Molar heat capacity of liquid water:

To determine molar heat capacity of water first of all we need to describe molar heat capacity and related terms.

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#### Molar Heat capacity:

The amount of energy that is required to added in the form of heat to one mole of the substance in order to an increase its temperature of one unit is known as molar heat capacity of that substance.

The molar heat capacity of any substance is “intrinsic” property; an intrinsic property is that does not depend on the size or shape of the amount in consideration.

cn = Q/ΔT

In above equation Q is heat and ΔT is the change in temperature. Generally heat capacity is reported as an intrinsic property that’s means it is a characteristic of a specific substance.

Molar heat capacity is measured by using a calorimeter. A bomb calorimeter can be used for calculations at constant volume. Coffee cup calorimeters are basically used for finding molar heat capacity at constant pressure.

### Units of Molar Heat Capacity of liquid water and other substances:

Unit used for molar heat capacity is of J/K/mol or J/mol·K, where J is joules, K is Kelvin, and m is number of moles. In SI units, molar heat capacity (symbol: cn) is the amount of heat which is required in joules which raise 1 mole of a substance 1 Kelvin.

Since an increment of temperature of one degree Celsius is consider same as an increment of one Kelvin and that is the same as joule per degree Celsius per mole (J/°C/mol).

Some units are not commonly used as heat is the kilogram-Calorie (Cal) or the cgs variant, the gram-calorie (cal). It’s also possible heat capacity may be expressed in terms of pound-mass using temperatures in degrees Fahrenheit.

Molar Heat Capacity versus Specific Heat Capacity

Molar heat capacity considers as the heat capacity per mole and the related term specific heat capacity is reflected as the heat capacity per unit mass. Specific heat capacity is also called as specific heat.

Sometimes scientific calculations apply volumetric heat capacity instead of specific heat based on mass. A periodic table arranged with the respect of the specific heat capacity of an element.

Specific heat differs from molar heat capacity in some aspects that it is measured per gram instead of per mole. The SI unit of specific heat capacity is joule per Kelvin times mole, J/K * mol.

The experimental value of molar heat capacity of liquid water is 75.348 J/mol K. It is calculated as the specific heat capacity of liquid water and the molar mass of water but specific heat capacity of liquid water is 4.186 J/gm K.

This means that each gram of liquid water needs 4.186 Joules of heat energy to raise its temperature by one degree Kelvin. One molar mass of water is equal to 18 grams.

Therefore the molar heat capacity becomes the product of both molar mass and specific heat capacity as 4.186 and 18. It can be describe as 75.348 Joules of heat energy is required to raise the temperature of 18 grams of liquid water by one degree Kelvin.

Temperature:

The temperature of any substance is an indication of its ability to transfer heat energy. The substances with high temperatures will transfer heat energy to objects with lower temperatures until their temperatures reached to same point.

#### Molar Heat Capacity of Water:

Heat capacity of water is extremely high. It required high energy to raise its temperature. Water in liquid form having a molar heat capacity “H2O: 75.338 J/K*mol (25°C, 101.325 kPa)” To determine the molar heat capacity first we required to determine the specific heat capacity and molar mass.

##### Determine the Specific Heat capacity of water:

A periodic table enlists the specific heat capacity of elements. Specific heat capacity differs from molar heat capacity as it is measured per gram instead of per mole.

If any substance is made of a single element then its specific heat capacity is listed in many periodic tables. For example the specific heat capacity of silver is about 0.23 J/g*K but If the substance is a compound of multiple elements then we need to determine its specific heat either experimentally or from an already-existing document.

Here we are determining the specific heat capacity of water by two hydrogen and one oxygen which is 4.184 J/ (g*K).

##### Calculate Molar Mass of water:

The periodic table indicates the molar mass of each element. If it is a compound then the molar mass must be calculated through ratios.

We want to determine molar mass of one mole of water in which involves 2 parts hydrogen and 1 part oxygen. Now we determine the molar mass of water by multiplying each of these parts by the corresponding masses of the elements:

2 x (1 gram/mol hydrogen) + (16 gram/mol oxygen) = 18 gram/mol water ##### Multiply Specific Heat of water with Molar Mass of water:

Multiply the specific heat of water with the molar mass of the water that results the molar heat capacity of water in joules per mol K. The specific heat capacity of water is 4.184 J/(g*K). Multiply this by the molar mass:

4.184 x 18 = 75.312 J/mol*K. This is molar heat capacity of water.

This property is commonly used in chemistry when amounts of substances are mostly taken as in moles rather than by mass or volume. The molar heat capacity any substance generally increases with the molar mass often varies with temperature and pressure and is different for each state of matter.

In case of water at atmospheric pressure, the (isobaric) molar heat capacity and just above the melting point is about 76 J/K * mol but molar heat capacity of ice is just below that point is about 37.84 J/K/mol.

While the substance is undergoing a phase transition, such as at melting or boiling points its molar heat capacity is technically infinite because the heat goes into changing its state rather than raising its temperature.

In informal chemistry circumstances the molar heat capacity may be called as just “heat capacity” or “specific heat”. However at international standards now suggested that “specific heat capacity” always refer to capacity per unit of mass to avoid possible confusion.

Therefore, the word “molar” not “specific”, should always used for this purpose.

###### Effect of impurities in molar heat capacity of water:

Specific heat of water decrease with addition of solute or impurities .for example increasing the amount of salts decrease the specific heat of water which affect directly molar heat capacity of water.

When we dissolve NaCl in water, the ions will be held in rigid form of water molecules. The greater concentration of salt minimizes the specific heat capacity of solution. ###### Affect of hydrogen bonds in molar heat capacity of water:

Water has strong intermolecular hydrogen bonds when in their liquid phase. These bonds allow enough space to store heat as potential energy of vibration, even at comparatively low temperatures.

Hydrogen bonds are known as a fact that liquid water stores nearly the theoretical limit of 3 R per mole of atoms, even at relatively low temperatures.

Hydrogen bonding is said to be highly responsible for the high heat capacity of liquid water. In the presence of strong H-bonding in water molecules more heat is required to increase the kinetic energy.

If more degree of freedom were responsible for it then CH4 might have been more heat capacity than that of water which is not the case so we can say only H-bonding is responsible for it. The mass kinetic energy is only a modest part of the total specific heat. Water molecules in a liquid state do not rotate in fact they liberate. Strong Intermolecular forces in water molecules replace free rotation with back and forth rocking motions.

The three rotational modes which all act as harmonic oscillators (the same is true of the translational modes. While the three internal vibrational modes are all at fairly large frequencies, and these three modes substantially frozen out of making a specific heat contribution, there is the interesting issue that the hydrogen atoms in a hydrogen bond may exchange back and forth between the two oxygen atoms which gives an additional specific heat contribution.

This gives us 3R for the translational motions plus 3R for the rotational motions and something substantial for the hydrogen bonds, giving us 9R or so the molar specific heat of liquid water is extremely high.