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Question

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.

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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 CO2 in the cylinder under the same conditions of temperature and pressure will also be same. It will be X.
From the ideal gas equation PV=nRT, 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 =1kg×1000g/kg=1000g.
The molar mass of hydrogen is 2 g/mol.
The number of moles of hydrogen present =massmolar mass=1000g2g/mol=500mol.
The number of moles of CO2= the number of moles of H2=500 moles.
The number of molecules of CO2=500moles×6.023×1023molecules/mole=3.012×1026 molecules.

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