Chapter 10, Problem 70A

(a)

Interpretation Introduction

Interpretation: The volume of 835 g of ${\text{SO}}_{\text{3}}$ at STP needs to be determined.

Concept Introduction: The pressure, volume, number of moles, and temperature are related to each other as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is the number of moles, R is the Universal gas constant and T is temperature.

Explanation of Solution

The mass of ${\text{SO}}_{\text{3}}$ is 835 g. The number of moles can be calculated as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Molar mass of ${\text{SO}}_{\text{3}}$ is 80.06 g/mol.

Substitute the values,

  $\begin{array}{c}n=\frac{835\text{ g}}{80.06\text{ g/mol}}\\ =10.43\text{ mol}\end{array}$

Now, at STP the value of temperature and pressure is 273.15 K and 1 atm respectively.

The volume is calculated as follows:

  $V=\frac{nRT}{P}$

Substitute the values,

  $\begin{array}{c}V=\frac{\left(10.43\text{ mol}\right)\left(0.082\text{ L atm/mol K}\right)\left(273.15\text{ K}\right)}{\left(1\text{ atm}\right)}\\ =233.2\text{ L}\end{array}$

Thus, a volume of 835 g of ${\text{SO}}_{\text{3}}$ at STP $233.2\text{ L}$ .

(b)

Interpretation Introduction

Interpretation: The mass in grams of a molecule of aspirin needs to be calculated.

Concept Introduction: Mass of a substance can be calculated from the number of moles and molar mass as follows:

  $m=n\times M$

Here, n is the number of moles and M is the molar mass.

Explanation of Solution

According to Avogadro’s law, 1 mol of aspirin there are $6.022\times {10}^{23}$ molecules thus, the number of moles of 1 molecule of aspirin will be:

  $n=\left(1\text{ molecule}\right)\left(\frac{1\text{ mol}}{6.022\times {10}^{23}\text{ molecules}}\right)$

Or,

  $n=1.66\times {10}^{-24}\text{ mol}$

Now, the molar mass of aspirin ${\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$ is 180.16 g/mol thus, mass can be calculated as follows:

  $m=n\times M$

Substitute the values,

  $\begin{array}{c}m=\left(1.66\times {10}^{-24}\text{ mol}\right)\left(180.16\text{ g/mol}\right)\\ =3.0\times {10}^{-22}\text{ g}\end{array}$

Thus, the mass of 1 molecule of aspirin is $3.0\times {10}^{-22}\text{ g}$.

(c)

Interpretation Introduction

Interpretation: The number of atoms in 5.78 mol of ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ .

Concept Introduction: According to Avogadro’s law, in 1 mol of a substance there are $6.022\times {10}^{23}$ units of that substance.

Explanation of Solution

The number of moles of ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is 5.78 mol. Here, ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is an ionic compound thus, the representative particles are formula units. The number of atoms can be calculated by multiplying the number of representative particles with the total number of moles of each element present in the compound.

First, calculate the number of formula units as follows:

  $\begin{array}{c}N=\left(5.78\text{ mol}\right)\left(\frac{6.022\times {10}^{23}\text{ formula units}}{1\text{ mol}}\right)\\ =3.48\times {10}^{24}\text{ formula units}\end{array}$

Now, the number of atoms can be calculated as follows:

  $\begin{array}{c}N=9\left(3.48\times {10}^{24}\right)\\ =3.132\times {10}^{25}\end{array}$

Thus, the number of atoms in 5.78 mol of ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is $3.132\times {10}^{25}$ atoms.