Question

A gas cylinder contains $12\times {10}^{24}$ molecules of oxygen gas. If Avogadro's number is $6.022\times {10}^{23}$. Calculate the mass of oxygen present in the cylinder.
The volume of oxygen at STP present in the cylinder (O=16).

Answer 1

Step 1: Given data:

Number of molecules for oxygen gas is $12\times {10}^{24}$

Avogadro's number is $6.022\times {10}^{23}$

Atomic mass of Oxygen is 16u

Step 2: Calculating the mass of oxygen:-

The mass of oxygen that is present is

$$\begin{gathered} =\frac{\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{present}}{\mathrm{Avogadro}\mathrm{number}}\times \mathrm{Molecular}\mathrm{mass} \\ =\frac{12\times {10}^{24}}{6.022\times {10}^{23}}\times 16\times 2 \\ =19.92\times 16\times 2 \\ =637.66\mathrm{g} \end{gathered}$$

Step 3: Calculating the volume of oxygen at STP:-

The volume of oxygen which is present in the cylinder at STP is

$$\begin{gathered} =\frac{\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{present}}{\mathrm{Avogadro}\mathrm{number}}\times \mathrm{Molecular}\mathrm{volume} \\ =\frac{12\times {10}^{24}}{6.022\times {10}^{23}}\times 22.4 \\ =19.92\times 22.4 \\ =446.208\mathrm{L} \end{gathered}$$

Therefore, The mass of oxygen present in the cylinder is $637.66\mathrm{g}$, the volume of oxygen at STP present in the cylinder is $446.208\mathrm{L}$.