Question

Which of the following represents the least number of molecules?

(a) 20.0 g of H₂O (18.02 g/mol)

(b) 77.0 g of CH₄ (16.06 g/mol)

(c) 68.0 g of CaH₂ (42.09 g/mol)

(d) 100.0 g of N₂O (44.02 g/mol)

(e) 84.0 g of HF (20.01 g/mol)

Short answer

The water of 20.0g has the least number of molecules that is as compared to methane, CaH₂, N₂O and HF.

Step-by-step solution

Determining number of molecules of H2O

The number of molecules or atoms in a compound is determined by the number of moles present. Generally, 1 mole consists of atoms (also known as Avagadro’s number).

As the mass of water is 20.0g and molecular mass is 18 g/mol so the moles of water will be

\(moles = \,\frac{{mass}}{{molar\,mass}}\)

\(\begin{align}moles = \,\frac{{20}}{{18}}\\ = \,1.11\end{align}\)

Therefore, the number of molecules in 1.11 moles of water is \(\) \(1.11\,\, \times \,6.022\, \times \,{10^{23}} = 6.69\, \times \,{10^{23}}\)

Determining number of molecules of CH4

The number of molecules or atoms in a compound is determined by the number of moles present. Generally, 1 mole consists of atoms (also known as Avagadro’s number).

As the mass of methane is 77.0g and molecular mass is 16 g/mol so the moles of methane will be

\(moles = \,\frac{{mass}}{{molar\,mass}}\)

\(moles = \frac{{77}}{{16}} = 4.81\)

Therefore, the number of molecules in 4.81 moles of water is \(1.61 \times 6.022 \times {10^{23}} = 10.04 \times {10^{23}}\)

Determining number of molecules of CaH2

The number of molecules or atoms in a compound is determined by the number of moles present. Generally, 1 mole consists of atoms (also known as Avagadro’s number).

As the mass of is 68.0g and molecular mass is 42.09 g/mol so the moles of will be

\(moles = \,\frac{{mass}}{{molar\,mass}}\)

\(moles = \frac{{68}}{{42.09}} = 1.61\)

Therefore, the number of molecules in 1.61 moles of is \(1.61 \times 6.022 \times {10^{23}} = 10.04 \times {10^{23}}\)

Determining number of molecules of N2O 

The number of molecules or atoms in a compound is determined by the number of moles present. Generally, 1 mole consists of atoms (also known as Avagadro’s number).

As the mass of is 100.0g and molecular mass is 44.02 g/mol so the moles of will be

\(moles = \,\frac{{mass}}{{molar\,mass}}\)

\(moles = \frac{{100}}{{44.02}} = 2.27\)

Therefore, the number of molecules in 2.27 moles of is \(2.27 \times 6.022 \times {10^{23}} = 13.68 \times {10^{23}}\)

Determining number of molecules of HF

The number of molecules or atoms in a compound is determined by the number of moles present. Generally, 1 mole consists of atoms (also known as Avagadro’s number).

As the mass of HF is 84 g and molecular mass is 20.01 g/mol so the moles of HF will be

\(moles = \,\frac{{mass}}{{molar\,mass}}\)

\(moles = \frac{{84}}{{20.02}} = 4.19\)

Therefore, the number of molecules in 4.19 moles of HF is \(4.19 \times 6.022 \times {10^{23}} = 25.26 \times {10^{23}}\)