Question

Given the balanced equation, calculate the mass of product that can be prepared from \(3.45 \mathrm{~g}\) of bismuth metal. $$2 \mathrm{Bi}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{BiCl}_{3}(s)$$

Short answer

The mass of \(\text{BiCl}_3\) produced is approximately 5.21 grams.

Step-by-step solution

Determine Molar Mass of Bismuth

First, we need to calculate the molar mass of bismuth (Bi). The atomic mass of bismuth is approximately 209 grams per mole.

Convert Mass to Moles

Convert the given mass of bismuth into moles using the formula: \[ \text{moles of Bi} = \frac{\text{mass of Bi (in grams)}}{\text{molar mass of Bi (in g/mol)}} \] Substitute the known values: \[ \text{moles of Bi} = \frac{3.45 \text{ g}}{209 \text{ g/mol}} \approx 0.0165 \text{ moles} \]

Use the Mole Ratio

From the balanced equation, the mole ratio of Bi to \(\text{BiCl}_3\) is 1:1. Therefore, the moles of bismuth will be equal to the moles of \(\text{BiCl}_3\).

Calculate Molar Mass of Product

Next, calculate the molar mass of \(\text{BiCl}_3\). The atomic masses are: Bi = 209 g/mol and Cl = 35.5 g/mol. So, the molar mass of \(\text{BiCl}_3\) is calculated as follows: \[ \text{molar mass of } \text{BiCl}_3 = 209 + (3 \times 35.5) = 209 + 106.5 = 315.5 \text{ g/mol} \]

Convert Moles of Product to Mass

Use the molar mass to convert the moles of \(\text{BiCl}_3\) into grams using the formula: \[ \text{mass of } \text{BiCl}_3 = \text{moles of } \text{BiCl}_3 \times \text{molar mass of } \text{BiCl}_3 \] Thus, \[ \text{mass of } \text{BiCl}_3 = 0.0165 \times 315.5 = 5.21 \text{ grams} \]

Key concepts

Mole Conversion

Mole conversion is a fundamental concept in chemistry that helps us connect the mass of a substance to the number of particles it contains. This is based on the mole, a unit that measures the amount of substance. We use Avogadro's number, which is approximately \(6.022 \times 10^{23}\), to define one mole of any substance. By converting mass to moles, we can easily find out how many molecules or atoms are present in a sample.

The process begins with determining the number of moles from a given mass using the formula:

• \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)

In the example of bismuth, with a mass of \(3.45\text{ g}\) and a molar mass of \(209\text{ g/mol}\), the conversion to moles helps us know how much of bismuth we actually have. By dividing the mass by the molar mass, we find the moles involved, enabling further chemical calculations.

Understanding mole conversion is a crucial step in stoichiometry that links all further calculations to real-world quantities.

Molar Mass Calculation

Molar mass is an essential concept in chemistry, representing the sum of all the atomic masses in a molecule or compound. It is expressed in grams per mole (g/mol), providing a bridge between the atomic and macroscopic worlds of chemistry.

To calculate the molar mass, we simply add up the atomic masses of all the elements present in the compound.

• For bismuth (Bi), the atomic mass is \(209\text{ g/mol}\).
• For chlorine (Cl), the atomic mass is \(35.5\text{ g/mol}\).

In the given chemical reaction, we calculate the molar mass of \(\text{BiCl}_3\) by considering the contribution of each atom:

• \(\text{Molar mass of } \text{BiCl}_3 = 209 + (3 \times 35.5) = 315.5 \text{ g/mol}\)

This calculated molar mass is then used to convert moles back into grams to find out the mass of product formed. Understanding molar mass calculation is vital for stoichiometry as it assists in determining the amount of reactants and products involved in chemical reactions.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. They are usually represented by balanced chemical equations which show the reactants on the left and the products on the right, separated by an arrow.

A balanced equation ensures that the number of atoms of each element is the same on both the reactant and product sides. It follows the law of conservation of mass, meaning mass is neither created nor destroyed. Consider the equation:

• \(2 \text{Bi}(s) + 3 \text{Cl}_2(g) \rightarrow 2 \text{BiCl}_3(s)\)

In this reaction, bismuth metal reacts with chlorine gas to form bismuth chloride. The coefficients (the numbers before each compound) indicate the mole ratio of reactants to products. Here, every 2 moles of bismuth reacts with 3 moles of chlorine gas to produce 2 moles of \(\text{BiCl}_3\), highlighting a 1:1 ratio between \(\text{Bi}\) and \(\text{BiCl}_3\).

Understanding chemical reactions and the stoichiometry involved is critical for predicting the outcome of reactions and for calculating the amounts of reactants needed or products formed.