Problem 95 - General Chemistry

Question

Formic acid, \(\mathrm{HCHO}_{2}\), was first discovered in ants ( formica is Latin for "ant"). In an experiment, \(5.48 \mathrm{~g}\) of formic acid was burned at constant pressure. $$ 2 \mathrm{HCHO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ If \(30.3 \mathrm{~kJ}\) of heat evolved, what is \(\Delta H\) per mole of formic acid?

Step-by-Step Solution

Answer

\(\Delta H\) is approximately \(-254.6 \text{ kJ/mol}\).

Step 1: Identify the given information

We have an experimental setup where 5.48 g of formic acid is combusted, releasing 30.3 kJ of energy. The molar mass of formic acid (HCHO₂) needs to be calculated first, with hydrogen (H) being 1 g/mol, carbon (C) being 12 g/mol, and oxygen (O) being 16 g/mol.

Step 2: Calculate the molar mass of formic acid

Formic acid, HCHO₂, has a molar mass calculated as follows: 1 (H) + 12 (C) + 16*2 (O) = 46 g/mol.

Step 3: Determine moles of formic acid combusted

The moles of formic acid combusted can be found using the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Thus, moles of formic acid = \( \frac{5.48 \text{ g}}{46 \text{ g/mol}} \approx 0.119 \text{ mol} \).

Step 4: Determine the heat evolved per mole of formic acid

The total heat evolved in the experiment is 30.3 kJ. To find the heat per mole of formic acid, use the formula \( \Delta H = \frac{\text{total heat released}}{\text{moles of formic acid}} \). Thus, \[ \Delta H = \frac{30.3 \text{ kJ}}{0.119 \text{ mol}} \approx 254.6 \text{ kJ/mol} \].

Key Concepts

Combustion Reaction

A combustion reaction involves a substance reacting quickly with oxygen to produce heat and light. In this exercise, formic acid undergoes a combustion reaction. The equation given is:

• 2 \(\mathrm{HCHO}_{2}\)(l) + \(\mathrm{O}_{2}\)(g) \(\longrightarrow\) 2 \(\mathrm{CO}_{2}\)(g) + 2 \(\mathrm{H}_{2}\0\)(l)

This reaction shows that formic acid is oxidized, turning into carbon dioxide and water.
This process releases energy, making it an exothermic reaction.
It's important to note that combustion reactions always need oxygen as a reactant.When dealing with such reactions, the goal is often to calculate energy changes, such as enthalpy changes, which are covered in later sections.

Molar Mass Calculation

Before you can determine the energy changes in a chemical reaction, you need to calculate molar masses. The molar mass is the mass of one mole of a substance. For formic acid, \(\mathrm{HCHO}_{2}\), calculating the molar mass involves adding the atomic masses from the periodic table:

• Hydrogen: 1 g/mol
• Carbon: 12 g/mol
• Oxygen (each): 16 g/mol

Adding these up for \(\mathrm{HCHO}_{2}\):
1 (H) + 12 (C) + 16 \(\times\) 2 (O) = 46 g/mol.
Knowing the molar mass allows you to convert between grams and moles, which is key when calculating heat per mole in chemical reactions.

Enthalpy Change Calculation

Enthalpy change (\(\Delta H\)) measures the change in heat content during a reaction at constant pressure. It's expressed in kilojoules per mole \((\text{kJ/mol})\).
To calculate \(\Delta H\) for a reaction, use the formula:

• \(\Delta H = \frac{\text{total heat released}}{\text{moles of substance burned}}\).

In our example exercise, burning 5.48 g of formic acid released 30.3 kJ of energy.
First, convert the mass of formic acid to moles using the molar mass (46 g/mol):

• \(\text{moles of formic acid} = \frac{5.48 \text{ g}}{46 \text{ g/mol}} \approx 0.119 \text{ mol}\).

Subsequently, calculate \(\Delta H\):

• \(\Delta H = \frac{30.3 \text{ kJ}}{0.119 \text{ mol}} \approx 254.6 \text{ kJ/mol}\).

This calculation tells us how much energy is released per mole of formic acid combusted.Understanding these concepts helps in analyzing exothermic or endothermic reactions.