Chapter 2, Problem 124GQ

Ma huang, an extract from the ephedra species of plants, contains ephedrine. The Chinese have used this herb for more than 5000 years to treat asthma. More recently, ephedrine has been used in diet pills that can be purchased over the counter in herbal medicine shops. However, very serious concerns have been raised regarding these pills following reports that their use led to serious heart problems.

(a) A molecular model of ephedrine is drawn below. From this determine the molecular formula for ephedrine and calculate its molar mass.

(b) What is the weight percent of carbon in ephedrine?

(c) Calculate the amount (moles) of ephedrine in a 0.125 g sample.

(d) How many molecules of ephedrine are there in 0.125 g? How many C atoms?

Interpretation Introduction

Interpretation: The molecular formula for ephedrine and its molar mass should be determined.

Concept introduction:

• $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$
• $\text{Number}\text{of}\text{atoms}\text{/}\text{molecules}=\text{Mole}\text{of}\text{substance×}\text{Avogadro}\text{number}$
• A chemical formula conveys us the number of atoms of each element in a compound. It contains the symbols of the atoms of the elements present in the compound as well as how many are for each element in the form of subscripts
• 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)
• Weight percentage is one way to represent the concentration of an element in a compound or a component in a mixture. Weight percent of elements of a compound is the ratio of weight of element to the weight of whole compound and multiplied with hundred.

Answer to Problem 124GQ

The molecular formula of ephedrine is ${\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}$ and it has $\text{165}\text{.1}\text{g/mol}$ molar mass

Explanation of Solution

Given,

The molecular model of ephedrine is,

  

There are ten carbon atoms, one oxygen atoms fifteen hydrogen atoms and one nitrogen atom

Therefore molecular formula of ephedrine is ${\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}$

Molar mass of ephedrine can be calculated as follows,

$\left(\text{10×}\underset{\text{mass}\text{of}\text{C}}{\text{12}\text{.01}}\right)\text{+}\left(\text{15×}\underset{\text{mass}\text{of}\text{H}}{\text{1}}\right)\text{+}\left(\text{1×}\underset{\text{mass}\text{of}\text{O}}{\text{16}}\right)\text{+}\left(\text{1×}\underset{\text{mass}\text{of}\text{N}}{\text{14}}\right)\text{=}\text{165}\text{.1}\text{g/mol}$

Molar mass of ephedrine is $\text{165}\text{.1}\text{g/mol}$

Interpretation Introduction

Interpretation: The weight for carbon present in ephedrine should be determined.

Concept introduction:

• $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$
• $\text{Number}\text{of}\text{atoms}\text{/}\text{molecules}=\text{Mole}\text{of}\text{substance×}\text{Avogadro}\text{number}$
• A chemical formula conveys us the number of atoms of each element in a compound. It contains the symbols of the atoms of the elements present in the compound as well as how many are for each element in the form of subscripts
• 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)
• Weight percentage is one way to represent the concentration of an element in a compound or a component in a mixture. Weight percent of elements of a compound is the ratio of weight of element to the weight of whole compound and multiplied with hundred.

Answer to Problem 124GQ

  The mass percent of carbon in ephedrine is $\text{72}\text{.74}\text{\%}$

Explanation of Solution

Mass percent of elements of a compound is the ratio of mass of element to the mass of whole compound and multiplied with hundred.

The molecular formula of the given ephedrine compound is ${\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}$ and its molar mass is $\text{165}\text{.1}\text{g/mol}$

And this compound namely ephedrine contains ten carbon atoms, molar mass of carbon atom is $12.01g/mol$

  $\begin{array}{l}\text{Molar}\text{Mass}\text{of}\text{Carbon}\text{in}\text{the}\text{compound}\\ \text{=}10\text{×12}\text{.01}\text{=}120.1\text{g/mol}\\ \\ \text{Mass}\text{percent}\text{of}\text{Carbon}\text{in}{\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{carbon}}{\text{Molar}\text{mass}\text{of}{\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}}\text{×100}\\ \text{=}\frac{120.1}{165.1}\text{×100}\text{=}72.74\text{\%}\end{array}$

Interpretation Introduction

Interpretation: The amount of ephedrine present in $0.125gsample$ of given ephedrine compound should be determined.

Concept introduction:

• $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$
• $\text{Number}\text{of}\text{atoms}\text{/}\text{molecules}=\text{Mole}\text{of}\text{substance×}\text{Avogadro}\text{number}$
• A chemical formula conveys us the number of atoms of each element in a compound. It contains the symbols of the atoms of the elements present in the compound as well as how many are for each element in the form of subscripts
• 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)
• Weight percentage is one way to represent the concentration of an element in a compound or a component in a mixture. Weight percent of elements of a compound is the ratio of weight of element to the weight of whole compound and multiplied with hundred.

Answer to Problem 124GQ

The amount of (moles) of ephedrine in $0.125gsample$ is $\text{0}\text{.000757}\text{mol}$

Explanation of Solution

The molecular formula of the given ephedrine compound is ${\text{C}}_{\text{10}}{\text{H}}_{\text{15}}\text{NO}$ and its molar mass is $\text{165}\text{.1}\text{g/mol}$

Amount of substance can be calculated by using the equation,

        $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$

Then the amount of ephedrine in $0.125g$ sample is,

                   $\text{=}\frac{\text{0}\text{.125}\text{g}}{\text{165}\text{.1}\text{g/mol}}\text{=}\text{0}\text{.000757}\text{mol}$

Interpretation Introduction

Interpretation: The molecules of ephedrine present in $0.125gsample$ of given ephedrine compound and the number of carbon atoms should be determined.

Concept introduction:

• $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$
• $\text{Number}\text{of}\text{atoms}\text{/}\text{molecules}=\text{Mole}\text{of}\text{substance×}\text{Avogadro}\text{number}$
• A chemical formula conveys us the number of atoms of each element in a compound. It contains the symbols of the atoms of the elements present in the compound as well as how many are for each element in the form of subscripts
• 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)
• Weight percentage is one way to represent the concentration of an element in a compound or a component in a mixture. Weight percent of elements of a compound is the ratio of weight of element to the weight of whole compound and multiplied with hundred.

Answer to Problem 124GQ

There are $\text{4}{\text{.56×10}}^{\text{20}}\text{molecules}$ of ephedrine and $\text{4}{\text{.56×10}}^{\text{21}}$ carbon atom in $0.125g$ sample of ephedrine given.

Explanation of Solution

$\text{Number}\text{of}\text{atoms}\text{/}\text{molecules}=\text{Mole}\text{of}\text{substance×}\text{Avogadro}\text{number}$

The number of moles of ephedrine in $0.125g$ sample is $\text{0}\text{.000757}\text{mol}$

The number of molecules of ephedrine in $0.125g$ sample,

        $\text{0}\text{.000757}\text{mol}\text{×}\text{6}\text{.022}{\text{×10}}^{\text{23}}\text{=}\text{4}{\text{.56×10}}^{\text{20}}\text{molecules}$

Weight percent of carbon in ephedrine is $72.74\%$.

The number of Carbon atom in $0.125g$ sample of ephedrine is,

                 $\begin{array}{l}\text{=}\frac{\text{72}\text{.74}}{\text{100}}\text{×0}\text{.125}\text{g×}\frac{\text{1}\text{mol}\text{C}}{\text{12}\text{.01}\text{g}}\text{×6}{\text{.022×10}}^{\text{23}}\\ \text{=}\text{4}\text{.56}{\text{×10}}^{\text{21}}\text{C}\text{atoms}\end{array}$