Answer : The number of ice cubes melt must be, 13
Explanation :
First we have to calculate the mass of water.
![\text{Mass of water}=\text{Density of water}\times \text{Volume of water}](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D%5Ctext%7BDensity%20of%20water%7D%5Ctimes%20%5Ctext%7BVolume%20of%20water%7D)
Density of water = 1.00 g/mL
Volume of water = 650 mL
![\text{Mass of water}=1.00g/mL\times 650mL=650g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D1.00g%2FmL%5Ctimes%20650mL%3D650g)
Now we have to calculate the heat released on cooling.
Heat released on cooling = ![m\times c\times (T_2-T_1)](https://tex.z-dn.net/?f=m%5Ctimes%20c%5Ctimes%20%28T_2-T_1%29)
where,
m = mass of water = 650 g
c = specific heat capacity of water = ![4.18J/g^oC](https://tex.z-dn.net/?f=4.18J%2Fg%5EoC)
= final temperature = ![29^oC](https://tex.z-dn.net/?f=29%5EoC)
= initial temperature = ![0^oC](https://tex.z-dn.net/?f=0%5EoC)
Now put all the given values in the above expression, we get:
Heat released on cooling = ![650g\times 4.18J/g^oC\times (29-0)^oC](https://tex.z-dn.net/?f=650g%5Ctimes%204.18J%2Fg%5EoC%5Ctimes%20%2829-0%29%5EoC)
Heat released on cooling = 78793 J = 78.793 kJ (1 J = 0.001 kJ)
As, 1 ice cube contains 1 mole of water.
The heat required for 1 ice cube to melt = 6.02 kJ
Now we have to calculate the number of ice cubes melted.
Number of ice cubes melted = ![\frac{\text{Total heat}}{\text{Heat for 1 ice cube}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BTotal%20heat%7D%7D%7B%5Ctext%7BHeat%20for%201%20ice%20cube%7D%7D)
Number of ice cubes melted = ![\frac{78.793kJ}{6.02kJ}](https://tex.z-dn.net/?f=%5Cfrac%7B78.793kJ%7D%7B6.02kJ%7D)
Number of ice cubes melted = 13.1 ≈ 13
Therefore, the number of ice cubes melt must be, 13