Question

The enthalpy of fusion of ice is $6.02KJ\;mo{l^{ - 1}}$ . The heat capacity of water is $4.18{({g^0}C)^{ - 1}}$ . What is the smallest number of ice cubes ${0^0}C$ , each containing one mole of water, that is needed to cool $500g$ liquid water from ${20^0}C\;{\text{to }}{0^0}C$ ?
(A) $1$
(B) $7$
(C) $14$
(D) $25$

Answer 1

We should know about the basic enthalpies of the reactions. The enthalpy of fusion of substance is also known as latent heat of fusion. It is defined as the change in energy of the substance to change its state from solid to liquid without a change in its pressure. With the help of the concept of enthalpy and heat capacity, we can calculate the required number of ice cubes.
Formula Used:
Heat capacity, $Q = ms\Delta T$
Where, $Q$ is the heat required, $m$ is the mass of the substance, $s$ is the specific heat of the substance, and $\Delta T$ is the temperature change.

Complete step by step answer:
First, we will understand the term heat capacity. Heat capacity is also known as the thermal capacity. It is defined as the amount of heat required to convert the substance from one form to another. It is supplied to a given mass of material. Now in the question, we have given that the enthalpy of fusion of ice is $6.02KJ\;mo{l^{ - 1}}$ and the heat capacity of water is $s = 4.18{({g^0}C)^{ - 1}}$ . Now we need to cool $500g$ liquid water ${20^0}C\;{\text{to }}{0^0}C$ . So we will substitute the given values in the formula and calculate the net heat required for conversion.
$Q = ms\Delta T$
$\Rightarrow Q = (500g) \times (4.18g) \times (20 - 0) = 41800J = 41.8KJ$
Now let the minimum number of ice cubes be $n$ . So the number of ice cubes required that will melt to absorb the heat will be calculated as $n = \dfrac{{41.8}}{{6.02}} = 7$
Therefore, the correct option is (B).

Note:
Specific heat capacity is very important as it gives us the measure of the energy or the heat required to cool down the given substance. On the other hand heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree.