A gas cylinder can hold $1 k g$ of hydrogen at room temperature and pressure:
If the number of molecules of hydrogen in the cylinder is $X$ , calculate the number of $C O_{2}$ molecules in the cylinder under the same conditions of temperature and pressure.

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Solution

A gas cylinder can hold 1 kg of hydrogen at room temperature and pressure:
If the number of molecules of hydrogen in the cylinder is X molecules, the number of molecules of $C O_{2}$ in the cylinder under the same conditions of temperature and pressure will also be same. It will be X.
From the ideal gas equation $P V = n R T$ , when pressure, volume and temperature are constant, the number of moles of two gases will be same. Hence, the number of molecules of two gases will be same.
Note:
A gas cylinder can hold 1 kg
The mass of hydrogen $= 1 k g \times 1000 g / k g = 1000 g$ .
The molar mass of hydrogen is 2 g/mol.
The number of moles of hydrogen present $= \frac{mass}{molar mass} = \frac{1000 g}{2 g / m o l} = 500 m o l$ .
The number of moles of $C O_{2} =$ the number of moles of $H_{2} = 500$ moles.
The number of molecules of $C O_{2} = 500 m o l e s \times 6.023 \times 10^{23} m o l e c u l e s / m o l e = 3.012 \times 10^{26}$ molecules.

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A gas cylinder can hold 1 kg of hydrogen at room temperature and pressure:If the number of molecules of hydrogen in the cylinder is X, calculate the number of CO2 molecules in the cylinder under the same conditions of temperature and pressure.

A gas cylinder can hold $1 k g$ of hydrogen at room temperature and pressure:
If the number of molecules of hydrogen in the cylinder is $X$ , calculate the number of $C O_{2}$ molecules in the cylinder under the same conditions of temperature and pressure.