Question

Approximately how many ice cubes must melt to cool 650 milliliters of water from 29°C to 0°C? Assume that each ice cube contains 1 mole of H2O and is initially at 0°C. ∆H(fusion) = 6.02 kJ/mol; ∆H(vaporization) = 40.7 kJ/mol c(solid) = 2.09 J/g°C; c(liquid) = 4.18 J/g°C; c(gas) = 1.97 J/g°C Enter your answer numerically.

Answer 1

Answer : The number of ice cubes melt must be, 13

Explanation :

First we have to calculate the mass of water.

$\text{Mass of water}=\text{Density of water}\times \text{Volume of water}$

Density of water = 1.00 g/mL

Volume of water = 650 mL

$\text{Mass of water}=1.00g/mL\times 650mL=650g$

Now we have to calculate the heat released on cooling.

Heat released on cooling = $m\times c\times (T_2-T_1)$

where,

m = mass of water = 650 g

c = specific heat capacity of water = $4.18J/g^oC$

$T_2$ = final temperature = $29^oC$

$T_2$ = initial temperature = $0^oC$

Now put all the given values in the above expression, we get:

Heat released on cooling = $650g\times 4.18J/g^oC\times (29-0)^oC$

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 = $\frac{\text{Total heat}}{\text{Heat for 1 ice cube}}$

Number of ice cubes melted = $\frac{78.793kJ}{6.02kJ}$

Number of ice cubes melted = 13.1 ≈ 13

Therefore, the number of ice cubes melt must be, 13