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 \( BrF_{3} \).

Step-by-step solution

1. Write down the unbalanced chemical equation

Based on the information given, we can write down the unbalanced chemical equation: \[ Br_{2} + F_{2} \rightarrow ? \]

2. Write the balanced chemical equation

We know that the reaction occurs at STP, which means that both reactants and products behave as ideal gases. The balanced chemical equation for the given reaction can be derived as follows: \[ Br_{2} + 3F_{2} \rightarrow 2BrF_{3} \] This equation indicates that one mole of bromine reacts with three moles of fluorine to produce two moles of the product.

3. Calculate the mole ratio of reactants:

At STP, the volume of a gas is directly proportional to the number of moles. Therefore, the mole ratio of the reactants is: \( \frac{n_{Br_{2}}}{n_{F_{2}}} = \frac{1.0 L}{3.0 L} = \frac{1}{3} \) where \( n_{Br_{2}} \) and \( n_{F_{2}} \) represent the moles of bromine and fluorine, respectively.

4. Compare the calculated mole ratio with the balanced chemical equation

According to the balanced chemical equation, 1 mole of bromine reacts with 3 moles of fluorine: \( \frac{n_{Br_{2}}}{n_{F_{2}}} = \frac{1}{3} \) This is the same as the calculated mole ratio of the reactants.

5. Determine the formula of the product

As we have the stoichiometry of the reaction from the balanced chemical equation and the volume of product formed, we can use that to determine the formula of the product. The balanced chemical equation: \[ Br_{2} + 3F_{2} \rightarrow 2BrF_{3} \] Since \(2.0 L\) of a product is formed, and we have this relationship from the balanced equation: \( 2 \: moles \: Product = 1.0 \: L \: Br_{2} \: reactant \) Thus, the product formed is \( BrF_{3} \). The formula of the product is \( BrF_{3} \).