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

$moles=\frac{mass}{molarmass}$

$\begin{array}{r}moles=\frac{20}{18}\\ =1.11\end{array}$

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

$moles=\frac{mass}{molarmass}$

$moles=\frac{77}{16}=4.81$

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

$moles=\frac{mass}{molarmass}$

$moles=\frac{68}{42.09}=1.61$

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

$moles=\frac{mass}{molarmass}$

$moles=\frac{100}{44.02}=2.27$

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

$moles=\frac{mass}{molarmass}$

$moles=\frac{84}{20.02}=4.19$

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