Question

The standard enthalpy of formation for sulfur dioxide gas is \(-296.8 \mathrm{kJ} / \mathrm{mol}\) . Calculate the amount of energy given off in \(\mathrm{kJ}\) when 30.0 \(\mathrm{g}\) of \(\mathrm{SO}_{2}(g)\) is formed from its elements.

Short answer

-138.95 kJ

Step-by-step solution

Determine the molar mass of \(\text{SO}_2\)

Calculate the molar mass of \(\text{SO}_2\) by adding the atomic masses of sulfur (S) and oxygen (O). The atomic mass of S is 32.06 g/mol and that of O is 16.00 g/mol. So, the molar mass of \(\text{SO}_2\) is: \[ \text{Molar Mass of SO}_2 = 32.06 \, \text{g/mol} + 2(16.00 \, \text{g/mol}) = 64.06 \, \text{g/mol} \]

Convert grams of \(\text{SO}_2\) to moles

Use the molar mass to convert 30.0 g of \(\text{SO}_2\) to moles. Use the formula: \[ \text{Number of moles} = \frac{\text{grams}}{\text{molar mass}} \] So, \[ \text{Number of moles of SO}_2 = \frac{30.0 \, \text{g}}{64.06 \, \text{g/mol}} \approx 0.468 \, \text{mol} \]

Calculate the energy given off

To find the energy given off, multiply the number of moles by the standard enthalpy of formation. The standard enthalpy of formation of \(\text{SO}_2\) is \(-296.8 \, \text{kJ/mol}\). Hence, the energy given off is: \[ \text{Energy} = \text{Number of moles} \times \text{standard enthalpy of formation} \] So, \[ \text{Energy} = 0.468 \, \text{mol} \times (-296.8 \, \text{kJ/mol}) \approx -138.95 \, \text{kJ} \]

Key concepts

Standard Enthalpy of Formation

Standard enthalpy of formation, often represented as \(\text{ΔH}_f^\text{o}\), is a crucial concept in chemistry. It refers to the heat change that occurs when one mole of a compound is formed from its elements in their standard states. Standard states mean the most stable form of the element at 1 atm pressure and typically at 25°C (298 K). For example, oxygen is considered to be O2 gas, and sulfur is S solid. The standard enthalpy of formation provides a reference point to determine how much energy is released or absorbed during chemical reactions. For sulfur dioxide (SO2), the standard enthalpy of formation is \(-296.8 \text{kJ/mol}\). This means when 1 mole of SO2 forms from sulfur and oxygen under standard conditions, 296.8 kJ of energy is released.

Molar Mass

The molar mass is the mass of one mole of a substance, which means it is the mass in grams of 6.022 \times\ 10^23 particles (usually atoms or molecules) of that substance. To find the molar mass of a compound, sum the atomic masses of all the atoms in its formula. For SO2, we need the atomic masses of sulfur (S) and oxygen (O). The atomic mass of sulfur is 32.06 g/mol, and the atomic mass of oxygen is 16.00 g/mol. Since there are two oxygen atoms in SO2, we multiply the atomic mass of oxygen by 2 and then add it to the atomic mass of sulfur: \[ \text{Molar Mass of SO}_2 = 32.06 \text{g/mol} + 2 \times 16.00 \text{g/mol} = 64.06 \text{g/mol} \] Understanding molar mass is vital because it allows us to convert between grams and moles, which is often necessary when dealing with chemical reactions.

Energy Given Off

When a chemical reaction occurs, energy is either absorbed or released. In the case of forming SO2 from sulfur and oxygen, energy is released. To calculate the energy given off, follow these steps:

• First, find the number of moles of SO2 using its molar mass and the given mass (30.0 grams) with the formula: \[ \text{Number of moles} = \frac{\text{grams}}{\text{molar mass}} = \frac{30.0 \text{g}}{64.06 \text{g/mol}} \] This gives approximately 0.468 moles of SO2.
• Then, multiply the number of moles by the standard enthalpy of formation of SO2 to get the energy released: \[ \text{Energy} = \text{Number of moles} \times \text{standard enthalpy of formation} = 0.468 \text{mol} \times (-296.8 \text{kJ/mol}) = -138.95 \text{kJ} \]

Therefore, approximately 138.95 kJ of energy is given off when 30.0 grams of SO2 forms from sulfur and oxygen.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It relies on balanced chemical equations to determine the proportions of substances involved. In stoichiometry, it's essential to understand:

• Balanced Equations: The chemical equation must be balanced, meaning the number of atoms of each element is the same on both sides of the reaction.
• Moles: Use the concept of moles to compare amounts of reactants and products.
• Converting Units: Conversion between units like grams, moles, and molecules is key.

For the reaction forming SO2, the balanced equation is: \[ S (s) + O_2 (g) \rightarrow SO_2 (g) \] Stoichiometry helps us use the molar mass of substances to go from grams to moles or vice versa and to understand how much of a product can be formed from given reactants. By understanding stoichiometry, we can accurately calculate quantities needed or produced in chemical reactions.