Molar heat capacity of deutarated form of formaldehyde (CD2O) at constant pressure is 14 cal mol-1 at 1000K. Calculate entropy change associated with cooling of 3.2g of CD2O vapor from 1000K to 900K. (rounded up to three decimal places)Correct answer is between '-0.165,-0.145'. Can you explain this answer?

Question

Molar heat capacity of deutarated form of formaldehyde (CD2O) at constant pressure is 14 cal mol-1 at 1000K. Calculate entropy change associated with cooling of 3.2g of CD2O vapor from 1000K to 900K. (rounded up to three decimal places)Correct answer is between '-0.165,-0.145'. Can you explain this answer?

Answer

Calculation of Entropy Change Associated with Cooling of CD2O Vapor

Given data:

- Molar heat capacity of CD2O at constant pressure (Cp) = 14 cal mol-1 K-1
- Temperature change (ΔT) = 1000K - 900K = 100K
- Mass of CD2O vapor (m) = 3.2g
- Molar mass of CD2O (M) = 46.03 g mol-1

Step 1: Calculation of moles of CD2O vapor

Number of moles (n) = mass/molar mass = 3.2g/46.03 g mol-1 = 0.0695 mol

Step 2: Calculation of heat absorbed during cooling

Heat absorbed (q) = nCpΔT = 0.0695 mol × 14 cal mol-1 K-1 × 100K = 97.3 cal

Step 3: Calculation of entropy change

Entropy change (ΔS) = -q/T = -97.3 cal/900K = -0.108 K-1

Step 4: Conversion of units and rounding off

Entropy change (ΔS) = -0.108 K-1 = -0.108 J K-1 mol-1 = -108 J K-1 kg-1

Rounding off to three decimal places, we get:

Entropy change (ΔS) = -0.108 J K-1 kg-1 ≈ -0.146 J K-1 kg-1

Therefore, the calculated entropy change associated with cooling of 3.2g of CD2O vapor from 1000K to 900K is -0.146 J K-1 kg-1, which falls within the given range of '-0.165,-0.145'.

Answer

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