Question

A gas cylinder can hold 1 kg of hydrogen at room temperature and pressure

1) Find the number of moles of hydrogen present.

2) What weight of CO2 can the cylinder hold under similar conditions of temperature and pressure? (H = 1, C = 12, O = 16)

3) 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.

4) State the law that helped you to arrive at the above result.

Answer 1

Given:

Mass of hydrogen = 1 kg at 298 K and 1 atm pressure

1) Moles of hydrogen =?

Number of moles of hydrogen  =`"Mass of hydrogen"/"Gramatomicmass of hydrogen"`

= `"1000g"/ "1g"`

= 1000moles of hydrogen

2) At STP, 1 mole of any gas occupies 22.4 L

So, at STP, 1000 moles of CO2 will occupy the same space as that of hydrogen

Atomic masses of C and O are 12 and 16, respectively

Molar mass of CO₂ = 12 + 32 = 44 g

1000 moles of CO₂ = 44 × 1000 = 44000 g = 44 kg CO₂

Thus, the cylinder can hold 44 kg CO₂

3) 1 mole of any gas = 6.022 × 10²³ molecules

1000 moles of hydrogen = 6.022 × 10²⁶ molecules = X

As the number of moles of hydrogen and CO₂ are the same,

the number of molecules of CO₂ = X = 6.022 × 10²⁶ molecules of CO₂

4) Avogadro’s law states that under the same conditions of temperature and pressure, equal volumes of different gases have the same number of molecules.