The molar heat capacity of water at constant pressure, C, is 75 J K⁻¹ mol⁻¹. When 1.0 kJ of heat is supplied t

Question

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

Accepted Answer

Given:
Molar heat capacity of water at constant pressure, C_p = 75 J K⁻¹ mol⁻¹
Heat supplied, q = 1.0 kJ = 1000 J
Mass of water, m = 100 g
Molar mass of water, M = 18 g mol⁻¹

Number of moles of water, n = m / M = 100 / 18 mol

The heat supplied at constant pressure is given by the formula:
q = n × C_p × ∆T

Substituting the values:
1000 = (100 / 18) × 75 × ∆T
∆T = (1000 × 18) / (100 × 75)
∆T = 180 / 75 = 2.4 K

Thus, the increase in temperature of the water is 2.4 K.

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