Question

2 kg of hydrogen (H2) is mixed with 2 kg of oxygen (O2). If the final mixture has a volume of 3 m3: Determine (a) molar mass (b) specific volume and (c) the molar specific volume of the final mixture.[Solution] [Discuss]

Answer 1

Step-by-step explanation:

The molar mass of a given substance corresponds and pertains to the unit mole of the mass substance which is stated in g/mol

no of moles of H = mass of H/molar mass of H

= 2 kg/ 2 g/mol

= 2000 g/ 2 g/mol

= 1000 moles

moles of O2 = mass (O2)/ molar mass (O2)

= 2 kg/ 32 g/mol

= 2000 g / 32 g/mol

= 62.5 moles

Total moles present = (1000 + 62.5) moles

= 1062.5 moles

= 1.063 kmol

Total mass = 2kg + 2kg

= 4 kg

no of moles = mass/molar mass

molar mass = mass/ no of moles

molar mass = 4 kg/ 1.063 kmol

molar mass = 3.763 kg/kmol

The specific volume of the final mixture can be determined by the relation:

`v_(mixture)=( V)/(m)`

where;

V = 3 m³

m = 4 kg

`v_(mixture)=( 3 \ m^3)/(4 \ kg)`

= 0.75 m³/ kg

For the final volume, The molar specific volume is:

`v_M = M_(mixture) *v_(mixture)`

where;

`M_(mixture) = 3.763`

`v_(mixture) = 0.75 \ m^3/ kg`

∴

`v_M = 3.763 \ kg/mol * 0.75 \ m^3/kg`

`\mathbf{v_M = 2.82 \ m^3/kmol}`