Chapter 2, Problem 2.13P

(a)

Interpretation Introduction

Interpretation:Mass of fluorine in $2.76\text{g}$ fluorite mineral is to be calculated.

Concept introduction:Total mass of a compound $\left(\text{AB}\right)$ is calculated by addition of the mass of its constituent element $\left(\text{A}\right)$ and $\left(\text{B}\right)$ .

The formula to calculate the mass of compound $\left(\text{AB}\right)$ is as follows:

  $\text{Mass}\text{of}\text{compound}\text{AB}=\text{Mass}\text{of}\text{element}\text{A}+\text{Mass}\text{of}\text{element}\text{B}$

Answer to Problem 2.13P

The mass of fluorine in the sample is $1.34\text{g}$ .

Explanation of Solution

Given information:

Total mass of fluorite sample $2.76\text{g}$ , mass of calcium in the sample is $1.42\text{g}$ .

The formula to calculate the mass of fluorine in fluorite sample is as follows:

  $\text{Total}\text{mass}\text{of}\text{fluorite sample}=\text{Mass}\text{of}\text{calcium}+\text{Mass}\text{of}\text{fluorine}$

Rearrange the above formula.

  $\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}-\text{Mass}\text{of}\text{calcium}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of calcium in fluorite sample is $1.42\text{g}$ .

Substitute the values in above formula.

  $\begin{array}{c}\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite sample}-\text{Mass}\text{of}\text{calcium}\\ =2.76\text{g}-1.42\text{g}\\ =1.34\text{g}\end{array}$

(b)

Interpretation Introduction

Interpretation: Mass fractions of calcium and fluorine are to be calculated in fluorite sample.

Concept introduction: To calculate the mass fraction of an element in a compound, divide the total mass of that element in that compound by total mass of that compound.

The formula to calculate the mass fraction of an element is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{an}\text{element}=\frac{\text{Total}\text{mass}\text{of}\text{that}\text{element}\text{in}\text{that}\text{compound}}{\text{Total}\text{mass}\text{of}\text{that}\text{compound}}$

Answer to Problem 2.13P

The mass fraction of calcium in fluorite sample is $0.5145$ and the mass fraction of fluorine in fluorite sample is $0.4855$ .

Explanation of Solution

Given information:

Total mass of fluorite sample $2.76\text{g}$ , mass of calcium in the sample is $1.42\text{g}$ .

The formula to calculate the mass of fluorine in fluorite sample is as follows:

  $\text{Total}\text{mass}\text{of}\text{fluorite sample}=\text{Mass}\text{of}\text{calcium}+\text{Mass}\text{of}\text{fluorine}$

Rearrange the above formula.

  $\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}-\text{Mass}\text{of}\text{calcium}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of calcium in fluorite sample is $1.42\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite sample}-\text{Mass}\text{of}\text{calcium}\\ =2.76\text{g}-1.42\text{g}\\ =1.34\text{g}\end{array}$

The formula to calculation the mass fraction of calcium in fluorite sample is done as follows:

  $\text{Mass}\text{fraction}\text{of}\text{calcium}\text{in}\text{fluorite}\text{sample}=\frac{\text{Total}\text{mass}\text{of}\text{calcium}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of calcium in fluorite sample is $1.42\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{calcium}\text{in}\text{fluorite}\text{sample}=\frac{\text{Total}\text{mass}\text{of}\text{calcium}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}\\ =\frac{1.42\text{g}}{2.76\text{g}}\\ =0.5145\end{array}$

Formula to calculate themass fraction of fluorine in fluorite sample is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{fluorine}\text{in}\text{fluorite}\text{sample}=\frac{\text{Total}\text{mass}\text{of}\text{fluorine}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of fluorine in fluorite sample is $1.34\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{fluorine}\text{in}\text{fluorite}\text{sample}=\frac{\text{Total}\text{mass}\text{of}\text{fluorine}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}\\ =\frac{1.34\text{g}}{2.76\text{g}}\\ =0.4855\end{array}$

(c)

Interpretation Introduction

Interpretation:Mass percent of calcium and fluorine are to be calculated in fluorite sample.

