Chapter 2, Problem 2.14P

(a)

Interpretation Introduction

Interpretation:

Whether the statement “a sample of potassium chloride from Chile contains the same percent by mass of potassium as one from Poland” obeys the law of mass conservation, the law of definite composition or the law of multiple proportions is to be determined.

Concept introduction:

The law of mass conservation - Introduced by the famous French chemist Antoine Lavoisier, the law states that there is no change in the total mass of the substances that go into any physical or chemical reaction.

The law of definite composition - This law can be defined as; a particular compound maintains an exact universal proportion of elements in its composition, irrespective of the source. The proposal for this law was made by Joseph Proust.

The multiple proportions law - The ratio of the weights of an element with variable mass is small whole numbers when it forms more than one compound by combining with an element with fixed weight.

Answer to Problem 2.14P

The statement “a sample of potassium chloride from Chile contains the same percent by mass of potassium as one from Poland” obeys the law of definite composition.

Explanation of Solution

The law of definite composition explains that a compound is formed upon the chemical bonding between two or more different elements in a fixed proportion.

The molecular formula for $\text{KCl}$. The molecule is formed by the combination of potassium and chloride ions. The ratio of potassium and chloride ions is $1:1$. This ratio is maintained in the molecule of potassium chloride irrespective of its source. Whether the sample of potassium chloride has been sourced from Chile or Poland, the composition remains the same throughout the globe.

Conclusion

The statement “a sample of potassium chloride from Chile contains the same percent by mass of potassium as one from Poland” obeys the law of definite composition due to the presence of one ion each of potassium and chloride in samples obtained from different sources.

(b)

Interpretation Introduction

Interpretation:

Whether the statement “a flashbulb contains magnesium and oxygen before use and magnesium oxide afterward, but its mass does not change”obeys the law of mass conservation, law of definite composition or the law of multiple proportions is to be determined.

Concept introduction:

The law of mass conservation - Introduced by the famous French chemist Antoine Lavoisier, the law states that there is no change in the total mass of the substances that go into any physical or chemical reaction.

The law of definite composition - This law can be defined as; a particular compound maintains an exact universal proportion of elements in its composition, irrespective of the source. The proposal for this law was made by Joseph Proust.

The multiple proportions law - The ratio of the weights of an element with variable mass is small whole numbers when it forms more than one compound by combining with an element with fixed weight.

Answer to Problem 2.14P

The statement “a flashbulb contains magnesium and oxygen before use and magnesium oxide afterward, but its mass does not change” obeys the law of mass conservation.

Explanation of Solution

The reaction for the formation of a molecule of magnesium oxide is as follows: $\text{2Mg}+{\text{O}}_2\to 2\text{MgO}$

The equation shows the presence of two atoms of magnesium on each side of the equation. There are two atoms of oxygen on each side of the equation as well. The total mass of the reactants and products can be calculated as follows:

$\begin{array}{ccc}\text{Atoms}& \text{Total mass on the reactant side}& \text{Total mass on the product side}\\ \text{Mg}& 2\times 24.305\text{ g}=48.61\text{ g}& 2\times 24.305\text{ g}=48.61\text{ g}\\ \text{O}& 2\times 15.999\text{ g}=31.998\text{ g}& 2\times 15.999\text{ g}=31.998\text{ g}\\ \text{Total Mass}& 80.608\text{ g}& 80.608\text{ g}\end{array}$

From the calculations above, the observation can be made that the total mass of the reactant is equal to that of the product.

Conclusion

The statement “a flashbulb contains magnesium and oxygen before use and magnesium oxide afterward, but its mass does not change” obeys the law of mass conservation. The comparisons made by calculating the total mass of reactants and products prove it.

(c)

Interpretation Introduction

Interpretation:

Whether the statement “arsenic and oxygen form one compound that is $65.2$ mass % arsenic and another that is $75.8$ mass % arsenic” obeys the law of mass conservation, law of definite composition or the law of multiple proportions is to be determined.

Concept introduction:

The law of mass conservation - Introduced by the famous French chemist Antoine Lavoisier, the law states that there is no change in the total mass of the substances that go into any physical or chemical reaction.

The law of definite composition - This law can be defined as; a particular compound maintains an exact universal proportion of elements in its composition, irrespective of the source. The proposal for this law was made by Joseph Proust.

The multiple proportions law - The ratio of the weights of an element with variable mass is small whole numbers when it forms more than one compound by combining with an element with fixed weight.

The mass fraction of an element in a compound is defined as the ratio of the sum of the masses of all the atoms of that element to that of the mass of one mole of compound.

