Question

A cylinder contains $68\text{g}$ of ammonia gas at S.T.P. How many molecules of ammonia are present in the cylinder?

$\left[\mathrm{N}-14,\mathrm{H}-1\right]$

Answer 1

Step 1: Given information

$68\text{g}$ of ammonia $\left({\text{NH}}_3\right)$ at S.T.P

Step 2: Calculation of gram molecular mass of ${\mathrm{NH}}_3$

Gram molecular mas of ${\mathrm{NH}}_3$

$$\begin{gathered} \text{=N}+3\text{H} \\ =\left(14+3\times 1\right)\text{g} \\ =17\text{g} \end{gathered}$$

Step 3: Calculation of number of molecules from given mass

• The following formula can be used to determine the number of molecules in the given mass of a substance:

$\mathrm{Number}\mathrm{of}\mathrm{molecules}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{substance}\mathrm{in}\mathrm{grams}\times 6.022\times {10}^{23}\text{molecules}}{\mathrm{Gram}\mathrm{molecular}\mathrm{mass}}$

Step 4: Calculation of number of molecules of ${\mathrm{NH}}_3$

$17\text{g}$ of ammonia contains $6.022\times {10}^{23}\text{molecules}$

$68\text{g}$ of ammonia will contain $\frac{6.022\times {10}^{23}\text{molecules}}{17\text{g}}\times 68\text{g=24.08}\times {10}^{23}\text{molecules}$

Hence, $24.08\times {10}^{23}\text{molecules}$ of ammonia are present in the cylinder.