Question

Consider the thermochemical equation for the combustion of acetone \(\left( \mathrm { C } _ { 3 } \mathrm { H } _ { 6 } \mathrm { O } \right) ,\) the main ingredicnt in nail polish remover. \(\mathrm { C } _ { 3 } \mathrm { H } _ { 6 } \mathrm { O } ( l ) + 4 \mathrm { O } _ { 2 } ( g ) \longrightarrow 3 \mathrm { CO } _ { 2 } ( g ) + 3 \mathrm { H } _ { 2 } \mathrm { O } ( g )\) $$\Delta H _ { \mathrm { rmn } } ^ { \circ } = - 1790 \mathrm { kJ }$$ If a bottle of nail polish remover contains 177\(\mathrm { mL }\) of acetone, how much heat is released by its complete combustion? The density of acetone is 0.788\(\mathrm { g } / \mathrm { mL }\) .

Short answer

The amount of heat released by the complete combustion of 177 mL of acetone is calculated using the density of acetone, the molar mass, and the heat of combustion.

Step-by-step solution

Calculate the mass of acetone

To find the heat released by the complete combustion of acetone, we must first find the mass of acetone that the 177 mL represents. Since density is given in grams per milliliter (\text{g/mL}), the mass (m) can be found by multiplying volume (V) by density (d). The formula is: \( m = V \times d \).

Calculate the number of moles of acetone

After finding the mass of acetone, the next step is to convert this mass into moles using the molar mass (\text{M}) of acetone (\text{C} _ {3}\text{H} _ {6}\text{O}). The molar mass of acetone can be calculated by adding the molar mass of each atom in the molecule. The molar mass of acetone is \(M_{\text{C}_{3}\text{H}_{6}\text{O}} = (3 \times 12.01) + (6 \times 1.008) + (1 \times 16.00) \text{g/mol}\). Then, we can use the formula \(\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\) to calculate the moles of acetone.

Calculate the amount of heat released

Using the thermochemical equation, every 1 mole of acetone that combusts releases -1790 kJ of heat. Knowing the number of moles of acetone, the total heat (Q) released can be found by multiplying the number of moles (\text{n}) by the heat of combustion (\text{H}). The formula is \( Q = n \times \Delta H _ { \text{rxn} } ^ { \circ } \). Since the question is asking for the amount of heat released, it is important to note that the heat of combustion should be negative, indicating that heat is being released.

Key concepts

Heat of Combustion

The heat of combustion is the energy released as heat when a compound undergoes complete combustion with oxygen under standard conditions. It's a crucial concept in thermochemistry because it helps us understand the energy changes during the combustion process. The acetone thermochemical equation provided in the exercise represents such a reaction, with the acetone (C₃H₆O) being the fuel.

In the given scenario, the heat of combustion is expressed as a negative number, \( -1790 \text{ kJ} \), to indicate that energy is being released, not absorbed. This heat is a form of energy typically measured in kilojoules per mole (kJ/mol). For every mole of acetone burned, 1790 kJ of energy is released, which can be used to calculate the total heat released during the combustion of a given amount of acetone.

Calculating Moles

In chemistry, the mole is a fundamental unit used to measure the amount of substance. One mole contains exactly 6.022 x 10²³ particles, be it atoms, molecules, ions, or electrons – this number is known as Avogadro's number. To understand how much of a substance we are dealing with in a reaction, we often need to calculate the number of moles from a given mass.

The formula \( \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \) is used to convert mass (in grams) to moles, given the molar mass of the substance in grams per mole (g/mol). In the acetone combustion problem, this calculation allows us to determine how many moles of acetone will react based on the mass of acetone in the bottle.

Molar Mass

Molar mass is the weight of one mole of a chemical element or chemical compound. It is expressed in units of grams per mole (g/mol) and can be calculated by summing the molar masses of the individual atoms composing the substance. You find the molar mass of each element on the periodic table and multiply it by the number of atoms of that element in the molecule.

For example, acetone (C₃H₆O) contains carbon, hydrogen, and oxygen. We calculate its molar mass by adding together the molar masses of three carbon atoms, six hydrogen atoms, and one oxygen atom. Identifying the molar mass is crucial because it relates the mass of a substance to the number of moles, a key step in many stoichiometric calculations.

Density and Mass Relationships

Density is an essential concept in chemistry and physics, providing a link between mass and volume. It is defined as the mass of a substance divided by its volume (\( \text{density} = \frac{\text{mass}}{\text{volume}} \) and is often given in grams per milliliter (g/mL).

In the context of the combustion of acetone, we use the substance's density to determine the mass of acetone in a given volume, here 177 mL of acetone. By multiplying the volume by the density, we ascertain the mass, which then sets the stage for us to progress to other calculations, such as determining moles and, eventually, the heat released upon combustion. This demonstrates how interconnected these concepts are in solving chemistry related problems.