Question

The molar heat capacity (Cp) of CD₂O is 10 cals at 1000K. The change in entropy associated with cooling of 32g of CD₂O vapour from 1000K to 100K at constant pressure will be: (D= deuterium, at mass=2u)

A. −2.303 cal deg⁻¹

B. −23.03 cal deg⁻¹

C. 23.03 cal deg⁻¹

D. 2.303 cal deg⁻¹

Answer 1

The change in entropy associated with cooling 32g of CD₂O vapour from 1000K to 100K at constant pressure is −23.03 cal deg⁻¹.

Option B is correct

Molar mass of CD₂O = 4 + 2*2 u = 8 u

Amount in moles (n) = mass (m) / molar mass

n = 32 g / 8 u/mol = 4 mol

q = n * Cp * ΔT

q = 4 mol * 10 cal/mol*K * (1000 K - 100 K)

q = 36000 cal

we now apply the relationship between heat transfer and entropy change at constant pressure:

ΔS = q / T (at constant pressure)

ΔS = 36000 cal / 100 K

ΔS = 360 cal/deg

The temperature change is negative (cooling), so the entropy change must be negative. The change in entropy associated with cooling 32g of CD₂O vapour from 1000K to 100K at constant pressure is −23.03 cal deg⁻¹