Chapter 8, Problem 128CP

itamin ${\text{B}}_{12}$ , cyancobalamin, is essential for human nutrition. Its molecular formula is ${\text{C}}_{63}{\text{H}}_{88}{\text{CoN}}_{14}{\text{O}}_{14}\text{P}$ . A lack of this vita min in the diet can lead to anemia. Cyanocohalamin is the form of the vitamin found in vitamin supplements.

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What is the molar mass of cyanocobalamin to two decimal places?

How many moles of cyanocohalamin molecules are present in 250 mg of cyanocobalamin?

What is the mass of 0.60 mole of cyanocobalamin?

How many atoms of hydrogen are in 1 .0 mole of cyanocobalamin?

What is the mass of $\text{1}\text{.0}\times {\text{10}}^7$ molecules of cyanocobalamin?

What is the mass (in grams) of one molecule of cyanocobalamin?

Interpretation Introduction

(a)

Interpretation:

The molar mass of cyanocobalamin upto two decimal places is to be calculated.

Concept Introduction:

A molar mass of a substance is the mass of the substance divided by the number of moles of the substance. The SI unit of molar mass of $\text{kg/mol}$ and other unit is $\text{g/mol}$.

The formula to calculate the molar mass is,

$\text{Molar mass of the substance}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Number}\text{of}\text{moles}}$.

Answer to Problem 128CP

The molar mass of cyanocobalamin to two decimal places is $1353.76\text{g/mol}$.

Explanation of Solution

The molecular formula of cyanocobalamnin is ${\text{C}}_{\text{63}}{\text{H}}_{\text{88}}{\text{CoN}}_{\text{14}}{\text{O}}_{\text{14}}\text{P}$.

The molar mass of carbon is $12\text{g/mol}$.

The molar mass of hydrogen is $1\text{g/mol}$.

The molar mass of oxygen is $15.99\text{g/mol}$.

The molar mass of nitrogen is $14\text{g/mol}$.

The molar mass of phosphorus is $30.97\text{g/mol}$.

The molar mass of cobalt is $58.93\text{g/mol}$.

The molar mass of cyanocobalamnin is calculated by the expression,

$\begin{array}{c}{\text{Molar mass of C}}_{\text{63}}{\text{H}}_{\text{88}}{\text{CoN}}_{\text{14}}{\text{O}}_{\text{14}}\text{P}=\left(63\times \text{molar}\text{mass}\text{of}\text{C}\right)+\left(88\times \text{molar}\text{mass}\text{of}\text{H}\right)\\ +\left(1\times \text{molar}\text{mass}\text{of}\text{Co}\right)+\left(14\times \text{molar}\text{mass}\text{of}\text{N}\right)\\ +\left(14\times \text{molar}\text{mass}\text{of}\text{O}\right)+\left(1\times \text{molar}\text{mass}\text{of}\text{P}\right)\end{array}$

Substitute the respective values of molar mass of each element in the above exopression.

$\begin{array}{c}{\text{Molar mass of C}}_{\text{63}}{\text{H}}_{\text{88}}{\text{CoN}}_{\text{14}}{\text{O}}_{\text{14}}\text{P}=\left(63\times 12\text{g/mol}\right)+\left(88\times 1\text{g/mol}\right)+\left(1\times 58.93\text{g/mol}\right)\\ +\left(14\times 14\text{g/mol}\right)+\left(14\times 15.99\text{g/mol}\right)+\left(1\times 30.97\text{g/mol}\right)\\ =1353.76\text{g/mol}\end{array}$

Thus, the molar mass of cyanocobalmaine is $1353.76\text{g/mol}$.

Interpretation Introduction

(b)

Interpretation:

The number of moles of cyanaocobalamin molecules present in $250\text{mg}$ of cyanaocobalamin is to be stated.

Concept Introduction:

A mole of a substance contains exactly $6.02214076\times {10}^{23}$ of atoms/molecules. It is used to measure the amount of the substance in SI units.

The formula to calculate the number of moles is:

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$.

Answer to Problem 128CP

The number of moles of cyanocobalamin molecules present in $250\text{mg}$ of cyanocobalamin is $1.85\times {10}^{-4}\text{mol}$.

Explanation of Solution

The given mass of cyanocobalamin is $250\text{mg}$.

The conversion of $\text{mg}$ to $\text{g}$ is done as,

$\text{1 mg}={10}^{-3}\text{g}$

Thus, the mass of cyanocobalamin is $0.250\text{ g}$.

The molar mass of cyanocobalamin is $1353.76\text{ g/mol}$.

The moles of cyanocobalamin is calculated by the expression,

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$

Substitute the value of mass and molar of cyanocobalamin in the above expression.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of cyanocobalamin}=\frac{0.25\text{g}}{1353.76\text{ g/mol}}\\ =1.85\times {10}^{-4}\text{mol}\end{array}$

The number of moles of cyanocobalamin molecules present in $250\text{mg}$ of cyanocobalamin is $1.85\times {10}^{-4}\text{mol}$.

Interpretation Introduction

(c)

Interpretation:

The mass of $0.60\text{mol}$ of cyanocobalamine is to be stated.

