Question

A sample of ammonia has a mass of 43.5 g. How many molecules are in this sample?

Answer 1

Mass of ammonia sample is 43.5 g. The molecular formula of ammonia is $NH_{3}$. The molecular formula is 17.031 g/mol.

To calculate the number of molecules of ammonia, first calculate the number of moles as follows:

$n=\frac{m}{M}$

Here, m is mass and M is molar mass, putting the values,

$n=\frac{43.5 g}{17.031g/mol}=2.55 mol$

Now, in mole there are $6.023\times 10^{23}$ molecules, this is known as Avogadro's number.

Since,

$1 mol\rightarrow 6.023\times 10^{23}molecules$

Thus,

$2.55 mol\rightarrow (2.55)(6.023\times 10^{23})=1.54\times 10^{24} molecules$

Therefore, number of molecules in the sample will be $1.54\times 10^{24} molecules$

Answer 2

1.54 · 10²⁴ molecules

Further explanation

Given:

A sample of ammonia has a mass of 43.5 g.

Question:

How many molecules are in this sample?

The Process:

Step-1

• Relative atomic mass: N = 14 and H = 1
• Relative molecular mass (Mr) of NH₃ = 14 + 3(1) = 17.

Step-2

Let us convert mass to mole for NH₃.

$\boxed{ \ n = \frac{mass}{Mr} \ } \rightarrow \boxed{ \ n = \frac{43.5}{17} = 2.56 \ moles \ }$

Step-3

And finally, let us convert moles to molecules for NH₃.

$\boxed{ \ n = \frac{number \ of \ molecules (N)}{Avogadro's \ number} \ } \rightarrow \boxed{ \ N = n \times 6.022 \cdot 10^{23} \ }$

$\boxed{ \ N = 2.56 \times 6.022 \cdot 10^{23} \ }$

Thus, the number of molecules are in this sample is $\boxed{ \ N = 1.54 \cdot 10^{24} \ }$ (round to three important figures)

_ _ _ _ _ _ _ _ _ _

Alternative Steps

$\boxed{ \ N = 43.5 \ g \times \frac{1 \ mol}{17 \ g} \times \frac{6.022 \times 10^{23} \ molecules}{1 \ mol} \ }$

$\boxed{ \ N = 1.54 \cdot 10^{24} \ }$ molecules

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