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The molar heat capacity of silver, measured at atmospheric pressure, is found to vary with temperature between 50 and 100 K by the empirical equation C = 0.318T – 0.00109T 2 – 0.628,where C is in J/mol . K and T is in K. Calculate the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K. the molar mass of silver is 107.87 g/mol.

The molar heat capacity of silver, measured at atmospheric pressure, is found to vary with temperature between 50 and 100 K by the empirical equation C = 0.318T – 0.00109T2 – 0.628,where C is in J/mol . K and T is in K. Calculate the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K. the molar mass of silver is 107.87 g/mol.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
To obtain Q, substitute 0.318T – 0.00109T2 -0.628 for C in the equation Q = n ∫ CdT, we get,
Q = n ∫90 K50 K CdT
= n [(0.318 J/mol.K2) T2/2 – (0.00109 J/mol.K3) T3/3 –(0.628 J/mol.K)T] 90 K50 K
= n (645.8 J/mol)
As the molar mass of silver is 107.87 g/mol, thus the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K will be,
Q = n (645.8 J/mol)
= [316 g/(107.87 g/mol)] (645.8 J/mol)
=189 J
From the above observation we conclude that, the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K would be 189 J.

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