Question

One gram sample of $N{H_4}N{O_3}$ is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by 6.12 K. The heat capacity of the system is $1.23{\text{ kJ}}{g^{ - 1}}{\deg ^{ - 1}}$ . What is the molar heat of decomposition for $N{H_4}N{O_3}$ ?
(A) - 7.53 kJ/mol
(B) -398.1 kJ/mol
(C) - 16.1 kJ/mol
(D) 602 kJ/mol

Answer 1

Hint : A chemical substance's molar heat capacity is the amount of energy that must be given to one mole of the material in the form of heat to induce a one-unit increase in temperature. It is also the specific heat capacity of the material times its molar mass, or the heat capacity of a sample of the substance divided by the amount of substance in the sample.

Complete Step By Step Answer:
The molar heat capacity of a substance, particularly a gas, can be substantially larger when the sample is allowed to expand while it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that inhibits expansion, similar to the specific heat (isochoric). However, the heat capacity ratio derived from the matching specific heat capacities is the same for both. This characteristic is especially important in chemistry, where moles are frequently used instead of mass or volume to specify the quantity of a material. The molar heat capacity is a property of matter that rises with molar mass, changes with temperature and pressure, and is unique to each state of matter.
The heat of reaction arising from the breakdown of a chemical into its components or other neutral compounds, particularly the quantity involved in the decomposition of a mole, is defined as
The expression for the heat evolved is $\;q = mS\Delta T$
The heat released when 1 g of ammonium nitrate decomposes is $q = 1 \times 1.23 \times 6.12$
The heat released when 1 mole of ammonium nitrate decomposes is $q = 1 \times 1.23 \times 6.12 \times 80 = 602.21\;{\text{kJ mo}}{{\text{l}}^{ - 1}}$
Hence option D is correct.

Note :
The molar heat capacity is sometimes known as "heat capacity" or "specific heat" in informal chemistry. To prevent any mistake, international standards currently propose that "specific heat capacity" always refer to capacity per unit of mass. As a result, the term "molar" rather than "specific" should always be used to describe this number.