A block of ice of mass $$120 \text{ g}$$ at temperature $$0°C$$ is put in $$300 \text{ g}$$ of water at $$25°C$$. The $$x$$ g of ice melts as the temperature of the water reaches $$0°C$$. The value of $$x$$ is ______.
[Use: Specific heat capacity of water $$= 4200 \text{ J kg}^{-1} \text{ K}^{-1}$$, Latent heat of ice $$= 3.5 \times 10^5 \text{ J kg}^{-1}$$]

Given:

Mass of ice: $$m_{ice} = 120 \text{ g} = 0.12 \text{ kg}$$

Temperature of ice: $$T_{ice} = 0°C$$

Mass of water: $$m_w = 300 \text{ g} = 0.3 \text{ kg}$$

Temperature of water: $$T_w = 25°C$$

Specific heat capacity of water: $$c = 4200 \text{ J kg}^{-1} \text{ K}^{-1}$$

Latent heat of ice: $$L = 3.5 \times 10^5 \text{ J kg}^{-1}$$

The water cools from $$25°C$$ to $$0°C$$. The heat released by the water is:

$$Q = m_w \cdot c \cdot \Delta T = 0.3 \times 4200 \times 25 = 31500 \text{ J}$$

This heat is used to melt the ice. The mass of ice that melts:

$$Q = m \cdot L$$

$$m = \dfrac{Q}{L} = \dfrac{31500}{3.5 \times 10^5} = 0.09 \text{ kg} = 90 \text{ g}$$

Therefore, the value of $$x$$ is $$\boxed{90}$$.