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The heat required to melt any solid substance, including NaCl (common salt), is the heat required to increase the temperature of the substance to its melting point plus the latent heat of fusion.
Heat required for both these purpose is directly proportional to its mass.
We know that the melting point of NaCl is 801 degrees Celsius. As the temperature of NaCl is given in the example is already 801 degrees Celsius, no heat is required for further raising the temperature,
Latent heat required for fusion can be calculated as:
Latent heat of fusion of NaCl per unit mass x Mass
The latent heat of fusion of NaCl is given as 28.16 kJ/mol
The mass of NaCl is given as 175.32 g.
We can convert this mass in grams to mass in mol by dividing it by molecular weight of NaC, which we know to be 58.4428.
Therefore: The mass of NaCl in mol is:
175.32 / molecular weight of NaCl = 175.32 /58.4428 mol
Substituting the values of latent heat of fusion in kJ/mol and weight of NaCl in mol, in the above equation for heat required for fusion as:
Heat required for fusion = Mass in mol x Heat of Fusion per mol.
= (175.32 /58.4428) x 28.16 = 84.4759 kJ
Rounding off 84.4759 to first decimal place we get:
Heat required for fusion = 84.50 kJ
The molecular formula of sodium chloride is NaCl, which could mean a mole of sodium chloride has its costituents a mole of sodium and a mole of chlorine, apart from the meaning that a molecule of sodium chloride is constitued of one atom of sodium and one atom of chlorine.
Therefore,one mole of sodium chloride has the mass of one mole of sodium+mass of one mole of chlorine = 22.99g+35.45g=58.44 g , as per the molecular formula of sodium chloride.Therefore the given 175.32g of sodium chloride is equal to 175.32/58.44 = 3 moles of sodium chloride.So the heat required for the fusion of 3 moles of sodium chloride at the rate of 28.16KJ per mole is =(28.16kJ)*3 = 84.48 Kj of heat energy.
Hope this helps.
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