The enthalpy of fusion of ice is 6.02 kJ `mol^(-1).` The heat capacity of water is `4.18 Jg^(-1)C^(4).` What is the smallest number of ice cubes at `0^(@)C,` each containing one mole of water, that are needed to cool 500g of liquid water from` 20^(@)C `to `0^(@)C?`

Explanation

Heat released to cool 500 g water from `20^(@)C` to `0^(@)C.`
`q = ms Delta T = 500 xx 4. 18 xx 20 = 41 800 J = 41. 8 kJ`
Number of moles of water (ice) that will melt to absorb `41. 8 kJ = ( 41. 8)/(6. 02) = 7`
`therefore ` Number of cubes of ice that will melt = 7.