Chapter 5, Problem 72P

What is the mass in grams of each quantity of vitamin D (molar mass 384.7 g/mol), which is needed for forming and maintaining healthy bones?

1. 3.6 mol
2. 0.58 mol
3. $7.3\times {10}^{24}\text{molecules}$
4. $6.56\times {10}^{22}\text{molecules}$

Interpretation Introduction

(a)

Interpretation:

The mass (in grams) of Vitamin D in $3.60\text{ mole}$ of Vitamin D is to be determined.

Concept Introduction:

Following is the formula that will be used to calculate the mass of the substance:

  $numberofmoles=\frac{mass}{Molarmass}$

Or,

  $mass=numberofmoles\times Molarmass$

Answer to Problem 72P

The mass of Vitamin D present in $3.60$ mol of is Vitamin D $1384.9g$.

Explanation of Solution

Number of moles of Vitamin D $\text{= 3}\text{.60 mol}$

Molar mass of Vitamin D $\text{= }384.7\text{ g/mol}$

The formula to be used to calculate the mass of Vitamin D −

  $numberofmoles=\frac{mass}{Molarmass}$

Or,

  $mass=numberofmoles\times Molarmass$

  $mass=3.60mol\times 384.7g/mol$

  $mass=1384.9g$

Thus, the mass of Vitamin D present in $3.60$ mol of Vitamin D is $1384.9g$.

Interpretation Introduction

(b)

Interpretation:

The mass (in grams) of Vitamin D in $0.580\text{ mole}$ of Vitamin D is to be determined .

Concept Introduction:

Following is the formula that will be used to calculate the mass of the substance:

  $numberofmoles=\frac{mass}{Molarmass}$

Or,

  $mass=numberofmoles\times Molarmass$

Answer to Problem 72P

The mass of Vitamin D present in $0.580$ mol of Vitamin D is $223.13g$.

Explanation of Solution

Number of moles of Vitamin D $\text{= 0}\text{.580 mol}$

Molar mass of Vitamin D $\text{= }384.7\text{ g/mol}$

The formula used to calculate the mass of Vitamin D is −

  $numberofmoles=\frac{mass}{Molarmass}$

Or,

  $mass=numberofmoles\times Molarmass$

  $mass=0.580mol\times 384.7g/mol$

$mass=223.13g$

Thus, the mass of Vitamin D present in $0.580$ mol of Vitamin D is $223.13g$.

Interpretation Introduction

(c)

Interpretation:

The mass (in grams) of Vitamin D in $\text{7}\text{.3}\times {\text{10}}^{24}$ molecules of Vitamin D is to be determined.

Concept Introduction:

In order to convert the number of molecules into grams, divide the number of molecules by Avogadro's number. This will give the value of the number of moles of that substance. Avogadro's number is $6.023\times {10}^{23}$ molecules. Then, the molar mass of the substance is multiplied by the number of moles. This will give the value of amount of substance in grams.

Answer to Problem 72P

The mass of Vitamin D present in $\text{7}\text{.3}\times {\text{10}}^{24}$ molecules of Vitamin D is $4663g$.

Explanation of Solution

Molar mass of Vitamin D $\text{= 384}\text{.7 g/mol}$

Molecules of Vitamin D= $\text{7}\text{.3}\times {\text{10}}^{24}$ molecules

Avogadro's number of $\text{=}$

  $6.023\times {10}^{23}$ molecules

Since,

  $\begin{array}{l}numberofmoles=\frac{numberofmolecules}{Avogadro\text{'}snumber}\\ massingrams=numberofmoles\times molarmass\\ or\\ massingrams=\frac{numberofmolecules}{Avogadro\text{'}snumber}\times molarmass\end{array}$

So,

  $mass=\frac{\text{7}\text{.3}\times {\text{10}}^{24}}{6.023\times {10}^{23}}\times 384.7g$

  $\text{mass =}4663g$

Thus, the mass of Vitamin D present in $\text{7}\text{.3}\times {\text{10}}^{24}$ molecules of Vitamin D is $4663g$.

Interpretation Introduction

(d)

Interpretation:

The mass (in grams) of Vitamin D in $\text{6}\text{.56}\times {\text{10}}^{22}$ molecules of Vitamin D is to be determined.

Concept Introduction:

In order to convert the number of molecules into grams, divide the number of molecules by Avogadro's number. This will give the value of the number of moles of that substance. Avogadro's number is $6.023\times {10}^{23}$ molecules. Then, the molar mass of the substance is multiplied by the number of moles. This will give the value of amount of substance in grams.

Answer to Problem 72P

The mass of Vitamin D present in $\text{6}\text{.56}\times {\text{10}}^{22}$ molecules of Vitamin D is $41.9g$.

Explanation of Solution

Molar mass of Vitamin D $\text{= }384.7\text{ g/mol}$

Molecules of Vitamin D = $\text{6}\text{.56}\times {\text{10}}^{22}$ molecules

Avogadro's number of $\text{=}$

  $6.023\times {10}^{23}$ molecules

Since,

  $\begin{array}{l}numberofmoles=\frac{numberofmolecules}{Avogadro\text{'}snumber}\\ massingrams=numberofmoles\times molarmass\\ or\\ massingrams=\frac{numberofmolecules}{Avogadro\text{'}snumber}\times molarmass\end{array}$

So,

  $mass=\frac{\text{6}\text{.56}\times {\text{10}}^{22}}{6.023\times {10}^{23}}\times 384.7g$

  $\text{mass = }41.9g$

The mass of Vitamin D present in $\text{6}\text{.56}\times {\text{10}}^{22}$ molecules of Vitamin D is $41.9g$.