Chapter 4, Problem 136SCQ

A weighed sample of iron (Fe) is added to liquid bromine (Br₂) and allowed to react completely. The reaction produces a single product, which can be isolated and weighed. The experiment was repeated a number of times with different masses of iron but with the same mass of bromine (see graph below).

1. (a) What mass of Br₂ is used when the reaction consumes 2.0 g of Fe?
2. (b) What is the mole ratio of Br₂ to Fe in the reaction?
3. (c) What is the empirical formula of the product?
4. (d) Write the balanced chemical equation tor the reaction of iron and bromine.
5. (e) What is the name of the reaction product?
6. (f) Which statement or statements best describe the experiments summarized by the graph?
   1. (i) When 1.00 g of Fe is added to the Br_2, Fe is the limiting reagent.
   2. (ii) When 3.50 g of Fe is added to the Br₂, there is an excess of Br₂.
   3. (iii) When 2.50 g of Fe is added to the Br₂, both reactanu are used up compietely.
   4. (iv) When 2.00 g of Fe is added to the Br₂, 10.8 g of product is formed. The percent yield must therefore be 20.0%.

Interpretation Introduction

Interpretation:

The mass of $B{r}_2$ used when the reaction consumes $2.0gof\text{}Fe$ has to be calculated.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

Explanation of Solution

Herein weighted sample of iron is added to liquid bromine and allowed to react completely. The reaction produces a single product which can be isolated and weighed.

The experiment was repeated a number of times with different masses of iron but with the same mass of bromine. The graphical representation for this reaction is,

                        

From the graph it is clear that, when $2gofFe$ consumed $11g$ of product is formed.

So that the mass of $B{r}_2$ used when the reaction consumes $2.0gof\text{}Fe$ is,

                  $\text{11}-\text{2}=\text{9}\text{g}$

The mass of $B{r}_2$ used when the reaction consumes $2.0gof\text{}Fe$ is $\text{9}\text{g}$

Interpretation Introduction

Interpretation:

The mole ratio of $B{r}_2$ to $Fe$ in the reaction has to be answered.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

Explanation of Solution

Herein weighted sample of iron is added to liquid bromine and allowed to react completely. The reaction produces a single product which can be isolated and weighed.

The experiment was repeated a number of times with different masses of iron but with the same mass of bromine. And $9g$ of $B{r}_2$ is used when the reaction consumes $2.0gof\text{}Fe$.

The mole ratio of $B{r}_2$ to $Fe$ in the reaction can be calculated from its number of moles as follows,

Number of moles in $9gofBr$ = $\frac{\text{9}\text{g}}{\text{80}\text{g/mol}}\text{=}\text{0}\text{.1125}\text{mol}$

Number of moles in $2gofFe$ = $\frac{\text{2}\text{g}}{\text{56}\text{g/mol}}\text{=}\text{0}\text{.0357}\text{mol}$

Mole ratios of elements are determined by dividing the number of moles of each element by the smallest amount present.

           $\frac{\text{0}\text{.1125}\text{mol}\text{Br}}{\text{0}\text{.0357}\text{mol}\text{Fe}}\text{=}\frac{\text{3}\text{.15}\text{mol}\text{Br}}{\text{1}\text{mol}\text{Fe}}$

Therefore the mole ratio of $B{r}_2$ to $Fe$ in the reaction is, $\text{Br:}\text{Fe}=\text{3:1}$         

Interpretation Introduction

Interpretation:

The empirical formula of the product has to be calculated.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

Explanation of Solution

Herein weighted sample of iron is added to liquid bromine and allowed to react completely. The reaction produces a single product which can be isolated and weighed.

The experiment was repeated a number of times with different masses of iron but with the same mass of bromine. And $9g$ of $B{r}_2$ is used when the reaction consumes $2.0gof\text{}Fe$.

