide given a certain mass. For example, if we have 652 kg of \text{H}_2\text{O}_2: \ \[ \text{Mass in grams} = 652 \text{ kg} \times 1000 = 652000 \text{ g} \] Next, convert it to moles: \ \[ \text{Moles} = \frac{652000 \text{ g}}{34 \text{ g/mol}} \rightarrow \text{approx. 19176 moles} \] Now we use the fact that the decomposition of 2 moles of \text{H}_2\text{O}_2 releases -196.1 kJ of heat. Therefore, for 19176 moles: \ \[ \text{Heat released} = 19176 \text{ moles} \times \frac{-196.1 \text{ kJ}}{2 \text{ moles}} = \text{approx. -1880037.8 kJ} \] Thus, decomposing 652 kg of \text{H}_2\text{O}_2} releases approximately -1880037.8 kJ of heat.

balanced chemical equation

In any chemical reaction, it is crucial to first write a balanced chemical equation. This ensures that the number of atoms of each element is the same on both sides of the reaction. The given equation: \[ 2 \text{H}_2\text{O}_2(l) \rightarrow 2 \text{H}_2\text{O}(l) + \text{O}_2(g) \] shows that: \ * 2 moles of hydrogen peroxide (\text{H}_2\text{O}_2\text{(l)}) decompose to produce 2 moles of water (\text{H}_2\text{O}\text{(l)}) and 1 mole of oxygen gas (\text{O}_2\text{(g)}) \
By balancing the equation, we confirm the conservation of mass and energy in the reaction.
Balancing is accomplished by ensuring that the number of atoms of each type on the left-hand side matches the right-hand side. If the reaction is not balanced, the conservation laws are violated, and the calculations would be incorrect.