Question

Arrange the following in order of increasing mass:

1.06 mol SF₄; 117g of CH₄;$\mathbf{8}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}{\mathbf{moleculesofCl}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$ and atoms of argon?

Short answer

The increasing the order of the mass is:

$1.06{\text{molSF}}_4{\text{<117gofCH}}_4{\text{<8.7×10}}^{23}{\text{moleculesofCl}}_2{\text{O}}_7{\text{<417×10}}^{23}\text{ofatomsofargon}$

Step-by-step solution

Number of mole

The number of moles (n) of a substance is equal to the “ratio” of the mass of the substance and the molar mass of that substance.

$\mathrm{Mole}\left(\mathrm{n}\right)=\frac{\mathrm{Mass}}{\mathrm{Molarmass}}$

In the form of Avogadro number:

$\text{Moles =}\frac{\text{Number of atoms of substance}}{\text{Avogadro number}}$

Calculation of the mass of 1.06 mole of SF4.

Mass of 1 mole of SF₄ = $1\times$mass of S + $4\times$mass of F.

role="math" localid="1663394525544" $\begin{array}{rcl}{\text{SF}}_4& =& 1\times 32\text{g}/\text{mol}+4\times 19\text{g}/\text{mol}\\ & =& \left(32+76\right)\text{g}/\text{mol}\\ & =& 109\text{g}/\text{mol}\end{array}$

role="math" localid="1663394533703" $\begin{array}{rcl}{\text{MassofmoleofSF}}_4& =& 109\text{g}/\text{mol}\times 1.06\text{mol}\\ & =& 115.54\text{g}\end{array}$

Calculation of the mass of 117g of CH4.

The number of moles is calculated as:

$$\begin{gathered} \text{Number of moles =}\frac{\text{Mass}}{\text{Molar mass}} \\ =\frac{117\mathrm{g}}{16\mathrm{g}/\mathrm{mol}} \\ =7.312\mathrm{mol}. \end{gathered}$$

Mass of 1 mole of ${\text{CH}}_4\text{=16g}$

Mass of $7.312$mole of

$$\begin{gathered} {\text{CH}}_4\text{=16×7.312} \\ =117\text{g} \end{gathered}$$

Calculation of the mass of 8.7×1023 molecules of Cl2O7

The number of moles is calculated as:

$$\begin{gathered} \text{Moles =}\frac{{\text{Number of atoms of Cl}}_2{O}_7}{\text{Avogadro number}} \\ =\frac{8.7\times {10}^{23}}{6.022\times {10}^{23}} \\ =1.445\text{mol.} \end{gathered}$$

Mass of 1 mole of ${\text{Cl}}_2{O}_7=183\text{g}$

Mass of 7.312 moles of

$$\begin{gathered} C{l}_2{O}_7=1.445\times 183 \\ C{l}_2{O}_7=264.435\text{g} \end{gathered}$$

Calculation of the mass of 417×1023 atoms of argon.

The number of moles is calculated as:

$$\begin{gathered} \text{Moles =}\frac{\text{Number of atoms of substance}}{\text{Avogadro number}} \\ =\frac{4.17\times {10}^{23}}{6.022\times {10}^{23}} \\ =64.26\text{mol} \end{gathered}$$

Mass of 1 mole of argonrole="math" localid="1663394604771" $=40\text{g}$

Mass of 64.26 moles of argon role="math" localid="1663394610913" $=40\times 64.26$

role="math" localid="1663394616340" $=2570.4\text{g}$

Thus, increasing the order of the mass is:

$1.06{\text{molSF}}_4<117{\text{gofCH}}_4<8.7\times {10}^{23}{\text{moleculesofCl}}_2{O}_7<417\times {10}^{23}\text{ofatomsofargon}$