The mole ratio of $B{r}_2$ to $Fe$ in the reaction can be calculated from its number of moles as follows,

Number of moles in $9gofBr$ = $\frac{\text{9}\text{g}}{\text{80}\text{g/mol}}\text{=}\text{0}\text{.1125}\text{mol}$

Number of moles in $2gofFe$ = $\frac{\text{2}\text{g}}{\text{56}\text{g/mol}}\text{=}\text{0}\text{.0357}\text{mol}$

Mole ratios of elements are determined by dividing the number of moles of each element by the smallest amount present.

           $\frac{\text{0}\text{.1125}\text{mol}\text{Br}}{\text{0}\text{.0357}\text{mol}\text{Fe}}\text{=}\frac{\text{3}\text{.15}\text{mol}\text{Br}}{\text{1}\text{mol}\text{Fe}}$

Therefore the mole ratio of $B{r}_2$ to $Fe$ in the reaction is, $\text{Br:}\text{Fe}=\text{3:1}$

The empirical formula gives the simplest whole number ratio. The translation of this ratio ($\frac{4}{1}$) to whole number ratio can usually be done quickly by trial and error.

So the empirical formula of product is ${\text{FeBr}}_{\text{3}}$.

Interpretation Introduction

Interpretation:

The balanced chemical equation for the reaction of iron and bromine has to be written.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

Explanation of Solution

Herein weighted sample of iron is added to liquid bromine and allowed to react completely. The reaction produces a single product which can be isolated and weighed.

The balanced equation for this reaction is,

            $\text{2Fe}\text{+}{\text{3Br}}_{\text{2}}\to {\text{2FeBr}}_{\text{3}}$

Interpretation Introduction

Interpretation:

The reaction product has to be predicted.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

Explanation of Solution

Herein weighted sample of iron is added to liquid bromine and allowed to react completely. The reaction produces a single product which can be isolated and weighed.

The balanced equation for this reaction is,

            $\text{2Fe}\text{+}{\text{3Br}}_{\text{2}}\to {\text{2FeBr}}_{\text{3}}$

The name of the product is $\text{Iron}\text{(III)}\text{bromide}\text{or}\text{Ferric}\text{bromide}$

Interpretation Introduction

Interpretation:

By using the graphical data given set of questions has to be answered.

Concept introduction:

• Empirical formula of a compound represents the smallest whole number relative ratio of elements in that compound.
• $Numberofmole=\frac{Givenmassofthesubs\tan ce}{Molarmass}$                 
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol).
• For chemical reaction balanced chemical reaction equation written in accordance with the Law of conservation of mass.
  • Law of conservation of mass states that for a reaction total mass of the reactant and product must be equal. Stoichiometric factor is a relationship between reactant and product which is obtained from the balanced chemical equation for a particular reaction.
  • Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.

The statement (i) “when $1.00g$ of $Fe$ is added to the $B{r}_2$, $Fe$ is the limiting reagent” is the correct statement to describe the experiments summarized by the graph.

Explanation of Solution

Reason for the correct option:

    

From the graph the mass of product produced is predominantly depend on the mass of iron. And so it is completely consumed in to product. Therefore Fe acts as the limiting reagent.  

Reason for the incorrect options:

Incorrect statement and its reasons are explained below,

 (ii) When $3.50g$ of Fe is added to the $B{r}_2$, there is an excess of $B{r}_2$.

In this condition $B{r}_2$ has to acts as a limiting reagent. But in this statement $B{r}_2$ is excess. Therefore this statement is incorrect.

(iii) When 2.50 g of Fe is added to the $B{r}_2$, both reactants are used up completely.

When $1.00g$ of $Fe$ is added to the $B{r}_2$, $Fe$ is the limiting reagent and so if 2.50 g of Fe is added to the $B{r}_2$, the reactant $B{r}_2$ has to be present in excess. Therefore this statement is incorrect.

(iv)When 2.00 g of Fe is added to the $B{r}_2$, 10.8 g of product is formed. The percent yield must therefore be 20.0%.

If 2.00 g of Fe is added to the $B{r}_2$, 11 g of product is formed. Here in this statement 10.8 g of product formed. So the percent yield will be more than 20.0%. And so this is an incorrect statement.