Question

At \(\mathrm{STP}, 1.0 \mathrm{L}\) \(\mathrm{Br}_{2}\) 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 is \(\mathrm{BrF}_3\).

Step-by-step solution

Determine the mole ratios

At STP (Standard Temperature and Pressure), 1 L of any gas contains the same number of moles. The volume ratio of the reactants, \(\mathrm{Br}_2\) and \(\mathrm{F}_2\), is 1:3, which means for every liter of \(\mathrm{Br}_2\), 3 liters of \(\mathrm{F}_2\) react completely with it. Let's denote the volume of the produced product as \(\mathrm{X}\)L.

Apply Avogadro's law

Assume that there are y moles of \(\mathrm{Br}_2\) that react completely with 3y moles of \(\mathrm{F}_2\) to yield 2y moles of the product. Now, apply Avogadro's law: at the same temperature and pressure, equal volumes of all gases contain the same number of moles. So if the moles of \(\mathrm{Br}_2\) is y, and the moles of \(\mathrm{F}_2\) needed to react completely is 3y, we can write the proportion: \( \frac{moles \space of \space Br_2}{moles \space of \space F_2} = \frac{1}{3} \) That is: \(\frac{y}{3y}= \frac{1}{3}\)

Determine the formula of the product

Since the reaction is balanced, 1 mole of \(\mathrm{Br}_2\) will react completely with 3 moles of \(\mathrm{F}_2\) (as we found from the proportion above), producing 2 moles of the product. This indicates that 1 \(\mathrm{Br}\) atom combines with 1.5 \(\mathrm{F}\) atoms to form the product. However, we cannot have a fraction of an atom in a chemical formula. To balance this, we can multiply both the reactants and the product by 2: \(2 \mathrm{Br}_2 + 3 \cdot 2 \mathrm{F}_2 \rightarrow 4 \mathrm{X}\) This means that 2 \(\mathrm{Br}\) atoms will react with 3 \(\mathrm{F}\) atoms, yielding 4 \(\mathrm{X}\) atoms. Therefore, the formula of the product, where \(\mathrm{Br}\) and \(\mathrm{F}\) are combined, is \(\mathrm{BrF}_3\).

Key concepts

STP (Standard Temperature and Pressure)

Standard Temperature and Pressure, known as STP, is a reference point used in chemistry to denote a set of conditions for experiments and calculations involving gases. These conditions are defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm (101.3 kPa). This standardization allows scientists to compare experimental results consistently.
Using STP conditions, it is easier to predict how gases will behave since they will follow the ideal gas laws more closely. At STP, one mole of any ideal gas occupies a volume of 22.414 liters. This consistent volume allows chemists to simplify calculations and compare reactions easily. In the exercise given, determining volume ratios at STP ensures that we can directly relate gas volumes to moles without complex conversions. Understanding volume relationships at STP is crucial when applying Avogadro's Law and calculating mole ratios in chemical reactions.

Avogadro's Law

Avogadro's Law is a fundamental principle in chemistry stating that equal volumes of gases, under the same temperature and pressure, contain an equal number of molecules. This law is significant because it makes it possible to correlate the volume of a gas with the number of moles, simplifying calculations involving gaseous reactions.
To apply Avogadro’s Law, you only need to ensure that the gases being compared are under identical conditions of temperature and pressure. For example, if you have multiple gases reacting at STP, you know that their volume ratios are equivalent to their mole ratios. In the exercise problem, Avogadro's Law allows us to conclude that 1 L of \(\mathrm{Br}_{2}\)must contain the same quantity of molecules as 1 L of \(\mathrm{F}_{2}\). When \(\mathrm{Br}_{2}\)reacts with \(\mathrm{F}_{2}\) at a 1:3 volume ratio, they produce a product as dictated by the conserved mole balance implied by their volumes.

Mole Ratios

Mole ratios are crucial in stoichiometry, allowing chemists to determine the proportions in which reactants combine to form products in a chemical reaction. These ratios are derived from the coefficients of a balanced chemical equation and are used to calculate the amounts of reactants needed or products formed.
In reactions involving gases, like the problem provided, STP conditions further simplify these calculations. From the exercise, we see that the volume ratio of the reactants \(\mathrm{Br}_{2}\)and \(\mathrm{F}_{2}\)is 1:3. At STP, this directly translates into a mole ratio, thanks to Avogadro’s Law. Therefore, for every 1 mole of \(\mathrm{Br}_{2}\), 3 moles of \(\mathrm{F}_{2}\) fully react forming the product. These ratios help us infer that the product formed is \(\mathrm{BrF}_{3}\).To ensure no fractions are present in the chemical formula, it is often necessary to multiply through by whole numbers, resulting in balanced whole number coefficients for the chemical equation. This step gives the precise stoichiometric balance needed in chemical equations, making it possible for chemists to predict reaction outcomes accurately.