Question

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

Short answer

The formula of the product is bromine trifluoride \(\mathrm{(BrF_3)}\).

Step-by-step solution

Recall the volume relationships at STP

At STP (standard temperature and pressure), 1 mol of any gas occupies 22.4 L. In reactions involving gases at STP, the volumes of gases are directly proportional to the moles of the gas and can be related by their stoichiometric coefficients.

Identify the balanced chemical equation

We need to identify the balanced chemical equation of the reaction between Bromine gas (\(\mathrm{Br_2}\)) and Fluorine gas (\(\mathrm{F_2}\)) to find the formula of the product. The balanced equation is: \(\mathrm{Br_2} + 3\mathrm{F_2} \rightarrow 2\mathrm{BrF_3}\) As we can see, bromine gas reacts with fluorine gas to form bromine trifluoride (BrF3).

Apply the volume relationships at STP

Now we have the balanced equation and the given volumes. Let's see how these volumes fit into the volume relationship of the chemical equation. Given: 1.0 L Br2 3.0 L F2 2.0 L Product Looking at the balanced chemical equation, notice that the ratio of the volumes of the gases is exactly the same as the ratio of the stoichiometric coefficients, i.e., \( \frac{1.0 L\ \mathrm{Br}_2}{3.0 L\ \mathrm{F}_2} = \frac{1}{3} \) And \( \frac{2.0 L\ \mathrm{PRODUCT}}{1.0 L\ \mathrm{Br}_2}=2 \) This relation confirms that the balanced chemical equation satisfies the volume relationship at STP.

Determine the formula of the product

From the balanced chemical equation, we've determined that the product is bromine trifluoride (\(\mathrm{BrF_3}\)).

Key concepts

Standard Temperature and Pressure

When we talk about reactions involving gases, it's fundamental to set a common reference for conditions under which the gas volumes are measured. This reference is known as Standard Temperature and Pressure (STP). STP is defined as a temperature of 273.15 Kelvin (0 degrees Celsius) and a pressure of 1 atmosphere. In these conditions, gases have a predictable behavior, and it's agreed that at STP, one mole of any ideal gas occupies 22.4 liters (L). This uniformity allows chemists to compare and predict gas volumes during chemical reactions.

Understanding these conditions is crucial not only for calculating gas volumes but also for interpreting experiments and laboratory results correctly. When a question mentions that a reaction is taking place at STP, as in the exercise provided, it's an invitation to apply this 22.4 L per mole volume in stoichiometric calculations.

Molar Volume of Gas

The molar volume of a gas is the volume occupied by one mole of the gas at specified conditions. At STP, the molar volume is a constant 22.4 L/mol for all ideal gases. This concept is a cornerstone of gas stoichiometry because it establishes a direct link between the number of moles of gas and the volume it occupies. It's like having a universal converter between the microscopic scale (moles, particles) and the macroscopic scale (liters, observable volumes).

To calculate the volume of a gas from the number of moles, simply multiply the number of moles by 22.4 L/mol at STP. Conversely, to find out the number of moles from a given volume, divide the volume by 22.4 L/mol. This straightforward relationship is immensely helpful in solving problems related to gas reactions under standard conditions.

Gas Volume Stoichiometry

Gas volume stoichiometry applies the principles of stoichiometry—ratios and proportions originating from the balanced chemical equation—to gases, focusing specifically on their volumes. Given the constant molar volume of a gas at STP, volume ratios between reactants and products directly translate to mole ratios. This means that, in a balanced chemical equation, the coefficients indicate not only the relative amounts of substances in moles but also the relative volumes of gases involved in the reaction at STP.

When dealing with a stoichiometric problem involving gases, like in our exercise, it's all about using the ratios of the volumes according to the balanced equation. If 1.0 L of Br2 reacts with 3.0 L of F2, following the 1:3 stoichiometric ratio, and 2.0 L of a product is formed per 1.0 L Br2, the product formation aligns with the balanced equation. Always ensure the equation is balanced before applying gas volume ratios, as this is the key to accurate stoichiometry solutions.

Chemical Reaction Balancing

Balanced chemical equations are at the heart of stoichiometry. They provide the blueprints for how atoms are rearranged during a chemical reaction, ensuring the law of conservation of mass is respected—meaning that atoms aren't created or destroyed. Each species involved in the reaction is represented with its correct formula, and coefficients are added to ensure that the number of atoms for each element is the same on both sides of the equation.

Looking at our exercise, the balanced chemical equation is essential for correlating the reactants' volumes to the products'. In the equation, \(\mathrm{Br_2} + 3\mathrm{F_2} \rightarrow 2\mathrm{BrF_3}\), the coefficients 1, 3, and 2 tell us how the volumes of the reacting gases and the product gas relate to one another. Always confirm you have a balanced equation because that is the roadmap to predicting volumes, masses, and other quantities of substances produced or required in the reaction.