Concept Introduction:

A mole of a substance contains exactly $6.02214076\times {10}^{23}$ of atoms/molecules. It is used to measure the amount of the substance in SI units.

The formula to calculate the number of moles is:

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$.

Answer to Problem 128CP

The mass of $0.60\text{mol}$ of cyanocobalamine is $\text{812}\text{.26 }\text{g}$.

Explanation of Solution

The given moles of cyanocobalamin is $0.60\text{mol}$.

The molar mass of cyanocobalamin is $1353.76\text{g/mol}$.

The mass of cyanocobalamin is calculated by the expression,

$\text{ Mass of the substance}\left(\text{g}\right)\text{=Number}\text{of}\text{moles}\times \text{Molar mass of the substance}$

Substitute the value of moles and molar of cyanocobalamin in the above expression.

$\begin{array}{c}\text{ Mass of cyanocobalamine}=\text{0}\text{.60}\times 1353.76\text{ g/mol}\\ =\text{812}\text{.26 }\text{g}\end{array}$

Thus, the mass of $0.60\text{mol}$ of cyanocobalamine is $\text{812}\text{.26 }\text{g}$.

Interpretation Introduction

(d)

Interpretation:

The atoms of hydrogen that are present in $1.0\text{mol}$ of cyanocobalamin are to be stated.

Concept Introduction:

A mole of a substance contains exactly $6.02214076\times {10}^{23}$ of atoms/molecules. It is used to measure the amount of the substance in SI units.

The formula to calculate the number of moles is:

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$.

Answer to Problem 128CP

The atoms of hydrogen that are present in $1.0\text{mol}$ of cyanocobalamin are $5.29\times {10}^{25}\text{atoms}$.

Explanation of Solution

The given moles of cyanocobalamin is $0.60\text{mol}$.

According to the molecular formula of cyanocobalamine that is ${\text{C}}_{\text{63}}{\text{H}}_{\text{88}}{\text{CoN}}_{\text{14}}{\text{O}}_{\text{14}}\text{P}$, there are total $88$ atoms of hydrogen present in cyanocobalamine.

If $1.0\text{mol}$ of substance contains $6.02214076\times {10}^{23}$ of atoms then one mole of cyanocobalamine contains $6.02214076\times {10}^{23}\times 88=5.29\times {10}^{25}\text{atoms of hydrogen}$

Thus, atoms of hydrogen that are present in $1.0\text{mol}$ of cyanocobalamin are $5.29\times {10}^{25}\text{atoms}$.

Interpretation Introduction

(e)

Interpretation:

The mass of $1\times {10}^7\text{molecules}$ of cyanocobalamine is to be stated.

Concept Introduction:

A mole of a substance contains exactly $6.02214076\times {10}^{23}$ of atoms/molecules. It is used to measure the amount of the substance in SI units.

The formula to calculate the number of moles is:

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$.

Answer to Problem 128CP

The mass of $1\times {10}^7\text{molecules}$ of cyanocobalamine is $244.80\times {10}^{-16}\text{g}$.

Explanation of Solution

The given number of molecules of cyanocobalamin is $1\times {10}^7\text{molecules}$.

The molar mass of cyanocobalamin is $1353.76\text{g/mol}$.

$1.0\text{mol}$ of substance contains $6.022\times {10}^{23}$ of atoms/molecules.

Thus, the mass of $1\times {10}^7\text{molecules}$ of cyanocobalamin is,

$\begin{array}{c}\text{Mass}=\frac{1353.76}{6.022\times {10}^{23}}\times {10}^7\\ =244.80\times {10}^{-16}\text{g}\end{array}$

Thus, the mass of $1\times {10}^7\text{molecules}$ of cyanocobalamine is $244.80\times {10}^{-16}\text{g}$.

Interpretation Introduction

(f)

Interpretation:

The mass of one molecule of cyanocobalamine is to be stated.

Concept Introduction:

A mole of a substance contains exactly $6.02214076\times {10}^{23}$ of atoms/molecules. It is used to measure the amount of the substance in SI units.

The formula to calculate the number of moles is:

$\text{Number}\text{of}\text{moles}=\frac{\text{ Mass of the substance}\left(\text{g}\right)}{\text{Molar mass of the substance}}$.

Answer to Problem 128CP

The mass of one molecule of cyanocobalamine is $244.80\times {10}^{-23}\text{g}$.

Explanation of Solution

The given number of molecules of cyanocobalamin is $1\times {10}^7\text{molecules}$.

The molar mass of cyanocobalamin is $1353.76\text{g/mol}$.

$1.0\text{mol}$ of substance contains $6.022\times {10}^{23}$ atoms/molecules.

Thus, the mass of $1$ molecule of cyanocobalamin is,

$\begin{array}{c}\text{Mass}=\frac{1353.76}{6.022\times {10}^{23}}\times 1\\ =244.80\times {10}^{-23}\text{g}\end{array}$

Thus, the mass of $1\text{molecule}$ of cyanocobalamine is $244.80\times {10}^{-23}\text{g}$.