Question

Find the equation which is used to determine the amount of heat required to melt 10 grams of ice?
A.${\text{Q = m}}{{\text{C}}_{{\text{sp}}}}\Delta {\text{T}}$
B.${\text{Q = n}}\Delta {\text{H}}$
C.${\text{K}}{\text{.E}}. = \dfrac{1}{2}{\text{m}}{{\text{v}}^{\text{2}}}$
D.${\text{P}}{\text{.E}}. = {\text{mgh}}$
E.${\text{PV}} = {\text{nRT}}$

Answer 1

Hint: For a phase transition, there is no change in temperature or in other words, the temperature remains constant during a phase transition. The required equation which is used to determine the amount of heat required to melt 10 grams of ice involves the number of moles and not the number of grams.

Complete step by step answer:
We know that the quantity of heat, either absorbed or evolved is denoted by the symbol ‘Q’. Now, if we carefully look at the expressions given in the question, we will see that only the first two equations involve the term ‘Q’. The remaining three equations do not involve the term ‘Q’.
Infact, the third equation given as ${\text{K}}{\text{.E}}. = \dfrac{1}{2}{\text{m}}{{\text{v}}^{\text{2}}}$ gives us the equation for the kinetic energy of a molecule with mass ‘m’ moving with a velocity ‘v’. The fourth equation given as ${\text{P}}{\text{.E}}. = {\text{mgh}}$ gives us the equation for the potential energy of an object where ‘m’ is the mass of the object, ‘g’ is the acceleration due to gravity and ‘h’ is the height or distance in meters. Lastly, the third equation given as ${\text{PV}} = {\text{nRT}}$ gives us the equation for an ideal gas where ‘R’ is the gas constant, ‘T’ is the temperature, ‘n’ is the number of moles of the gas, ‘P’ is the pressure and ‘V’ is the volume. Hence, these three equations cannot be used to determine the amount of heat required to melt ice.
Now, the first equation ${\text{Q = m}}{{\text{C}}_{{\text{sp}}}}\Delta {\text{T}}$ involves temperature change and is used to determine temperature change when there is no transition of phase of a substance. Since, temperature remains constant during phase transformation, this option is also wrong.
Only the second equation ${\text{Q = n}}\Delta {\text{H}}$ , where ‘n’ is the number of moles of the substance, $\Delta {\text{H}}$ is the enthalpy of fusion of the substance (ice in this case), gives the relationship between how much heat is involved when ‘n’ moles of ice is undergoing a phase change.

Hence, option B is correct.

Note:
In case of water, the molar enthalpy of fusion is found to be equal to $6.02{\text{kJ/mol}}$ . This indicates that $6.02{\text{kJ/mol}}$ of heat is needed to convert 1 mole of solid ice at its melting point to liquid water at its melting point. If we want to calculate the amount of heat required to convert 3 moles of ice to liquid water at its melting point, then ‘n’ will be equal to 3 and we will have:
${\text{Q = 3}} \times 6.02 = 18.06{\text{kJ/mol}}$