The mass of ice to be melted is
1 g = 10⁻³ kg.
Let m = the mass of steam required to melt the ice.
For water,
The latent heat of vaporization is 2260 kJ/kg
The latent heat of fusion is 334 kJ/kg
The steam should give up its latent heat of vaporization to melt the ice, which gives up its latent heat of fusion.
Therefore
(m kg)*(2260 kJ/kg) = (10⁻³ kg)*(334 kJ/kg)
m = 1.478 x 10⁻⁴ kg = 0.1478 g
Answer: 0.148 g
