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Chemistry Question on Thermodynamics

The molar heat capacity of water at constant pressure, C, is 75 JK–1mol–1. When 1.0 KJ of heat is supplied to 100 g of water which is free to expand, the increase in temperature of water is:

A

1.2 K

B

2.4 K

C

4.8 K

D

6.6 K

Answer

2.4 K

Explanation

Solution

Given:
Q = 1.0kJ = 1000 J (since 1 kJ = 1000 J)
m = 100 g
c = 75 J/mol⋅K
The molar mass of water (H2O) is approximately 18 g/mol.
Number of moles (n) = Mass  (in  g) Molar  mass of  water  (in g/mol)\frac {\text {Mass \ (in \ g) }}{\text {Molar \ mass\ of \ water \ (in\ g/mol)}}
n = 10018\frac {100}{18} = 5.56 mol
Now Q = mcΔT
1000J = (5.56 mol) × (75 J/mol⋅K) × ΔT
ΔT = 1000 J(5.56 mol)×(75 J/mol⋅K)\frac {1000\ J }{(5.56\ mol)×(75\ J/mol⋅K)}
ΔT ≈ 2.4 K

So, the correct option is (B): 2.4 K