$\text{Mass fraction of X}=\frac{\text{Mass of element X in compound A }}{\text{mass of compound A}}$

Mass percent of an element represents the percentage concentration of that element in a compound. It is equal to the mass fraction expressed as a percentage. The general formula to calculate the mass percent of an element A in a compound is as follows:

$\begin{array}{c}\text{Mass \% of element A}=\left(\frac{\text{Mass of element X in compound A }}{\text{mass of compound A}}\right)\left(100\right)\\ =\left(\text{Mass fraction of A}\right)\left(100\right)\end{array}$

Answer to Problem 2.14P

The statement “arsenic and oxygen form one compound that is $65.2\text{mass }\%$ arsenic and another that is $75\text{ mass }\%$ arsenic” obeys the law of multiple proportions.

Explanation of Solution

The two compounds arsenic formed by the combination of arsenic and oxygen atoms are ${\text{As}}_2{\text{O}}_3$ and ${\text{As}}_2{\text{O}}_5$. In both the compounds, the atoms of arsenic remain the same, while the atoms of oxygen are 3 and 5 respectively.

The total mass of ${\text{As}}_2{\text{O}}_3$ can be calculated as follows:

${\text{The total mass of As}}_2{\text{O}}_3=\left[\left(2\right)\left(\text{molar mass of As}\right)+\left(3\right)\left(\text{molar mass of O}\right)\right]$ (1)

Substitute $75\text{ g}$ for the molar mass of $\text{As}$ and $16\text{ g}$ for the molar mass of $\text{O}$ in equation (1).

$\begin{array}{c}{\text{The total mass of As}}_2{\text{O}}_3\text{is}=\left[\left(2\right)\left(75\text{ g}\right)+\left(3\right)\left(16\text{ g}\right)\right]\\ =150\text{ g}+48\text{ g}\\ =198\text{ g}\end{array}$

The mass of arsenic $\left(\text{As}\right)$ present in the compound ${\text{As}}_2{\text{O}}_3$ is,

$\text{mass of As}=\left(\text{number of atoms of As}\right)\left(\text{molar mass of As}\right)$ (2)

Substitute 2 for number of atoms of $\text{As}$ and $75\text{ g}$ for the molar mass of $\text{As}$ in equation (2).

$\begin{array}{c}\text{mass of As}=\left(\text{2}\right)\left(75\text{ g}\right)\\ =150\text{ g}\end{array}$

The formula to calculate the mass percent of arsenic in ${\text{As}}_2{\text{O}}_3$ is,

$\text{mass \% of As}=\left(\frac{\text{mass of As}}{{\text{mass of As}}_{\text{2}}{\text{O}}_{\text{3}}}\right)100\text{ \%}$ (3)

Substitute $150\text{ g}$ for the mass of $\text{As}$ and $198\text{ g}$ for the mass of ${\text{As}}_2{\text{O}}_3$ in equation (3).

$\begin{array}{c}\text{mass \% of As}=\left(\frac{150\text{ g}}{198\text{ g}}\right)100\text{ \%}\\ =75.75\%\end{array}$

The total mass of ${\text{As}}_2{\text{O}}_5$ can be calculated as follows:

${\text{The total mass of As}}_2{\text{O}}_5=\left[\left(2\right)\left(\text{molar mass of As}\right)+\left(5\right)\left(\text{molar mass of O}\right)\right]$ (4)

Substitute $75\text{ g}$ for the molar mass of $\text{As}$ and $16\text{ g}$ for the molar mass of $\text{O}$ in equation (4).

$\begin{array}{c}{\text{The total mass of As}}_2{\text{O}}_5\text{is}=\left[\left(2\right)\left(75\text{ g}\right)+\left(5\right)\left(16\text{ g}\right)\right]\\ =150\text{ g}+80\text{ g}\\ =230\text{ g}\end{array}$

The formula to calculate the mass percent of arsenic in ${\text{As}}_2{\text{O}}_5$ is,

$\text{mass \% of As}=\left(\frac{\text{mass of As}}{{\text{mass of As}}_2{\text{O}}_5}\right)100\text{ \%}$ (5)

Substitute $150\text{ g}$ for the mass of $\text{As}$ and $230\text{ g}$ for the mass of ${\text{As}}_2{\text{O}}_3$ in equation (5).

$\begin{array}{c}\text{mass \% of As}=\left(\frac{150\text{ g}}{230\text{ g}}\right)100\text{ \%}\\ =65.20\%\end{array}$

The number of atoms of arsenic being constant in both the compounds, the arsenic atoms combines with oxygen atoms whose proportions are different in both the compounds.

The total mass of oxygen atoms in compound ${\text{As}}_2{\text{O}}_3$ and compound ${\text{As}}_2{\text{O}}_5$ are $\text{48 g}$ and $\text{80 g}$ respectively. The masses of oxygen which combine with a fixed mass of arsenic bear a simple ratio of $3:5$.

Conclusion

The statement “arsenic and oxygen form one compound that is $65.2\text{mass }\%$ arsenic and another that is $75\text{ mass }\%$ arsenic” obeys the law of multiple proportions due to the ratio of the masses of oxygen atoms in the compounds being $3:5$, which represents the ratio of small whole numbers.