Chapter 5, Problem 5.99AP

(a)

Interpretation Introduction

Interpretation:

The molar mass of sucrose has to be given.

Answer to Problem 5.99AP

The molar mass of sucrose is $\text{342}\text{.3}\text{g/mol}\text{.}$

Explanation of Solution

The formula weight of sucrose is calculated as,

  $\begin{array}{l}\text{12}\text{C}\text{atoms}\text{×}\text{12}\text{.01}\text{amu}\text{=}\text{144}\text{.12}\text{amu}\\ \text{22}\text{H}\text{atoms×1}\text{.008}\text{amu}\text{=}\text{22}\text{.176}\text{amu}\\ \text{11}\text{O}\text{atoms×16}\text{.00}\text{amu}\text{=}\underset{\_}{\text{176}\text{.00}\text{amu}}\\ \text{Formula weight}\text{of}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\text{=342}\text{.296}\text{amu}\end{array}$

Since, the formula weight of sucrose is $\text{342}\text{.3}\text{amu,}$ the molar mass of sucrose is $\text{342}\text{.3}\text{g/mol}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The equation of sucrose with water to give ethanol and carbon dioxide has to be balanced.

Answer to Problem 5.99AP

The balanced equation of sucrose with water to give ethanol and carbon dioxide is,

  ${\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)\stackrel{}{\to }\text{4}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}\left(\text{l}\right)\text{+4}{\text{CO}}_{\text{2}}\left(\text{g}\right)$

Explanation of Solution

The given equation is,

  ${\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)\stackrel{}{\to }{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}\left(\text{l}\right){\text{+CO}}_{\text{2}}\left(\text{g}\right)$

The carbons in both ethanol and carbon dioxide have to be balanced.

Place the coefficient $\text{4}$ to balance carbons in the product side (before ${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}$ and ${\text{CO}}_{\text{2}}$).

Place the coefficient $\text{4}$ to balance oxygen in the product side (before ${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}$ and ${\text{CO}}_{\text{2}}$).

Place the coefficient $\text{4}$ to balance hydrogen in the product side (before ${\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}$).

The balanced equation of sucrose with water to give ethanol and carbon dioxide is,

  ${\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)\stackrel{}{\to }\text{4}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}\left(\text{l}\right)\text{+4}{\text{CO}}_{\text{2}}\left(\text{g}\right)$

(c)

Interpretation Introduction

Interpretation:

The number of moles of ethanol formed from $\text{2}$ mole of sucrose has to be given.

Answer to Problem 5.99AP

The number of moles of ethanol formed from $\text{2}$ mole of sucrose is $\text{8}\text{moles}\text{.}$

Explanation of Solution

Given,

Moles of sucrose are $\text{2}$ moles.

The balanced equation of sucrose with water to give ethanol and carbon dioxide is,

  ${\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)\stackrel{}{\to }\text{4}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}\left(\text{l}\right)\text{+4}{\text{CO}}_{\text{2}}\left(\text{g}\right)$

The number of moles of ethanol formed from $\text{2}$ mole of sucrose is calculated as,

  $\text{2}\cancel{\text{mol}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}}\text{×}\frac{\text{4}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}}{\text{1}\cancel{\text{mol}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}}}\text{=8}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}$

The number of moles of ethanol formed from $\text{2}$ mole of sucrose is $\text{8}\text{moles}\text{.}$

(d)

Interpretation Introduction

Interpretation:

The number of grams of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose has to be given.

Answer to Problem 5.99AP

The number of grams of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose is $\text{18}\text{.4}\text{g}\text{.}$

Explanation of Solution

Given,

Grams of sucrose are $\text{34}\text{.2 g}\text{.}$

The balanced chemical equation is,

  $\text{2 Na}\left(\text{s}\right)\text{+2}{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\stackrel{\text{Δ}}{\to }\text{2}\text{NaOH}\left(\text{aq}\right){\text{+H}}_{\text{2}}\left(\text{g}\right)$

Grams can be converted into moles using the conversion factor:

  $\frac{\text{1}\text{mol}}{\text{Molar}\text{mass}}$

The number of moles present in $\text{34}\text{.2 g}$ of sucrose is calculated as,

  $\text{34}\text{.2}\cancel{\text{g}}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}\text{×}\frac{\text{1}\text{mol}}{\text{342}\cancel{\text{g}}}\text{=0}\text{.1}\text{mol}$

The number of moles present in $\text{34}\text{.2 g}$ of sucrose is $\text{0}\text{.1}\text{mol}\text{.}$

The number of moles of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose is calculated as,

  $\text{0}\text{.1}\cancel{\text{mol}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}}\text{×}\frac{\text{4}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}}{\text{1}\cancel{\text{mol}{\text{C}}_{\text{12}}{\text{H}}_{\text{22}}{\text{O}}_{\text{11}}}}\text{=0}\text{.4}\text{mol}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}$

The number of moles of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose is $\text{0}\text{.4}\text{moles}\text{.}$

Moles can be converted into grams using the conversion factor:

  $\frac{\text{Molar}\text{mass}}{\text{1}\text{mol}}$

The number of grams of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose is calculated as,

  $\text{0}\text{.4}\cancel{\text{mol}}\text{×}\frac{\text{46}\text{.07}\text{g}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\text{O}}{\text{1}\cancel{\text{mol}}}\text{=18}\text{.42}\text{g}$

The number of grams of ethanol that is formed from $\text{34}\text{.2 g}$ of sucrose is $\text{18}\text{.4}\text{g}\text{.}$