Mass of water vapor is 0.48 gms.
Weight of the aluminium block is 55 gms.
Heat of vaporization of water at 25 degree Celsius is 44.0 kJ/mol.
The amount of heat given by the condensation is:
q = Heat of vaporization × Mass of vapor / Molar mass of steam
= 44.0 kJ/mol ×0.48 g / 18 g/mol
= 1.173 kJ
Now the final temperature of the metal block is calculated by the formula:
q = m × c × ΔT
q = m × c × (T₂ - T₁)
Here, q is the amount of heat, m is the mass of the metal, c is the specif heat of the metal, T₁ is initial temperature, and T₂ is the final temperature.
Now, substituting the values we get,
1.173 kJ = 55 g × 0.903 J/g. ° C * (T₂ - 25°C)
1.173 × 10³ J = 55 g × 0.903 J/g. degree C × (T₂ - 25°C)
1.173 × 10³ = 49.665 ° C * (T₂ - 25° C)
T₂ = 49° C.
Thus, the final temperature of the metal block is 49° C.
