Chapter 10.14, Problem 72AAP

To determine

The mole fraction of each component in polycrylonitrile material.

The mole fraction of each component in polystrene material.

The mole fraction of each component in polybutadlene material.

Answer to Problem 72AAP

The mole fraction of each component in polycrylonitrile material is $\underset{\_}{0.324}$.

The mole fraction of each component in polystrene material is $\underset{\_}{\text{0}\text{.382}}$.

The mole fraction of each component in polybutadlene material is $\underset{\_}{\text{0}\text{.294}}$.

Explanation of Solution

Show the bonding structure of the polyacryonitrile, polybutadlene, and polystyrene as:

Express the mole fraction of polyacrylonitrile.

    $\text{Mole}\text{fraction}\text{of}\text{polyacrylonitrile}=\frac{N_{\text{polyacrylonitrile}}}{\left[\begin{array}{l}{N}_{\text{polyacrylonitrile}}\\ +N_{\text{polybutadlene}}\\ +N_{\text{polystyrene}}\end{array}\right]}$      (I)

Here the number of moles of polystyrene is $N_{\text{polystyrene}}$ and the number of mole of polyacrylonitrile is $N_{\text{polyacrylonitrile}}$.

Express the mole fraction of polybutadlene.

    $\text{Mole}\text{fraction}\text{of}\text{polybutadlene}=\frac{N_{\text{polybutadlene}}}{\left[\begin{array}{l}{N}_{\text{polyacrylonitrile}}\\ +N_{\text{polybutadlene}}\\ +N_{\text{polystyrene}}\end{array}\right]}$      (II)

Express the mole fraction of polystyrene.

    $\text{Mole}\text{fraction}\text{of}\text{polystrene}=\frac{N_{\text{polystyrene}}}{\left[\begin{array}{l}{N}_{\text{polyacrylonitrile}}\\ +N_{\text{polybutadlene}}\\ +N_{\text{polystyrene}}\end{array}\right]}$      (III)

Conclusion:

The average molecular mass of the polyacrylonitrile is $53\text{g}/\text{mol}$.

The average molecular mass of the polybutadlene is $54\text{g}/\text{mol}$.

The average molecular mass of the polystyrene is $105\text{g}/\text{mol}$.

Calculate the number of moles of polyacrylonitrile of 100 g of copolymer.

    $\begin{array}{c}{N}_{\text{polyacrylonitrile}}=\frac{25\text{g}}{53\text{g}/\text{mol}}\\ =0.472\text{mole}\end{array}$

Calculate the number of moles of polybutadlene of 100 g of copolymer.

    $\begin{array}{c}{N}_{\text{polybutadlene}}=\frac{30\text{g}}{54\text{g}/\text{mol}}\\ =0.556\text{mole}\end{array}$

Calculate the number of moles of polystyrene of 100 g of copolymer.

    $\begin{array}{c}{N}_{\text{polystyrene}}=\frac{45\text{g}}{105\text{g}/\text{mol}}\\ =0.429\text{mole}\end{array}$

Substitute $0.472\text{mole}$ for $N_{\text{polyacrylonitrile}}$, $0.556\text{mole}$ for $N_{\text{polybutadlene}}$, and $0.429\text{mole}$ for $N_{\text{polystyrene}}$ in Equation (I).

    $\begin{array}{c}\text{Mole}\text{fraction}\text{of}\text{polyacrylonitrile}=\frac{0.472\text{mole}}{0.472\text{mole}+0.566\text{mole}+0.429\text{mole}}\\ =\frac{0.472\text{mole}}{1.457\text{mole}}\\ =0.324\end{array}$

Thus, the mole fraction of each component in polycrylonitrile material is $\underset{\_}{0.324}$.

Substitute $0.472\text{mole}$ for $N_{\text{polyacrylonitrile}}$, $0.556\text{mole}$ for $N_{\text{polybutadlene}}$, and $0.429\text{mole}$ for $N_{\text{polystyrene}}$ in Equation (II).

    $\begin{array}{c}\text{Mole}\text{fraction}\text{of}\text{polybutalene}=\frac{0.472\text{mole}}{0.472\text{mole}+0.566\text{mole}+0.429\text{mole}}\\ =\frac{0.556\text{mole}}{1.457\text{mole}}\\ =0.382\end{array}$

Thus, the mole fraction of each component in polybutalene material is $\underset{\_}{\text{0}\text{.382}}$.

Substitute $0.472\text{mole}$ for $N_{\text{polyacrylonitrile}}$, $0.556\text{mole}$ for $N_{\text{polybutadlene}}$, and $0.429\text{mole}$ for $N_{\text{polystyrene}}$ in Equation (III).

    $\begin{array}{c}\text{Mole}\text{fraction}\text{of}\text{polystrene}=\frac{0.429\text{mole}}{0.472\text{mole}+0.566\text{mole}+0.429\text{mole}}\\ =\frac{0.429\text{mole}}{1.457\text{mole}}\\ =0.294\end{array}$

Thus, the mole fraction of each component in polystrene material is $\underset{\_}{\text{0}\text{.294}}$.