Concept introduction: To calculate the mass fraction of an element in a compound, divide the total mass of that element in that compound by total mass of that compound.

The formula to calculate the mass fraction of an element is as follows:

  $\text{Mass}\text{fraction}\text{of element}=\frac{\text{Total}\text{mass}\text{of}\text{that}\text{element}\text{in}\text{that}\text{compound}}{\text{Total}\text{mass}\text{of}\text{that}\text{compound}}$

Formula to calculate the mass percent of an element is as follows:

  $\text{Mass}\text{percent}\text{of}\text{an}\text{element}=\left(\text{Mass}\text{fraction}\text{of}\text{that}\text{element}\text{in}\text{compound}\right)\left(100\right)\%$

Answer to Problem 2.13P

The mass percent of calcium is $51.45\%$ and the mass percent of fluorine is $48.55\%$ .

Explanation of Solution

Given information:

Total mass of fluorite sample $2.76\text{g}$ , mass of calcium in the sample is $1.42\text{g}$ .

The formula to calculate the mass of fluorine in fluorite sample is as follows:

  $\text{Total}\text{mass}\text{of}\text{fluorite sample}=\text{Mass}\text{of}\text{calcium}+\text{Mass}\text{of}\text{fluorine}$

Rearrange the above formula.

  $\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}-\text{Mass}\text{of}\text{calcium}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of calcium in fluorite sample is $1.42\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{of}\text{fluorine}=\text{Total}\text{mass}\text{of}\text{fluorite sample}-\text{Mass}\text{of}\text{calcium}\\ =2.76\text{g}-1.42\text{g}\\ =1.34\text{g}\end{array}$

The formula to calculate the mass fraction of calcium in fluorite sample is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{calcium}=\frac{\text{Total}\text{mass}\text{of}\text{calcium}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of calcium in fluorite sample is $1.42\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{calcium}=\frac{\text{Total}\text{mass}\text{of}\text{calcium}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}\\ =\frac{1.42\text{g}}{2.76\text{g}}\\ =0.5145\end{array}$

Formula to calculate the mass fraction of fluorine in fluorite sample is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{fluorine}=\frac{\text{Total}\text{mass}\text{of}\text{fluorine}\text{in}\text{}\text{fluorite}\text{sample}}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}$

Total mass of fluorite sample is $2.76\text{g}$ .

Mass of fluorine in fluorite sample is $1.34\text{g}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{fluorine}=\frac{\left(\begin{array}{l}\text{Total}\text{mass}\text{of}\text{fluorine}\text{in}\\ \text{}\text{fluorite}\text{sample}\end{array}\right)}{\text{Total}\text{mass}\text{of}\text{fluorite}\text{sample}}\\ =\frac{1.34\text{g}}{2.76\text{g}}\\ =0.4855\end{array}$

Formula to calculate the mass percent of calcium from mass fraction of calcium is as follows:

  $\text{Mass}\text{percent}\text{of}\text{calcium}\text{in fluorite}\text{sample}=\left(\text{Mass}\text{}\text{fraction}\text{}\text{of}\text{calcium}\right)\left(100\right)\%$

Mass fraction of calcium in sample is 0.5145.

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{calcium}\text{in}\text{the}\text{fluorite}\text{sample}=\left(\text{Mass}\text{}\text{fraction}\text{}\text{of}\text{calcium}\right)\left(100\right)\%\\ =\left(0.5145\right)\left(100\right)\%\\ =51.45\%\end{array}$

Formula to calculate the mass percent of fluorine from mass fraction of fluorine is as follows:

  $\text{Mass}\text{percent}\text{of}\text{fluorine}\text{in}\text{the}\text{fluorite}\text{sample}=\left(\text{Mass}\text{}\text{fraction}\text{}\text{of}\text{fluorine}\right)\left(100\right)\%$

Mass fraction of fluorine in sample is 0.4855.

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{fluorine}\text{in}\text{the}\text{fluorite}\text{sample}=\left(\text{Mass}\text{}\text{fraction}\text{}\text{of}\text{fluorine}\right)\left(100\right)\%\\ =\left(0.4855\right)\left(100\right)\%\\ =48.55\%\end{array}$