Question

At STP, \(1.0 \mathrm{L}\) \(Br\) \(_{2}\) reacts completely with \(3.0 \mathrm{L} \mathrm{F}_{2}\), producing \(2.0 \mathrm{L}\) of a product. What is the formula of the product? (All substances are gases.)

Short answer

The formula of the product produced when 1.0 L Br₂ reacts completely with 3.0 L F₂ at STP is BrF₃.

Step-by-step solution

Identify the given information and write down the balanced equation

First, let's identify the given information: - 1.0 L of Br₂ reacts completely - 3.0 L of F₂ are also reacting - 2.0 L of a product is produced The balanced equation is currently unknown, so we'll represent it as follows: Br₂(g) + F₂(g) ⟶ Product(g)

Use Avogadro's law

According to Avogadro's law, at the same temperature and pressure, equal volumes of different gases contain an equal number of molecules (or moles). Therefore, we can determine the mole ratios of the reactants and the product based on the given volumes. From the given information, we know: - 1.0 L Br₂ = 1 mole Br₂ - 3.0 L F₂ = 3 moles F₂ - 2.0 L Product = 2 moles Product

Determine the mole ratio of the reactants and product

Now that we have the moles of the reactants and product, we can determine their ratios. For Br₂ and F₂, we notice that the ratio of Br₂ to F₂ is 1:3 (1 mole Br₂: 3 moles F₂), and the product ratio is 2 moles. To find the complete ratio of the reactants to the product, let's use a bit of intuition. We know that Br₂ and F₂ are diatomic (Br₂ & F₂). Since Br₂ is interacting with three times more F₂, it is logical to deduce that each Br might form a bond with three F atoms. Thus, we can propose a probable product - BrF₃.

Revise the original balanced equation and confirm the mole ratios

With the probable formula of the product, we can now revise the original balanced equation: Br₂(g) + 3F₂(g) ⟶ 2BrF₃(g) Now, let's confirm the mole ratios with this equation: - 1 mol Br₂ : 3 mol F₂ - Producing 2 mol of BrF₃ The revised balanced equation is consistent with the given information in terms of both reactant ratios and product volume. Hence, we can conclude:

Answer the question

The formula of the product produced when 1.0 L Br₂ reacts completely with 3.0 L F₂ at STP is BrF₃.

Key concepts

Avogadro's law

Avogadro's law is a fundamental concept in chemistry that relates the volume of gases to the number of molecules they contain, provided that they are under the same conditions of temperature and pressure. According to this law, equal volumes of gases, at the same temperature and pressure, will have the same number of molecules. This important principle allows chemists to compare the amounts of gases by simply looking at their volumes.

In the exercise, we use Avogadro's law to deduce the amounts of each reactant and product because they are all gases measured at standard temperature and pressure (STP). By assuming one mole of gas corresponds to one liter, the problem tells us:

• 1.0 L of Br₂ equals 1 mole of Br₂.
• 3.0 L of F₂ equals 3 moles of F₂.
• 2.0 L of the product equals 2 moles of the product.

This use of Avogadro's law enables us to apply stoichiometry without knowing the specific compound volumes or pressures beyond their measured amounts, thereby simplifying the calculation and understanding of the reaction.

Balanced chemical equation

A balanced chemical equation is essential to understanding the stoichiometry of a reaction. It ensures that the same number of each type of atom appears on both sides of the equation, reflecting the conservation of mass. In chemistry, balancing equations involves adjusting the coefficients placed before compounds to reflect equal numbers of atoms for each element involved in the reaction.

In the case of this reaction:

• The balanced equation proposed is: \( Br₂(g) + 3F₂(g) \rightarrow 2BrF₃(g)\)

This equation reflects that 1 molecule of \(Br₂\) reacts with 3 molecules of \(F₂\), producing 2 molecules of \(BrF₃\). This setup fulfills the requirements of having balanced numbers of \(Br\) and \(F\) atoms on both sides of the equation, thus confirming the correct stoichiometry.

Gas reactions at STP

Standard Temperature and Pressure (STP) is a reference point commonly used in chemistry to standardize different measurements. At STP, the temperature is considered to be 0°C (273.15 K) and the pressure is 1 atmosphere (atm). These conditions simplify calculations involving gases because 1 mole of any ideal gas occupies a volume of 22.4 liters.

Using STP conditions in the exercise allows for straightforward interpretation and comparison of gas volumes without additional conversions for temperature or pressure differences:

• A calculated volume corresponds directly to the number of moles due to Avogadro's law.
• It makes the reaction scalable for hypothetical scenarios where different quantities of gases are used.

Understanding reactions at STP provides a foundation for more complex gas calculations under varying conditions.bul> This is vital for predicting reaction outcomes and in real-world applications, such as industrial chemical processes or atmospheric studies.